Ãëàâíàÿ      Ó÷åáíèêè - Ðàçíûå     Ëåêöèè (ðàçíûå) - ÷àñòü 32

 

Ïîèñê            

 

Àâòîìàòèçèðîâàííûé àíàëèç ïðîåêòèðîâàíèÿ íà ìèêðîóðîâíå

 

             

Àâòîìàòèçèðîâàííûé àíàëèç ïðîåêòèðîâàíèÿ íà ìèêðîóðîâíå

Ìèíèñòåðñòâî îáðàçîâàíèÿ è íàóêè Ðåñïóáëèêè Êàçàõñòàí

Êàðàãàíäèíñêèé Ãîñóäàðñòâåííûé Òåõíè÷åñêèé Óíèâåðñèòåò

Êàôåäðà ____ÑÀÏÐ______

ÏÎßÑÍÈÒÅËÜÍÀß ÇÀÏÈÑÊÀ

ê êóðñîâîé ðàáîòå

Ïî äèñöèïëèíå: "Ìîäåëèðîâàíèå ñèñòåì è êîìïëåêñîâ"

Òåìà: "Àâòîìàòèçèðîâàííûé àíàëèç ïðîåêòèðîâàíèÿ íà ìèêðîóðîâíå"

Ðóêîâîäèòåëü

(ïîäïèñü) (äàòà)

Ñòóäåíò

(ïîäïèñü) (äàòà)

2009

Ñîäåðæàíèå

Ââåäåíèå

1. Çàäàíèå

2. Ðàçðàáîòêà êîíöåïòóàëüíîé ìîäåëè è ðàñ÷åòíîé ñõåìû îáúåêòà àíàëèçà

3. Âûáîð ìåòîäà àâòîìàòèçèðîâàííîãî àíàëèçà îáúåêòà ïðîåêòèðîâàíèÿ

3.1 Ìåòîä êîíå÷íûõ ðàçíîñòåé

3.2 Ìåòîä êîíå÷íûõ ýëåìåíòîâ

4. Âûáîð è êðàòêîå îïèñàíèå ïðîãðàììíûõ è òåõíè÷åñêèõ ñðåäñòâ àâòîìàòèçèðîâàííîãî àíàëèçà

4.1 COSMOS

4.2 ANSYS

5. Ïîñòðîåíèå äèñêðåòíîé ìîäåëè îáúåêòà àíàëèçà è ïðîãðàììíîé ìîäåëè

6. Ïëàíèðîâàíèå ìàøèííûõ ýêñïåðèìåíòîâ è èõ ðåàëèçàöèÿ

7. Àíàëèç è èíòåðïðåòàöèÿ ðåçóëüòàòîâ ìîäåëèðîâàíèÿ

Çàêëþ÷åíèå

Ñïèñîê èñïîëüçóåìîé ëèòåðàòóðû

Ïðèëîæåíèÿ

Ââåäåíèå

 äàííîì êóðñîâîì ïðîåêòå òðåáóåòñÿ ñïðîåêòèðîâàòü íàïðÿæåííî-äåôîðìèðîâàííîå ñîñòîÿíèå èññëåäóåìîãî îáúåêòà ïðè çàäàííûõ ãðàíè÷íûõ óñëîâèÿõ è óñòàíîâèòü çàâèñèìîñòè äëÿ íåãî îò ãåîìåòðè÷åñêèõ ïàðàìåòðîâ íà îñíîâå ìàøèííîãî ýêñïåðèìåíòà.

 õîäå âûïîëíåíèÿ äàííîãî êóðñîâîãî ïðîåêòà íàì íåîáõîäèìî áóäåò ðàçðàáîòàòü êîíöåïòóàëüíóþ ìîäåëü îáúåêòà, ïîñòðîèòü ðàñ÷åòíóþ ñõåìó îáúåêòà ìîäåëèðîâàíèÿ, ðàçðàáîòàòü ìîäåëü äëÿ àâòîìàòèçèðîâàííîãî àíàëèçà, ñîçäàòü êîìàíäíûé ôàéë, ïîó÷èòü ðåãðåññèîííûå çàâèñèìîñòè èññëåäóåìûõ äàííûõ. Êðîìå òîãî, ïî óêàçàíèþ ïðåïîäàâàòåëÿ íåîáõîäèìî ïðîâåñòè êà÷åñòâåííóþ è êîëè÷åñòâåííóþ îöåíêè èññëåäóåìûõ õàðàêòåðèñòèê ìîäåëèðóåìîãî îáúåêòà äëÿ ñðàâíåíèÿ ñ ðåçóëüòàòàìè èìèòàöèîííîãî ýêñïåðèìåíòà.

Ïîñëå ðÿäà ïðîãîíîâ ïîëó÷åííîé ìîäåëè íà ÏÝÂÌ è ïîëó÷åíèÿ ðåçóëüòàòîâ ìàøèííîãî ýêñïåðèìåíòà ñ òðåáóåìîé òî÷íîñòüþ íåîáõîäèìî áóäåò ïðîâåñòè èõ èíòåðïðåòàöèþ è àíàëèç â òåðìèíàõ îáúåêòà ìîäåëèðîâàíèÿ, à çàòåì îôîðìèòü ïîÿñíèòåëüíóþ çàïèñêó è ãðàôè÷åñêóþ ÷àñòü êóðñîâîãî ïðîåêòà.

Êîíöåïòóàëüíàÿ ìîäåëü íåîáõîäèìî áóäåò ïðîâåðèòü íà íåïðîòèâîðå÷èâîñòü è ïîëíîòó îïèñàíèÿ, äëÿ ÷åãî íàäî óáåäèòüñÿ, ÷òî çàäàíèå ñîäåðæèò âñþ íåîáõîäèìóþ êà÷åñòâåííóþ è êîëè÷åñòâåííóþ èíôîðìàöèþ îá îáúåêòå. Äàëåå ìîäåëü ïðîâåðÿþò íà îòñóòñòâèå íåôîðìàëèçîâàííûõ è íåðåàëèçóåìûõ îïèñàíèé, ñèòóàöèé, ñîîòíîøåíèé. Çàòåì íåîáõîäèìî ïðîâåñòè (ñîãëàñíî çàäàíèþ) êà÷åñòâåííóþ è êîëè÷åñòâåííóþ îöåíêè õàðàêòåðèñòèê ïðîöåññà ôóíêöèîíèðîâàíèÿ îáúåêòà.

Èòîãîì êóðñîâîãî ïðîåêòà ÿâëÿåòñÿ òåõíè÷åñêàÿ äîêóìåíòàöèÿ â âèäå ðàçðàáîòàííûõ ñõåì è ïðîãðàììíîãî îáåñïå÷åíèÿ ìîäåëèðîâàíèÿ îáúåêòà, ðåçóëüòàòû ìàøèííîãî ýêñïåðèìåíòà ñ ìîäåëüþ îáúåêòà, âêëþ÷àÿ âûâîäû è ðåêîìåíäàöèè ïî èõ èñïîëüçîâàíèþ ïðè èññëåäîâàíèè è ðàçðàáîòêå ðåàëüíîãî îáúåêòà, ïîÿñíèòåëüíàÿ çàïèñêà, ñîäåðæàùàÿ äîêóìåíòàöèþ ïî âûïîëíåíèþ àâòîìàòèçèðîâàííîãî àíàëèçà îáúåêòà ìîäåëèðîâàíèÿ.

1. Çàäàíèå

Òðåáóåòñÿ ñïðîåêòèðîâàòü íàïðÿæåííî-äåôîðìèðîâàííîå ñîñòîÿíèå èññëåäóåìîãî îáúåêòà ïðè çàäàííûõ ãðàíè÷íûõ óñëîâèÿõ è óñòàíîâèòü çàâèñèìîñòè äëÿ íåãî îò ãåîìåòðè÷åñêèõ ïàðàìåòðîâ íà îñíîâå ìàøèííîãî ýêñïåðèìåíòà.

Ìàòåðèàë - ñòàëü;

Ìîäóëü óïðóãîñòè E=200000 ÌÏà;

Êîýôôèöèåíò Ïóàññîíà v=0,3.

2. Ðàçðàáîòêà êîíöåïòóàëüíîé ìîäåëè è ðàñ÷åòíîé ñõåìû îáúåêòà àíàëèçà

Öåëüþ äàííîãî ýòàïà ÿâëÿåòñÿ ïîñòðîåíèå êîíöåïòóàëüíîé (ñîäåðæàòåëüíîé) ìîäåëè ïðîöåññà ôóíêöèîíèðîâàíèÿ îáúåêòà ñ ïðîâåäåíèåì åãî ôîðìàëèçàöèè.

Âíåøíèå âîçäåéñòâèÿ íà îáúåêò ïðîåêòèðîâàíèÿ âûðàæåíû â âèäå ñèëû íàãðóæåíèÿ 100 ÌÏà. Ñèëû ðàñïðåäåëåíû ðàâíîìåðíî.

Òàêèì îáðàçîì, íàì íåîáõîäèìî ïîñòðîèòü ôèãóðó, èçîáðàæåííóþ íà ðèñóíêå 2.1

Ðèñóíîê 2.1 - Îáúåêò àíàëèçà

3. Âûáîð ìåòîäà àâòîìàòèçèðîâàííîãî àíàëèçà îáúåêòà ïðîåêòèðîâàíèÿ

Ìîäåëèðîâàíèå ìíîãî÷èñëåííûõ ôèçè÷åñêèõ, áèîëîãè÷åñêèõ è õèìè÷åñêèõ ÿâëåíèé ÷àñòî ïðèâîäèò ê ðåøåíèþ ëèíåéíûõ è íåëèíåéíûõ óðàâíåíèé èëè ñèñòåì óðàâíåíèé â ÷àñòíûõ ïðîèçâîäíûõ. Ñóùåñòâóþò òðàäèöèîííûå ìàòåìàòè÷åñêèå ñðåäñòâà, ïîçâîëÿþùèå ïîëó÷èòü ðåøåíèå â îïðåäåëåííûõ ñëó÷àÿõ, íî äëÿ ðåøåíèÿ êîíêðåòíûõ ïðîáëåì, âîçíèêàþùèõ â íàóêå è òåõíèêå, íåâîçìîæíî îáîéòèñü áåç èñïîëüçîâàíèÿ ÷èñëåííûõ ìåòîäîâ. Ñ ðîñòîì ïðîèçâîäèòåëüíîñòè ÝÂÌ ÷èñëåííîå ìîäåëèðîâàíèå ïðèîáðåòàåò îñîáîå çíà÷åíèå, ò.ê ïîçâîëÿåò äîïîëíèòü èëè äàæå çàìåíèòü ïðÿìîé ýêñïåðèìåíò. Ïîñëåäíèé ÷àñòî äîðîã, åãî ïîñòàíîâêà áûâàåò òðóäîåìêîé èëè âîîáùå íåâîçìîæíîé.  íàñòîÿùåå âðåìÿ ñóùåñòâóåò ðÿä ðàçëè÷íûõ ìåòîäîâ àâòîìàòèçèðîâàííîãî àíàëèçà. Ñðåäè íèõ íàèáîëåå ïîïóëÿðíûìè ÿâëÿþòñÿ ìåòîäû êîíå÷íûõ ýëåìåíòîâ è êîíå÷íûõ ðàçíîñòåé.

3.1 Ìåòîä êîíå÷íûõ ðàçíîñòåé

Ìåòîä êîíå÷íûõ ðàçíîñòåé îòíîñèòñÿ ê ìåòîäàì ñåòîê è ñîäåðæèò òðè ýòàïà:

1 ýòàï - Äèñêðåòèçàöèÿ - íà äàííîì ýòàïå îáëàñòü ðåøåíèÿ ðàçáèâàåòñÿ íà ñåòêó, êàê ïðàâèëî, ðåãóëÿðíóþ, â äàëüíåéøåì â óçëàõ ñåòêè áóäóò îïðåäåëåíû óçëîâûå çíà÷åíèÿ èñêîìîé ôóíêöèè.

2 ýòàï - Àïïðîêñèìàöèÿ - çäåñü îñóùåñòâëÿåòñÿ ïåðåõîä îò äèôôåðåíöèàëüíîãî îïåðàòîðà ê ðàçíîñòíîìó àíàëîãó.

3 ýòàï - Àëãåáðàèçàöèÿ - ïîäñòàíîâêà ðàçíîñòíûõ àíàëîãîâ äèôôåðåíöèàëüíûõ îïåðàòîðîâ â èñõîäíîå óðàâíåíèå è ïîëó÷åíèå ñèñòåìû àëãåáðàè÷åñêèõ óðàâíåíèé.

3.2 Ìåòîä êîíå÷íûõ ýëåìåíòîâ

Ýòîò ìåòîä â íàñòîÿùåå âðåìÿ äîñòèã òàêîãî óðîâíÿ, ÷òî ìíîãèå ÷àñòî ñîìíåâàþòñÿ - ìîæåò ëè ïîÿâèòüñÿ ëó÷øèé ìåòîä. Äèàïàçîí ïðèìåíèìîñòè ÌÊÝ, èõ ýôôåêòèâíîñòü è ñðàâíèòåëüíàÿ ëåãêîñòü ðåàëèçàöèè, äåëàþò èõ ñåðüåçíûìè ñîïåðíèêàìè äëÿ ëþáîãî ìåòîäà. Äîñòîèíñòâàìè ÌÊÝ ÿâëÿþòñÿ ãèáêîñòü è ðàçíîîáðàçèå ñåòîê, ñòàíäàðòíûå ïðèåìû ïîñòðîåíèÿ äèñêðåòíûõ çàäà÷ äëÿ ïðîèçâîëüíûõ îáëàñòåé, ïðîñòîòà ó÷åòà åñòåñòâåííûõ êðàåâûõ óñëîâèé. Êðîìå òîãî, ìàòåìàòè÷åñêèé àíàëèç ÌÊÝ ÿâëÿåòñÿ áîëåå ïðîñòûì, åãî ìåòîäû ïðèìåíèìû ê áîëåå øèðîêîìó êëàññó çàäà÷, à îöåíêè ïîãðåøíîñòåé ïðèáëèæåííûõ ðåøåíèé ïîëó÷àþòñÿ ïðè ìåíåå æåñòêèõ îãðàíè÷åíèÿõ, ÷åì â ìåòîäå êîíå÷íûõ ðàçíîñòåé. Ñëàáîé ñòîðîíîé ÿâëÿåòñÿ òî, ÷òî îí ïî èäåå ïðåäñòàâëÿåò ñîáîé ñõåìó äèñêðåòèçàöèè âñåãî òåëà, à ýòî íåèçáåæíî âåäåò ê áîëüøîìó êîëè÷åñòâó ÊÝ, îñîáåííî â òðåõìåðíûõ çàäà÷àõ ñ óäàëåííûìè ãðàíèöàìè, â ïðåäåëàõ êàæäîé èç êîòîðûõ íå âñå íåèçâåñòíûå ïåðåìåííûå èçìåíÿþòñÿ íåïðåðûâíî.

ÌÊÝ â îáùåì ñëó÷àå ñîñòîèò èç òðåõ ýòàïîâ:

Äèñêðåòèçàöèÿ - ôèçè÷åñêàÿ îáëàñòü ðåøåíèÿ çàäà÷è ðàçáèâàåòñÿ íà íåêîòîðûå ïîäîáëàñòè èëè êîíå÷íûå ýëåìåíòû.

Àïïðîêñèìàöèÿ - èñêîìàÿ ôóíêöèÿ àïïðîêñèìèðóåòñÿ ôóíêöèåé ñïåöèàëüíîãî âèäà íà êàæäîì êîíå÷íîì ýëåìåíòå. Êîýôôèöèåíòû àïïðîêñèìàöèè ñòàíîâÿòñÿ îñíîâíûìè íåèçâåñòíûìè â çàäà÷àõ.

Àëãåáðàèçàöèÿ - ïîäñòàíîâêà àïïðîêñèìèðóþùèõ êîýôôèöèåíòîâ â îïðåäåëÿþùåå óðàâíåíèå ïîçâîëÿåò ïîëó÷èòü ñèñòåìó àëãåáðàè÷åñêèõ óðàâíåíèé îòíîñèòåëüíî óçëîâûõ çíà÷åíèé èñêîìîé ôóíêöèè.

Ñðàâíèâàÿ ýòè äâà ìåòîäà ìîæíî ñêàçàòü, ÷òî êàæäûé èç ìåòîäîâ èìååò ñâîè ïðåèìóùåñòâà. Íî ó ìåòîäà êîíå÷íûõ ðàçíîñòåé áîëüøå íåäîñòàòêîâ, íàïðèìåð, ñëîæíîñòü ðåøåíèÿ çàäà÷ â ñëó÷àå íåîäíîðîäíîé îáëàñòè ðåøåíèÿ, íàëè÷èå íåëèíåéíîñòåé.

Îòñóòñòâèå ðåøåíèÿ ïðè íåäîñòàòî÷íûõ óñëîâèÿõ äàþò ïðàâî èñïîëüçîâàòü äëÿ ðåàëèçàöèè ïîñòàâëåííîé çàäà÷è ÌÊÝ. ÌÊÝ, â öåëÿõ óïðîùåíèÿ ðàñ÷åòà çàäà÷è, ìîæåò áûòü ðåàëèçîâàí ïî ñðåäñòâàì ïðîãðàììû ANSYS.

4. Âûáîð è êðàòêîå îïèñàíèå ïðîãðàììíûõ è òåõíè÷åñêèõ ñðåäñòâ àâòîìàòèçèðîâàííîãî àíàëèçà

 íàñòîÿùåå âðåìÿ ñóùåñòâóåò øèðîêèé ðÿä ñèñòåì èíæåíåðíûõ ðàñ÷åòîâ.  äàííîì êóðñîâîì ïðîåêòå äëÿ ñðàâíåíèÿ áûëè âûáðàíû äâå ïðîãðàììû - ANSYS è COSMOS.

4.1 COSMOS

COSMOS ñî÷åòàåò íàäåæíîñòü, òî÷íîñòü è áûñòðîòó ðàñ÷åòîâ ñ ïðîñòîòîé èñïîëüçîâàíèÿ, à íàëè÷èå øèðîêèõ ðàñ÷åòíûõ âîçìîæíîñòåé - ñ äîñòóïíîñòüþ (öåíà ñèñòåìû íåâûñîêà äëÿ ïðîäóêòà òàêîãî êëàññà).

COSMOS ñîðèåíòèðîâàí íà ðåøåíèå çàäà÷è ñêâîçíîé àâòîìàòèçàöèè ïðîåêòèðîâàíèÿ, ïîçâîëÿÿ èíòåãðèðîâàòü ðàñ÷åòíûé àíàëèç â åäèíóþ ïðîãðàììíóþ ñèñòåìó.

COSMOS èìååò ðÿä ïðåèìóùåñòâ:

Èíòåðôåéñ ïîëüçîâàòåëÿ - ïîçâîëÿåò áûñòðî îñâàèâàòü òåõíîëîãèþ ðàñ÷åòîâ.

Ñèñòåìà êîìàíä åñòåñòâåííî îòðàæàåò ñòàäèè ðàñ÷åòíîãî àíàëèçà.

Âîçìîæíîñòü óãëóáëåííîãî àíàëèçà ïî ìåðå îñâîåíèÿ ñèñòåìû.

Ïðîñòåéøèå ðàñ÷åòû äîñòóïíû ñ ïåðâîãî æå ñåàíñà ðàáîòû.

Îïåðàòèâíûå ñðåäñòâà ãðàôè÷åñêîãî îòîáðàæåíèÿ èñõîäíûõ äàííûõ è ïîëó÷åííûõ ðåçóëüòàòîâ.

Ãåîìåòðè÷åñêîå ìîäåëèðîâàíèå âîçìîæíî êàê âíóòðåííèìè ñðåäñòâàìè ñèñòåìû, òàê è íà îñíîâå äàííûõ, èìïîðòèðóåìûõ èç ïîïóëÿðíûõ ïàêåòîâ ìîäåëèðîâàíèÿ.

Ìîäóëüíîå ñòðîåíèå ñïîñîáñòâóåò ôîðìèðîâàíèþ ñèñòåìû â çàâèñèìîñòè îò ïîòðåáíîñòåé è ôèíàíñîâûõ âîçìîæíîñòåé ïîëüçîâàòåëÿ.

Ñðåäñòâà àâòîìàòèçàöèè ïîäãîòîâêè ðàñ÷åòîâ ïîçâîëÿþò ïðîâîäèòü îöåíî÷íûå ðàñ÷åòû ïðîåêòèðîâùèêàì, íå èìåþùèì ãëóáîêîé ïîäãîòîâêè: àâòîìàòè÷åñêîå ïîñòðîåíèå ïðîñòðàíñòâåííûõ ñåòîê êîíå÷íûõ ýëåìåíòîâ ñ èçìåëü÷åíèåì åå â ìåñòàõ êîíöåíòðàöèè íàïðÿæåíèé, íàëè÷èå ìîäóëÿ îïòèìèçàöèè êîíñòðóêöèé.

FFE-ìåòîäû ñêîðîñòíîãî ðàñ÷åòà ñîêðàùàþò âðåìÿ ðàñ÷åòà â äåñÿòêè ðàç, ïðè ýòîì èñïîëüçîâàíèå ñèñòåìíûõ ðåñóðñîâ (îïåðàòèâíàÿ ïàìÿòü, äèñêîâîå ïðîñòðàíñòâî) óìåíüøàåòñÿ íà ïîðÿäîê. Ïîâûøåíèå ïðîèçâîäèòåëüíîñòè ðàñ÷åòîâ ïðè ýòîì êà÷åñòâåííî èçìåíÿåò ïîäõîä ê èñïîëüçîâàíèþ COSMOS: â ðåçóëüòàòå îòáðàñûâàåòñÿ íåîáõîäèìîñòü óïðîùåíèÿ ñëîæíûõ ïðîñòðàíñòâåííûõ ìîäåëåé, à ýòî óæå - çíà÷èòåëüíûé ñêà÷îê â ïðîèçâîäèòåëüíîñòè è îïåðàòèâíîñòè ïðîöåññà êîíñòðóêòîðñêîé äîâîäêè.

Ôóíêöèîíàëüíûå âîçìîæíîñòè:

Îïðåäåëåíèå ïàðàìåòðîâ íàïðÿæåííî-äåôîðìèðîâàííîãî ñîñòîÿíèÿ

Òåïëîâûå ðàñ÷åòû

Äèíàìèêà

Ôèçè÷åñêàÿ è ãåîìåòðè÷åñêàÿ íåëèíåéíîñòü

Ëàìèíàðíûå è òóðáóëåíòíûå ïîòîêè

Ýëåêòðîìàãíèòíûå ðàñ÷åòû

Îïòèìèçàöèÿ êîíñòðóêöèé

Áèáëèîòåêà ìàòåðèàëîâ

Ïîäãîòîâêà äàííûõ äëÿ äðóãèõ ïðîãðàìì ÌÊÝ

4.2 ANSYS

Ìíîãîöåëåâîé êîíå÷íî-ýëåìåíòíûé ïàêåò äëÿ ïðîâåäåíèÿ àíàëèçà â øèðîêîì êðóãå èíæåíåðíûõ çàäà÷. Îñîáåííîñòüþ ïðîãðàììû ÿâëÿåòñÿ ôàéëîâàÿ ñîâìåñòèìîñòü âñåõ ÷ëåíîâ ñåìåéñòâà ANSYS äëÿ âñåõ èñïîëüçóåìûõ ïëàòôîðì. Ìíîãîöåëåâàÿ íàïðàâëåííîñòü ïðîãðàììû ïîçâîëÿåò èñïîëüçîâàòü îäíó è òó æå ìîäåëü äëÿ ðåøåíèÿ òàêèõ ñâÿçàííûõ çàäà÷, êàê ïðî÷íîñòü ïðè òåïëîâîì íàãðóæåíèè, âëèÿíèå ìàãíèòíûõ ïîëåé íà ïðî÷íîñòü êîíñòðóêöèè, òåïëîìàññîïåðåíîñ â ýëåêòðîìàãíèòíîì ïîëå.

Âíóòðåííèé ÿçûê ïðîãðàììèðîâàíèÿ APDL ïîçâîëÿåò ïðîãðàììèðîâàòü ëþáûå ïðîöåäóðû, ïàðàìåòðèçîâàòü ïîñòðîåíèå ìîäåëè, ðàñ÷åò è âûâîä ðåçóëüòàòîâ. ANSYS ïîçâîëÿåò ïîäêëþ÷àòü ïîëüçîâàòåëüñêèå ìîäåëè, íàïèñàííûå íà FORTRAN, C++.

Ïðîãðàììà ANSYS îáëàäàåò ìíîãèìè âîçìîæíîñòÿìè êîíå÷íî-ýëåìåíòíîãî àíàëèçà - îò ïðîñòîãî ëèíåéíîãî ñòàòè÷åñêîãî äî ñëîæíîãî íåëèíåéíîãî äèíàìè÷åñêîãî (íåñòàöèîíàðíîãî). Ïðîöåäóðà òèïîâîãî ðàñ÷åòà ìîæåò áûòü ðàçäåëåíà íà òðè îñíîâíûõ ýòàïà:

Ïîñòðîåíèå ìîäåëè.

Ïðèëîæåíèå íàãðóçîê (âêëþ÷àÿ è ãðàíè÷íûå óñëîâèÿ) è ïîëó÷åíèå ðåøåíèÿ.

Ïðîñìîòð è àíàëèç ðåçóëüòàòîâ.

Ïîñòðîåíèå ìîäåëè (Preprocessor)

Ýòîò ýòàï âêëþ÷àåò îïðåäåëåíèå òèïîâ êîíå÷íûõ ýëåìåíòîâ, èõ êîíñòàíò, ñâîéñòâ ìàòåðèàëà è ãåîìåòðèè ìîäåëè.

Çàäàíèå òèïîâ ýëåìåíòîâ (ElementType)

Áèáëèîòåêà êîíå÷íûõ ýëåìåíòîâ ïðîãðàììû ANSYS ñîäåðæèò áîëåå 100 òèïîâ, êàæäûé èç êîòîðûõ îïðåäåëÿåò, ñðåäè ïðî÷åãî, ïðèìåíèìîñòü ýëåìåíòà ê òîé îáëàñòè ðàñ÷åòîâ (ïðî÷íîñòíîé, òåïëîâîé, ìàãíèòíûé è ýëåêòðè÷åñêèé àíàëèç, äâèæåíèå æèäêîñòè èëè ñâÿçàííûå çàäà÷è), õàðàêòåðíóþ ôîðìó ýëåìåíòà (ëèíåéíóþ, ïëîñêóþ, â âèäå áðóñêà è ò.ä.), à òàêæå äâóìåðíîñòü è òðåõìåðíîñòü ýëåìåíòà êàê ãåîìåòðè÷åñêîãî òåëà.

Çàäàíèå êîíñòàíò ýëåìåíòîâ (RealConstants)

Êîíñòàíòû ýëåìåíòà - ýòî ñâîéñòâà ñïåöèôè÷åñêèå äëÿ äàííîãî òèïà ýëåìåíòà, òàêèå êàê ïàðàìåòðû ïîïåðå÷íîãî ñå÷åíèÿ áàëî÷íîãî ýëåìåíòà.

Çàäàíèå ñâîéñòâ ìàòåðèàëîâ (MaterialProps)

Ñâîéñòâà ìàòåðèàëà òðåáóþòñÿ äëÿ áîëüøèíñòâà òèïîâ ýëåìåíòîâ. Â çàâèñèìîñòè îò îáëàñòè ïðèëîæåíèÿ ñâîéñòâà ìîãóò áûòü ëèíåéíûìè, íåëèíåéíûìè è\èëè àíèçîòðîïíûìè.

Ñîçäàíèå ãåîìåòðè÷åñêîé ìîäåëè (-Modeling-)

Îñíîâíîé öåëüþ íà ýòàïå ðàçðàáîòêè ãåîìåòðè÷åñêîé ìîäåëè ÿâëÿåòñÿ ñîçäàíèå àäåêâàòíîé êîíå÷íî-ýëåìåíòíîé ìîäåëè, ñîñòîÿùåé èç óçëîâ è ýëåìåíòîâ. Ïðè ñîçäàíèè êîíå÷íî-ýëåìåíòíîé ìîäåëè èñïîëüçóþòñÿ òðè ìåòîäà: òâåðäîòåëüíîå ìîäåëèðîâàíèå, êàðêàñíîå ìîäåëèðîâàíèå è ïðÿìàÿ ãåíåðàöèÿ ñåòêè.

Çàäàíèå íàãðóçîê è ïîëó÷åíèå ðåøåíèÿ (Solution)

Íà ýòîì ýòàïå âûáèðàåòñÿ òèï àíàëèçà è óñòàíîâëåíèå åãî îïöèé, ïðèêëàäûâàþòñÿ íàãðóçêè, îïðåäåëÿþòñÿ îïöèè äëÿ âûáîðà øàãà ïî íàãðóçêå è èíèöèèðóåòñÿ ðåøåíèå.

Ïðèëîæåíèå íàãðóçîê (-Loads-)

Ïîä íàãðóçêàìè ïîíèìàþòñÿ êàê âíåøíèå è âíóòðåííèå óñèëèÿ, òàê è ãðàíè÷íûå óñëîâèÿ â âèäå îãðàíè÷åíèé íà ïåðåìåùåíèÿ.  ïðîãðàììå ANSYS íàãðóçêè ðàçäåëåíû íà 6 êàòåãîðèé:

îãðàíè÷åíèÿ ñòåïåíè ñâîáîäû;

ñèëû;

ïîâåðõíîñòíûå íàãðóçêè;

îáúåìíûå ñèëû;

èíåðöèîííûå íàãðóçêè;

íàãðóçêè äëÿ ñâÿçíûõ çàäà÷.

Áîëüøèíñòâî ýòèõ íàãðóçîê ìîæåò áûòü ïðèëîæåíî èëè ê òâåðäîòåëüíîé ìîäåëè, èëè ê êîíå÷íî-ýëåìåíòíîé ìîäåëè.

Çàïóñê íà ñ÷åò

Ïî êîìàíäå SOLVE ïðîãðàììà îáðàùàåòñÿ çà èíôîðìàöèåé î ìîäåëè è íàãðóçêàõ ê áàçå äàííûõ è âûïîëíÿåò âû÷èñëåíèÿ. Ðåçóëüòàòû çàïèñûâàþòñÿ â ñïåöèàëüíûé ôàéë è áàçó äàííûõ. Ïðè ýòîì â áàçå äàííûõ ìîæåò õðàíèòüñÿ òîëüêî îäèí íàáîð ðåçóëüòàòîâ, òîãäà êàê â ôàéë ìîãóò áûòü çàïèñàíû ðåçóëüòàòû äëÿ âñåõ øàãîâ ðåøåíèÿ.

Ïðîñìîòð ðåçóëüòàòîâ

Ïîñòïðîöåññîð ïðåäíàçíà÷åí äëÿ âèçóàëèçàöèè ðåçóëüòàòîâ çàäà÷è. Ïðè ýòîì êàê ïðàâèëî èñïîëüçóþò:

Íàëîæåíèå äåôîðìèðîâàííîé ñåòêè íà íåäåôîðìèðîâàííóþ.

Ïîñòðîåíèå ýïþð (ïåðåìåùåíèé, íàïðÿæåíèé è äåôîðìàöèé) äëÿ çàäàííîé îáëàñòè ðåøåíèé.

 ïðîãðàììå ANSYS äîñòóïíû ñëåäóþùèå âèäû ïðî÷íîñòíîãî àíàëèçà:

Ñòàòè÷åñêèé àíàëèç - âû÷èñëåíèå ïåðåìåùåíèé, íàïðÿæåíèé è ò.ä. â óñëîâèÿõ ñòàòè÷åñêîãî íàãðóæåíèÿ;

Ìîäàëüíûé àíàëèç - îïðåäåëåíèå ñîáñòâåííûõ ÷àñòîò è ôîðì êîëåáàíèé;

Ãàðìîíè÷åñêèé àíàëèç - îïðåäåëåíèå îòêëèêà êîíñòðóêöèè íà ãàðìîíè÷åñêèå ñîñòàâëÿþùèå âîçìóùàþùåé íàãðóçêè;

Äèíàìè÷åñêèé àíàëèç - îïðåäåëåíèå îòêëèêà êîíñòðóêöèè íà äåéñòâèå ïðîèçâîëüíîé íàãðóçêè êàê ôóíêöèè âðåìåíè;

Ñïåêòðàëüíûé àíàëèç - ðàñøèðåíèå ìîäàëüíîãî àíàëèçà äëÿ âû÷èñëåíèÿ íàïðÿæåíèé è äåôîðìàöèé ïðè äåéñòâèè ñïåêòðà ÷àñòîò èëè ñëó÷àéíîé âèáðàöèè;

Àíàëèç óñòîé÷èâîñòè - ðàñ÷åò êðèòè÷åñêèõ íàãðóçîê è îïðåäåëåíèå ôîðì ïîòåðè óñòîé÷èâîñòè.

Òàêèì îáðàçîì, ñðàâíèâàÿ äâå ïðîãðàììû, ó÷èòûâàÿ ïðåèìóùåñòâà è íåäîñòàòêè êàæäîé äëÿ äàííîãî êóðñîâîãî ïðîåêòà áûë âûáðàí ïðîãðàììíûé ïàêåò ANSYS.

5. Ïîñòðîåíèå äèñêðåòíîé ìîäåëè îáúåêòà àíàëèçà è ïðîãðàììíîé ìîäåëè

Ïðåæäå âñåãî, íåîáõîäèìî ïðîàíàëèçèðîâàòü ñâîþ äåòàëü. Åñëè, âûäàííàÿ â êà÷åñòâå çàäàíèÿ, äåòàëü ñèììåòðè÷íà, òî ñëåäóåò ñòðîèòü òîëüêî îäíó ÷àñòü äåòàëè.  äàííîé ðàáîòå ìû ïîñòðîèì òîëüêî ÷åòâåðòü äåòàëè (Ðèñóíîê 5.1), òàê êàê äåòàëü ìîæíî ðàçáèòü íà 4 îäèíàêîâûå ÷àñòè.

Ðèñóíîê 5.1 - Âèä ÷åòâåðòè äåòàëè

 äàííîé çàäà÷å ïàðàìåòðè÷åñêè çàäàííûìè (òî åñòü èõ ìîæíî áóäåò ìåíÿòü â ïðîãðàììå) áóäóò ñëåäóþùèå ïàðàìåòðû: r, R, h (ðèñóíîê 5.2).

r- âíóòðåííèé ðàäèóñ ñêâîçíîãî îòâåðñòèÿ;

R- ðàäèóñ âíóòðåííåé âûåìêè;

h- âûñîòà âíóòðåííåé âûåìêè;

h
R

r

Ðèñóíîê 5.2 - Áàçîâûå ðàçìåðû

Íàãðóçêó ïðèëîæèì íà îáëàñòü S (ñì. ðèñóíîê 5.3).

Îáëàñòü S

Ðèñóíîê 5.3 - Âèä îáëàñòè ñ íàãðóçêîé

Ïîñëå ðåøåíèÿ âûøå èçëîæåííûõ âîïðîñîâ ìîæíî ïåðåõîäèòü ê ïîñòðîåíèþ.

Çàïóñê ïðîãðàììû ANSYS

1. Ïåðâè÷íûé çàïóñê (çàïóñêàåì ïåðâûé ðàç çà ñåàíñ ðàáîòû)

Ïóñê>Ïðîãðàììû>ANSYSED55>Interactive.

 ïîëå WorkingDirectory ââåñòè ñâîþ ðàáî÷óþ äèðåêòîðèþ (èìÿ äèðåêòîðèè è âñå ïóòè ê íåé äîëæíû áûòü íà àíãëèéñêîì ÿçûêå).

Íàïðèìåð: Ñ: \BASKET\PLATE

Äàëåå íàæàòü RUN

2. Ïîñëåäóþùèå çàïóñêè.

Ïóñê>Ïðîãðàììû>ANSYSED55>RunInteractiveNow

Ïðèìå÷àíèå: â ñêîáêàõ áóäóò óêàçàíû êîìàíäû â áëîêíîòå, ñîîòâåòñòâóþùèå êîìàíäàì â ïðîãðàììå ANSYS.

1. Îïðåäåëåíèå èìåíè ôàéëà

Âåðõíåå ìåíþ File>ChangeJobname …

Ââåñòè èìÿ ôàéëà (íà àíãëèéñêîì ÿçûêå)

OK

(/FILNAM, <èìÿ ôàéëà>)

2. Îïðåäåëåíèå çàãîëîâêà çàäà÷è

Âåðõíåå ìåíþ File>Change Title …

Ââåñòè çàãîëîâîê çàäà÷è (íà àíãë)

OK

(/TITLE, <çàãîëîâîê>)

3. Âõîä â ïðåïðîöåññîð

Âûáðàòü ïóíêò Preprocessor ãëàâíîãî ìåíþ

(/PREP7)

4. Çàäàíèå òèïà ýëåìåíòà

Main Menu >Preprocessor> Element Type> Add/Edit/Delete

Âûáðàòü Add…

Solid10node 92

Close

(ET,1,92)

5. Çàäàíèå ñâîéñòâ ìàòåðèàëà

Main Menu>Preprocessor>Material Props>Polynomial

EX - ìîäóëü óïðóãîñòè - ââåñòè 200000

(MP,EX,1, 200000)

NUXY - êîýôôèöèåíò Ïóàññîíà - ââåñòè 0.3

(MP,NUXY,1,0.3)

6. Çàäàíèå áàçîâûõ ðàçìåðîâ

(r=6)

(R=13)

(c=6)

7. Ïîñòðîåíèå êîíòðîëüíûõ òî÷åê (ðèñóíîê 5.4):

Main menu>Preprocessor>Modeling>Create>Keypoints>In Active Cs

(k,1,0,0,0! çàäàíèå òî÷åê äëÿ îñíîâàíèÿ

k,2,60,0,0

k,3,60,-50,0

k,4,15,-50,0

k,5,15,-40,0

k,6,0,-40,0)

Ðèñóíîê 5.4 - Çàäàíèå êîíòðîëüíûõ òî÷åê

8. Ïîñòðîåíèå ëèíèé ÷åðåç êîíòðîëüíûå ëèíèè (ðèñóíîê 5.5):

Main menu>Preprocessor>Modeling>Create>Lines>Lines>In Active Coord

(L,1,2! çàäàíèå ëèíèé äëÿ îñíîâàíèÿ

L,2,3

L,3,4

L,4,5

L,5,6

L,6,1)

Ðèñóíîê 5.5 - Ïîñòðîåíèå ëèíèé

9. Îáúåäèíåíèå ëèíèé â îáëàñòü (ðèñóíîê 5.6):

Main Menu>Preprocessor>Modeling>Create>Areas>Arbitrary>By Lines

âûáðàòü ìûøêîé âñå ëèíèè, çàòåì íàæàòü ÎÊ.

(al,all) ! îáúåäèíåíèå ëèíèé â îáëàñòü

Ðèñóíîê 5.6 - Îáúåäèíåíèå ëèíèé â îáëàñòü

10. Ïîëó÷åííóþ îáëàñòü íåîáõîäèìî âûòÿíóòü (ðèñóíîê 5.7):

Modeling-Operate - Extrude - Areas - By XYZ offset

(voffst,1,25) ! âûòÿãèâàíèå îáëàñòè íà âûñîòó

Ðèñóíîê 5.7 - Âûòÿãèâàíèå îáëàñòè íà âûñîòó

11. Çàìåíà ëîêàëüíîé ñèñòåìû êîîðäèíàò:

WorkPlane-Local Coordinate System - Create Local CS - At WP Origin…

(local,100,0,0,0,-25,0,0,0,0,,

wpcsys,1,100)

12. Ïîñòðîåíèå êîíòðîëüíûõ òî÷åê è ñîåäèíåíèå èõ ëèíèÿìè â íîâîé ñèñòåìå êîîðäèíàò, çàòåì îáúåäèíÿåì èõ â îáëàñòü è âûòÿãèâàåì íà âûñîòó. Ðåçóëüòàò ýòîãî ýòàïà ïðèâåäåí íà ðèñóíêå 5.8.

(k,13,0,0,0

k,14,25,0,0

k,15,0,-25,0

L,13,14

L,14,15

L,15,13

al, 19, 20,21

voffst,9,35)

Ðèñóíîê 5.8 - Ïîñòðîåíèå äåòàëè

13. Çàòåì îïÿòü ìåíÿåì ñèñòåìó êîîðäèíàò è ñòðîèì êîíòðîëüíûå òî÷êè, ñîåäèíÿåì èõ â ëèíèè.

(local,100,0,0,0,-60,0,0,0,0,,

wpcsys,1,100

k, 19,0,-13,0

k, 20,13,0,0

L,16, 19

L,16, 20)

14. Ñòðîèì äóãó, çàòåì äâå ëèíèè è äóãó îáúåäèíÿåì â îáëàñòü è âûòÿãèâàåì åå íà âûñîòó.

(larc, 19, 20,16,13! ïîñòðîåíèå äóãè

al,28,29,30

voffst,14,6)

15 Âû÷èòàíèå èç îäíîãî îáú¸ìà äðóãîãî (Ðèñóíîê 5.9):

Main menu>Preprocessor>Modeling>Operate>Subtract>Volumes

(vsbv,2,3! âû÷èòàíèå îáú¸ìîâ)

Ðèñóíîê 5.9 - Âû÷èòàíèå îáúåìà

16. Çàòåì îïÿòü ìåíÿåì ñèñòåìó êîîðäèíàò è ñòðîèì êîíòðîëüíûå òî÷êè, ñîåäèíÿåì èõ â ëèíèè, ñòðîèì äóãó, âñå ýòî îáúåäèíÿåì â îáëàñòü è âûòÿãèâàåì íà âûñîòó è òàêèì îáðàçîì ïîëó÷àåì öèëèíäð.

(local,100,0,0,0,-54,0,0,0,0,,

wpcsys,1,100

k,24,0,-6,0! ïîñòðîåíèå êîíòðîëüíûõ òî÷åê

k,25,6,0,0

L,21,24! ïîñòðîåíèå ëèíèé

L,21,25

larc,24,25,21,6! ïîñòðîåíèå äóãè

al,22,24,25! îáúåäèíåíèå â îáëàñòü

voffst,10,54) ! âûòÿãèâàíèå íà âûñîòó

17. Îáúåäèíåíèå îáú¸ìîâ:

Main Menu>Preprocessor>Modeling>Operate>Add>Volumes

Âûáðàòü ìûøêîé îáú¸ìû è íàæàòü ÎÊ.

(vadd,1,4) ! îáúåäèíåíèå îáú¸ìîâ

18 Çàòåì âû÷èòàåì èç îäíîãî îáúåìà ïîëó÷åííûé ðàíåå öèëèíäð (ðèñóíîê 5.10).

(vsbv,3,2) ! âû÷èòàíèå îáúåìîâ

Ðèñóíîê 5.10 - Âû÷èòàíèå îáúåìîâ

19. Çàäàíèå ðàçìåðà êîíå÷íûõ ýëåìåíòîâ:

Main Menu>Preprocessor>Meshing>Size Cntrls>ManualSize>Global>Size

 ïîëå Size ââåñòè ðàçìåð êîíå÷íîãî ýëåìåíòà = 5.

(smrtsize,all,5) ! çàäàíèå ðàçìåðà êîíå÷íîãî ýëåìåíòà

20. Ðàçáèåíèå îáúåìà íà êîíå÷íûå ýëåìåíòû (ðèñóíîê 5.11):

Main Menu>Preprocessor>Meshing>Mesh>Volumes>FreeMain

(vmesh,all)

Ðèñóíîê 5.11 - Ðàçáèåíèå íà êîíå÷íûå ýëåìåíòû

21. Âûõîä èç ïðåïðîöåññîðà:

(FINISH)

22. Âõîä â ïðîöåññîð:

(/SOLU)

23. Çàêðåïëåíèå îáëàñòåé ïî âñåì ñòåïåíÿì ñâîáîäû:

Main Menu>Solution>Define Loads>Apply>Structural>Displacement>On AreasMain

Âûäåëèòü ìûøêîé íóæíûå îáëàñòè è íàæàòü ÎÊ.

(da,26,all)

24. Çàêðåïëåíèå ñèììåòðèè îáëàñòåé:

Menu>Solution>Define Loads>Apply>Structural>Displacement>Symmetry B. C. >On Areas

Âûäåëèòü ìûøêîé íóæíûå îáëàñòè è íàæàòü ÎÊ.

(da,8,uy

da,21,uy

da,3,ux

da, 20,ux)

25. Ïðèëîæåíèå íàãðóçêè ê îáëàñòÿì (ðèñóíîê 5.12):

Main Menu>Solution>Define Loads>Apply>Structural>Pressure>On Areas

Âûáðàòü ìûøêîé íóæíûå îáëàñòè, â ïîëå Valueíàáðàòü 100, è íàæàòü ÎÊ.

(sfa,9,,pres,100)

Ðèñóíîê 5.12 - Ïðèëîæåíèå íàãðóçêè

26. Âûïîëíåíèå ðàñ÷åòà (SOLVE)

27. Âûõîä èç ïðîöåññîðà (FINISH)

28. Âõîä â ïîñòïðîöåññîð îáùåãî ïîëüçîâàíèÿ

(/POST1)

29. Ïðîñìîòð ðåçóëüòàòîâ (ðèñóíîê 5.13).

Main Menu>General Postproc>Plot Results

Âûáðàòü ðåæèì ïðîñìîòðà.

(plnsol,u,sum,0,1)

Ðèñóíîê 5.13 - Ïðîñìîòð ðåçóëüòàòîâ

6. Ïëàíèðîâàíèå ìàøèííûõ ýêñïåðèìåíòîâ è èõ ðåàëèçàöèÿ

Äàííûé ìàøèííûé ýêñïåðèìåíò áóäåò âêëþ÷àòü â ñåáÿ èçìåíåíèå ïàðàìåòðîâ ìîäåëè ñ îòêëîíåíèåì ±5 ìì.

Äèàïàçîí ïàðàìåòðîâ èçìåíÿåòñÿ ñëåäóþùèì îáðàçîì:

r îò 4 äî 9;

R îò 11 äî 15;

H îò 1 äî 10;

Èçìåíÿÿ ïàðàìåòðû ìîäåëè, ìû ïîñðåäñòâîì ïðîãðàììû ANSYS, ñíèìàëè çíà÷åíèÿ σx , σy , σz . Òàê êàê èçìåíÿåìûõ ïàðàìåòðîâ áûëî 3 è íóæíî áûëî ïðîâåñòè îïûòû âî âñåõ êîìáèíàöèÿõ, ìû ïîëó÷èëè 27 îïûòîâ, êîòîðûå ïðåäñòàâëåíû â òàáëèöå 6.1.

Òàáëèöà 6.1 - Ðåçóëüòàòû ïðàêòè÷åñêèõ îïûòîâ

¹ îïûòà r R H σx σy σz
1 6 13 6 61.84 62.746 107.573
2 6 13 1 49.494 47.841 96.654
3 6 13 10 54.293 64.308 97.772
4 6 11 6 73.727 68.827 108.093
5 6 15 6 58.683 54.223 106.188
6 6 11 1 52.754 53.011 107.432
7 6 11 10 44.734 56.755 105.237
8 6 15 1 46.811 48.589 108.531
9 6 15 10 47.373 52.555 97.67
10 4 13 6 46.682 48.097 81.004
11 4 11 6 48.93 41.278 82.495
12 4 15 6 53.186 47.617 80.986
13 4 11 1 38.02 44.192 95.672
14 4 11 10 49.812 41.77 91.161
15 4 15 1 37.227 37.348 95.51
16 4 15 10 41.7 44.667 91.307
17 9 11 6 101.439 114.478 131.362
18 9 11 1 168.002 159.947 125.308
19 9 11 10 92.06 90.598 126.622
20 9 13 6 111.459 110.351 120.552
21 9 13 1 148.791 163.141 118.298
22 9 13 10 102.164 115.427 120.214
23 9 15 6 104.629 146.047 127.884
24 9 15 1 158.741 148.498 129.646
25 9 15 10 107.96 115.379 129.244
26 4 13 1 41.357 38.541 93.753
27 4 13 10 38.244 35.417 94.541

Àíàëèç ïîëó÷åííûõ çàâèñèìîñòåé ïðîâîäèëñÿ ñ ïîìîùüþ ïðîãðàììû ANETR.

Ñîçäàííûé è ðåàëèçîâàííûé íåòðàäèöèîííûé ìåòîä ïðîãðàììû ANETR áàçèðóåòñÿ íà ðàçðàáîòêàõ ïðîôåññîðà Ì.Ì. Ïðîòîäüÿêîíîâà. Îí ïîçâîëÿåò ðàáîòàòü â äàííûìè óïðàâëÿåìîãî è íåóïðàâëÿåìîãî ýêñïåðèìåíòîâ.

Ìåòîä óíèâåðñàëåí êàê â îáëàñòè ïðèìåíåíèÿ, òàê è â âàðèàíòàõ ïîñòðîåíèÿ ìîäåëè: ìîäåëè ìîãóò èìåòü âèä ñóììû, ïðîèçâåäåíèÿ ÷àñòíûõ çàâèñèìîñòåé, èõ êîìáèíàöèè, ñ ïîñëåäîâàòåëüíîé íåéòðàëèçàöèåé âëèÿíèÿ ïðèîðèòåòíûõ àðãóìåíòîâ èëè áåç òàêîâîé. Âàæíûì ïðåèìóùåñòâîì ìåòîäà ÿâëÿåòñÿ âîçìîæíîñòü ñ äîëæíûì óðîâíåì íàäåæíîñòè îöåíèòü âëèÿíèå òåõ àðãóìåíòîâ, êîòîðûå â òðàäèöèîííûõ ìåòîäàõ áóäóò èñêëþ÷åíû èç àíàëèçà êàê íå âëèÿþùèå íà öåëåâóþ ôóíêöèþ ñóùåñòâåííî (íàïðèìåð, ïî êðèòåðèþ Ôèøåðà). Ýòî îáåñïå÷èâàåòñÿ ïðîöåäóðîé ïîñëåäîâàòåëüíîé íåéòðàëèçàöèè âëèÿíèÿ íà ôóíêöèþ ñèëüíî äåéñòâóþùèõ àðãóìåíòîâ, ïðè êîòîðîé è íà÷èíàåò ïðîÿâëÿòüñÿ âëèÿíèå áîëåå "ñëàáûõ" àðãóìåíòîâ. Ìåòîä äåòåðìèíèðîâàí, ò.å. ïîçâîëÿåò îãðàíè÷èâàòü âûáîð ìîäåëè èçâåñòíûìè äàííûìè ïî òåîðèè ïðîöåññà (òèï óðàâíåíèé, ïðåäåëû è ò.ä.).

Íà âûõîäå ïðîãðàììà, êðîìå àíàëèòè÷åñêîãî õàðàêòåðà ÷àñòíûõ ñâÿçåé, äàåò èõ ãðàôèêè, îöåíêó íàäåæíîñòè. Ðàíæèðóåò ôàêòîðû ïî ñèëå âîçäåéñòâèÿ íà ðåçóëüòàò, ïîçâîëÿåò âûäåëèòü ñóùåñòâåííî âëèÿþùèå ôàêòîðû. Ãðàôèêè ÷àñòíûõ ñâÿçåé ïîçâîëÿþò ïðîâîäèòü îïòèìèçàöèþ ïðîöåññà áåç ïðèìåíåíèÿ ñïåöèàëüíîãî ìàòåìàòè÷åñêîãî àïïàðàòà.

Ðàçðàáîòêà ìîäåëåé ñâîäèòñÿ ê ïîñëåäîâàòåëüíîìó âûïîëíåíèþ ñëåäóþùèõ ýòàïîâ:

Ïëàíèðîâàíèå ýêñïåðèìåíòà;

Ïðîâåäåíèå ýêñïåðèìåíòà;

Ñîñòàâëåíèå çàêàçà íà ìîäåëè;

Àíàëèç ìîäåëè.

Äëÿ íà÷àëà ìû ôîðìèðóåì ôàéë äëÿ ðàáîòû ñ ïðîãðàììîé ANETR:

Äëÿ σx :

B=6; E=2; G=1; L=11; P=1;

4=F (1; 2;3);

1 6 13 6 61.84 62.746 107.573

2 6 13 1 49.494 47.841 96.654

3 6 13 10 54.293 64.308 97.772

4 6 11 6 73.727 68.827 108.093

5 6 15 6 58.683 54.223 106.188

6 6 11 1 52.754 53.011 107.432

7 6 11 10 44.734 56.755 105.237

8 6 15 1 46.811 48.589 108.531

9 6 15 10 47.373 52.555 97.67

10 4 13 6 46.682 48.097 81.004

11 4 11 6 48.93 41.278 82.495

12 4 15 6 53.186 47.617 80.986

13 4 11 1 38.02 44.192 95.672

14 4 11 10 49.812 41.77 91.161

15 4 15 1 37.227 37.348 95.51

16 4 15 10 41.7 44.667 91.307

17 9 11 6 101.439 114.478 131.362

18 9 11 1 168.002 159.947 125.308

19 9 11 10 92.06 90.598 126.622

20 9 13 6 111.459 110.351 120.552

21 9 13 1 148.791 163.141 118.298

22 9 13 10 102.164 115.427 120.214

23 9 15 6 104.629 146.047 127.884

24 9 15 1 158.741 148.498 129.646

25 9 15 10 107.96 115.379 129.244

26 4 13 1 41.357 38.541 93.753

27 4 13 10 38.244 35.417 94.541

/*

Äëÿ σy :

Ìåíÿåì òîëüêî âåðõíþþ ÷àñòü ôàéëà. Êóäà ââîäèì äàííûå:

B=6; E=2; G=1; L=11; P=2;

5=F (1; 2;

3);

Äëÿ σz :

Ìåíÿåì òîëüêî âåðõíþþ ÷àñòü ôàéëà. Êóäà ââîäèì äàííûå:

B=6; E=2; G=1; L=11; P=1;

6=F (1; 2;

3);

Ïîñëå îáðàáîòêè ìû ïîëó÷àåì ñëåäóþùèå ðåçóëüòàòû

Äëÿ σx :

Àïïðîêñèìèðóþùèå óðàâíåíèÿ:

Ïî 1-ìó ôàêòîðó:

Y1= A * X**2 + B * X + C

Ãäå A= 3.42944E+00 B= - 2.90415E+01 C= 1.05229E+02

Ïî 2-ìó ôàêòîðó:

Y2= A * X**2 + B * X + C

Ãäå A= 2.27839E-01 B= - 6.26915E+00 C= 1.15724E+02

Ïî 3-ìó ôàêòîðó:

Y3= A + B * X

Ãäå A= 8.46799E+01 B= - 2.00161E+00

Âèä îáîáùåííîãî óðàâíåíèÿ

Y=Y (1) *Y (2) *Y (3) / 5.378386E+03

Ïîäñòàâèâ â óðàâíåíèå Y óðàâíåíèÿ ïî âñåì òðåì ôàêòîðàì ñ ñîîòâåòñòâóþùèìè êîýôôèöèåíòàìè ïîëó÷èì:

Äàííîå óðàâíåíèå ÿâëÿåòñÿ çàâèñèìîñòüþ σx îò áàçîâûõ ðàçìåðîâ.

ÑÊÎ%= 32.11

Äëÿ σy :

Àïïðîêñèìèðóþùèå óðàâíåíèÿ:

Ïî 1-ìó ôàêòîðó:

Y1= 1/ (A + B * X)

Ãäå A= 3.67374E-02 B= - 3.21271E-03

Ïî 2-ìó ôàêòîðó:

Y2= A + B / X

Ãäå A= 8.46504E+01 B= - 1.10833E+02

Ïî 3-ìó ôàêòîðó:

Y3 = A + B * X

Ãäå A= 8.45668E+01 B= - 1.51408E+00

Âèä îáîáùåííîãî óðàâíåíèÿ

Y= Y (1) *Y (2) *Y (3) / 5.774019E+03

Ïîäñòàâèâ â óðàâíåíèå Y óðàâíåíèÿ ïî âñåì òðåì ôàêòîðàì ñ ñîîòâåòñòâóþùèìè êîýôôèöèåíòàìè ïîëó÷èì:

Äàííîå óðàâíåíèå ÿâëÿåòñÿ çàâèñèìîñòüþ σy îò áàçîâûõ ðàçìåðîâ.

ÑÊÎ%= 28.00

Äëÿ σz :

Àïïðîêñèìèðóþùèå óðàâíåíèÿ:

Ïî 1-ìó ôàêòîðó:

Y1= A + B * X

Ãäå A= 6.08987E+01 B= 7.17218E+00

Ïî 2-ìó ôàêòîðó:

Y2= A * X**2 + B * X + C

Ãäå A= 1.10477E+00 B= - 2.88999E+01 C= 1.86047E+02

Ïî 3-ìó ôàêòîðó:

Y3 = A * X**2 + B * X + C

Ãäå A= 8.42139E-02 B= - 1.13545E+00 C= 2.58845E+00

Âèä îáîáùåííîãî óðàâíåíèÿ

Y= Y (1) +Y (2) +Y (3)

Ïîäñòàâèâ â óðàâíåíèå Y óðàâíåíèÿ ïî âñåì òðåì ôàêòîðàì ñ ñîîòâåòñòâóþùèìè êîýôôèöèåíòàìè ïîëó÷èì:

Äàííîå óðàâíåíèå ÿâëÿåòñÿ çàâèñèìîñòüþ σz îò áàçîâûõ ðàçìåðîâ.

ÑÊÎ%= 28.69

7. Àíàëèç è èíòåðïðåòàöèÿ ðåçóëüòàòîâ ìîäåëèðîâàíèÿ

 ðåçóëüòàòå ïðîáíîãî ðàñ÷åòà ïðè ïàðàìåòðàõ r = 5 R=12 H=3, ñ ïîìîùüþ ïðîãðàììû ANSYS áûëî ïîëó÷åíî:

σx = 48,517 σy = 59,969 σz = 89, 192

Ïðè ðàñ÷åòå ñ ïîìîùüþ óðàâíåíèé ïîëó÷åííûõ ÷åðåç ANETR ìû ïîëó÷èëè:

σx = 49.06472 σy = 50.55656 σz = 95.03471

Ñðàâíèâàÿ çíà÷åíèÿ ïðîáíîãî ðàñ÷åòà, ïîëó÷åííûå ñ ïîìîùüþ ANSYS ìîæíî ñêàçàòü, ÷òî ðàñõîæäåíèÿ ñîâñåì íåçíà÷èòåëüíûå.

Äàííûå çíà÷åíèÿ ÑÊÎ ïîêàçûâàþò, ÷òî óðàâíåíèÿ äëÿ ìîäåëè áûëè íàéäåíû ïðàâèëüíî è èõ âîçìîæíî èñïîëüçîâàòü â ïðàêòè÷åñêèõ çàäà÷àõ â çàäàííîì äèàïàçîíå.

Çàêëþ÷åíèå

 õîäå âûïîëíåíèÿ äàííîãî êóðñîâîãî ïðîåêòà áûëè ðåøåíû âñå ïîñòàâëåííûå çàäà÷è, à èìåííî:

1. Ñîçäàíà ðàñ÷åòíàÿ ñõåìà àíàëèçà íà îñíîâàíèè ñðàâíèòåëüíîãî àíàëèçà ÷èñëåííûõ ìåòîäîâ, à òàêæå ïðîãðàììíûõ è òåõíè÷åñêèõ ñðåäñòâ èõ îñóùåñòâëåíèÿ;

2. Ñîçäàí âûáîð ìåòîäà àâòîìàòèçèðîâàííîãî àíàëèçà îáúåêòà ïðîåêòèðîâàíèÿ;

3. Ñïëàíèðîâàí è ïðîâåäåí ýêñïåðèìåíò, àíàëèçèðóÿ ðåçóëüòàòû êîòîðîãî, ïðèõîäèì ê âûâîäó, ÷òî äàííàÿ ìîäåëü ìîæåò èñïîëüçîâàòüñÿ ñ ïàðàìåòðàìè: r = 5 R = 12 H=3

Ñïèñîê èñïîëüçóåìîé ëèòåðàòóðû

1. Íóðãóæèí Ì.Ð., Ñòåïàíîâ Ï.Á. Ïðèêëàäíàÿ òåîðèÿ ñèñòåì. Ìèêðî - è ìàêðîìîäåëèðîâàíèå: ó÷åáíîå ïîñîáèå. - Êàðàãàíäà: ÊàðÏÒÈ, 1994. -132ñ.

2. Íóðãóæèí Ì.Ð., Äàíåíîâà Ã.Ò., Êàöàãà Ò.ß. Ìàòåìàòè÷åñêîå ìîäåëèðîâàíèå: êóðñîâîå ïðîåêòèðîâàíèå. - Êàðàãàíäà: ÊàðÃÒÓ, 2001. -102ñ.

3. Íóðãóæèí Ì.Ð., Äàíåíîâà Ã.Ò. Ìîäåëèðîâàíèå ñèñòåì è êîìïëåêñîâ: Ëàáîðàòîðíûé ïðàêòèêóì: Ó÷åáíîå ïîñîáèå. - Êàðàãàíäà: ÊàðÃÒÓ, 2006. -97ñ.

Ïðèëîæåíèÿ

Ïðèëîæåíèå À

Ðåçóëüòàòû ANETR äëÿ σx

B=6; E=2; G=1; L=11; P=2;4=F (1; 2;3);

1 6.18400E+01 6.00000E+00 1.30000E+01 6.00000E+00

2 4.94940E+01 6.00000E+00 1.30000E+01 1.00000E+00

3 5.42930E+01 6.00000E+00 1.30000E+01 1.00000E+01

4 7.37270E+01 6.00000E+00 1.10000E+01 6.00000E+00

5 5.86830E+01 6.00000E+00 1.50000E+01 6.00000E+00

6 5.27540E+01 6.00000E+00 1.10000E+01 1.00000E+00

7 4.47340E+01 6.00000E+00 1.10000E+01 1.00000E+01

8 4.68110E+01 6.00000E+00 1.50000E+01 1.00000E+00

9 4.73730E+01 6.00000E+00 1.50000E+01 1.00000E+01

10 4.66820E+01 4.00000E+00 1.30000E+01 6.00000E+00

11 4.89300E+01 4.00000E+00 1.10000E+01 6.00000E+00

12 5.31860E+01 4.00000E+00 1.50000E+01 6.00000E+00

13 3.80200E+01 4.00000E+00 1.10000E+01 1.00000E+00

14 4.98120E+01 4.00000E+00 1.10000E+01 1.00000E+01

15 3.72270E+01 4.00000E+00 1.50000E+01 1.00000E+00

16 4.17000E+01 4.00000E+00 1.50000E+01 1.00000E+01

17 1.01439E+02 9.00000E+00 1.10000E+01 6.00000E+00

18 1.68002E+02 9.00000E+00 1.10000E+01 1.00000E+00

19 9.20600E+01 9.00000E+00 1.10000E+01 1.00000E+01

20 1.11459E+02 9.00000E+00 1.30000E+01 6.00000E+00

21 1.48791E+02 9.00000E+00 1.30000E+01 1.00000E+00

22 1.02164E+02 9.00000E+00 1.30000E+01 1.00000E+01

23 1.04629E+02 9.00000E+00 1.50000E+01 6.00000E+00

24 1.58741E+02 9.00000E+00 1.50000E+01 1.00000E+00

25 1.07960E+02 9.00000E+00 1.50000E+01 1.00000E+01

26 4.13570E+01 4.00000E+00 1.30000E+01 1.00000E+00

27 3.82440E+01 4.00000E+00 1.30000E+01 1.00000E+01

Min 3.72270E+01 4.00000E+00 1.10000E+01 1.00000E+00

Max 1.68002E+02 9.00000E+00 1.50000E+01 1.00000E+01

Ž‘ = 7.334E+01 ‘ŠŽ = 3.899E+01 ‘Š’ = 27

---------------------------------------------------------------

3_

3.72E+01 6.34E+01 8.95E+01 1.16E+02 1.42E+02 1.68E+02

X Y YP KT 4.00E+00+---------+---------+---------+---------+---------+-

4.00000E+00 4.39064E+01 4.39337E+01 9! 3 2@211

! *

! *

! *

4.50E+00+ *

! *

! *

! *

! *

5.00E+00+ *

! *

! *

! *

! *

5.50E+00+ *

! *

! *

! *

! *

6.00E+00+ *

6.00000E+00 5.44121E+01 5.44394E+01 9! 1211@11 1

! *

! *

! *

6.50E+00+ *

! *

! *

! *

! *

7.00E+00+ *

! *

! *

! *

! *

7.50E+00+ *

! *

! *

! *

! *

8.00E+00+ *

! *

! *

! *

! *

8.50E+00+ *

! *

! *

! *

! *

9.00E+00+ *

9.00000E+00 1.21694E+02 1.21639E+02 9! 1 2111 @ 1 1 1

3$

‚ˆ„ 11 “�€‚�…�ˆŸ �Ž 1 ”€Š’Ž�“ Y = A * X**2 + B * X + C

A= 3.42944E+00 B= - 2.90415E+01 C= 1.05229E+02

CKO= 1.69351E+01 CKO%= 43.4 CKO CP. = 3.92639E-02

3_

3.72E+01 6.34E+01 8.95E+01 1.16E+02 1.42E+02 1.68E+02

X Y YP KT 1.10E+01+---------+---------+---------+---------+---------+-

1.10000E+01 7.43864E+01 7.43320E+01 9! 1 1111 @ 1 1 1

! *

! *

! *

1.14E+01+ *

! *

! *

! *

! *

1.18E+01+ *

! *

! *

! *

! *

1.22E+01+ *

! *

! *

! *

! *

1.26E+01+ *

! *

! *

! *

! *

1.30E+01+ *

1.30000E+01 7.27027E+01 7.27299E+01 9! 1 1 11 1 1 @ 1 1 1

! *

! *

! *

1.34E+01+ *

! *

! *

! *

! *

1.38E+01+ *

! *

! *

! *

! *

1.42E+01+ *

! *

! *

! *

! *

1.46E+01+ *

! *

! *

! *

! *

1.50E+01+ *

1.50000E+01 7.29233E+01 7.29506E+01 9! 1 1 2 1 1 @ 11 1

3$

‚ˆ„ 11 “�€‚�…�ˆŸ �Ž 2 ”€Š’Ž�“ Y = A * X**2 + B * X + C

A= 2.27839E-01 B= - 6.26915E+00 C= 1.15724E+02

CKO= 3.89802E+01 CKO%= 100.0 CKO CP. = 3.92639E-02

3_

3.72E+01 6.34E+01 8.95E+01 1.16E+02 1.42E+02 1.68E+02

X Y YP KT 1.00E+00+---------+---------+---------+---------+---------+-

1.00000E+00 8.23552E+01 8.26783E+01 9! 2 1 111 @ 1 1 1

! *

! *

! *

1.90E+00+ *

! *

! *

! *

! *

2.80E+00+ *

! *

! *

! *

! *

3.70E+00+ *

! *

! *

! *

! *

4.60E+00+ *

! *

! *

! *

! *

5.50E+00+ *

! *

! *

6.00000E+00 7.33972E+01 7.26703E+01 9! 2 1 11 @ 11 1

! *

6.40E+00+ *

! *

! *

! *

! *

7.30E+00+ *

! *

! *

! *

! *

8.20E+00+ *

! *

! *

! *

! *

9.10E+00+ *

! *

! *

! *

! *

1.00E+01+ *

1.00000E+01 6.42600E+01 6.46639E+01 9! 1 1111 1 @ 1 1 1

3$

‚ˆ„ 1 “�€‚�…�ˆŸ �Ž 3 ”€Š’Ž�“ Y = A + B * X

A= 8.46799E+01 B= - 2.00161E+00

CKO= 3.82575E+01 CKO%= 98.1 CKO CP. = 5.24895E-01***********************************************************************************************************************

‘ŠŽ = 1.25204418E+01 R = 9.39903264E-01

***********************************************************************************************************************

Ž ’ Š ‹ Ž � … � ˆ Ÿ

27 - 1.72726E-01 9 - 3.74577E-01 25 1.27272E+00 16 3.16672E+00 10 3.50867E+00 7 - 3.91772E+00

22 - 4.20056E+00 11 4.80567E+00 5 5.02351E+00 3 6.68985E+00 26 - 7.76209E+00 20 - 8.07520E+00

1 8.34282E+00 6 - 9.45141E+00 12 9.88168E+00 14 1.05491E+01 2 - 1.13707E+01 15 - 1.20411E+01

13 - 1.21811E+01 21 1.27948E+01 8 - 1.42384E+01 23 - 1.52679E+01 19 - 1.66475E+01 4 1.90514E+01

17 - 2.07282E+01 24 2.23321E+01 18 2.90101E+01

***********************************************************************************************************************

‚ˆ„ Ž�Ž�™…��ŽƒŽ “P€‚�…�ˆŸ

Y (4) =Y (1) *Y (2) *Y (3) / 5.378386E+03

***********************************************************************************************************************

ƒ�€”ˆŠ ˆ‡Œ…�…�ˆŸ ‘ Š Ž

3_

0.00E+00 7.80E+00 1.56E+01 2.34E+01 3.12E+01 3.90E+01

OT ‘�…„�…ƒŽ ‡�€-…�ˆŸ ”“�Š-ˆˆ ‘ Š Ž = 3.89876382E+01+---------+---------+---------+---------+---------*

! 20 40 60 80 100%

!

�Ž‘‹… *** ”€Š’Ž�€ ‘ Š Ž = 1.25204418E+01+ *

3$

***********************************************************************************************************************

”ŽPŒ“‹ŸP ŒŽ„…‹ˆ

„€’€: 28/4/2008 Ž’P€�Ž’€�Ž 27 Ž�›’Ž‚ ‡€Š€‡-ˆŠ:

B=6; E=2; G=1; L=11; P=2;

4=F (1; 2;

3);

------------------------------------------------------------------------------------------------------------------

! N! N! KŽ�””ˆ-ˆ…�’› “P€‚�…�ˆ‰! CKO%!! ‘ŠŽ. ‘�%!

! €Pƒ! “P-Ÿ! - ----------------------------------------------------------! - -------------! R! - -------------!

!!! A! B! C! D! 100!! 100!

! - ---! - ---! - -------------! - -------------! - -------------! - -------------! - -------------! - -------------! - -------------!

!!!!!!!!!!

! 1! 11! 3.4294362E+00! - 2.9041529E+01! 1.0522883E+02!! 43.4!! 0.1!

!!!!!!!!!!

! 2! 11! 2.2783876E-01! - 6.2691519E+00! 1.1572414E+02!! 100.0!! 8.2!

!!!!!!!!!!

! 3! 1! 8.4679913E+01! - 2.0016056E+00!!! 98.1!! 109.6!

!!!!!!!!!!

! ***! ***!!!!! 32.1! 9.3990326E-01!!

!!!!!!!!!!

------------------------------------------------------------------------------------------------------------------

DMAX = 2.9010124E+01 ( 18)

CKO% = 32.11

ŠŽ�””ˆ-ˆ…�’ ”ˆ˜…P€ F = 9.69649; F (001) = 2.52846; F (005) = 1.92428

‚›�Ž‹�ˆ‹

***********************************************************************************************************************

Ïðèëîæåíèå Á

Ðåçóëüòàòû ANETR äëÿ σy

B=6; E=2; G=1; L=11; P=2;

5=F (1; 2;3);

1 6.27460E+01 6.00000E+00 1.30000E+01 6.00000E+00

2 4.78410E+01 6.00000E+00 1.30000E+01 1.00000E+00

3 6.43080E+01 6.00000E+00 1.30000E+01 1.00000E+01

4 6.88270E+01 6.00000E+00 1.10000E+01 6.00000E+00

5 5.42230E+01 6.00000E+00 1.50000E+01 6.00000E+00

6 5.30110E+01 6.00000E+00 1.10000E+01 1.00000E+00

7 5.67550E+01 6.00000E+00 1.10000E+01 1.00000E+01

8 4.85890E+01 6.00000E+00 1.50000E+01 1.00000E+00

9 5.25550E+01 6.00000E+00 1.50000E+01 1.00000E+01

10 4.80970E+01 4.00000E+00 1.30000E+01 6.00000E+00

11 4.12780E+01 4.00000E+00 1.10000E+01 6.00000E+00

12 4.76170E+01 4.00000E+00 1.50000E+01 6.00000E+00

13 4.41920E+01 4.00000E+00 1.10000E+01 1.00000E+00

14 4.17700E+01 4.00000E+00 1.10000E+01 1.00000E+01

15 3.73480E+01 4.00000E+00 1.50000E+01 1.00000E+00

16 4.46670E+01 4.00000E+00 1.50000E+01 1.00000E+01

17 1.14478E+02 9.00000E+00 1.10000E+01 6.00000E+00

18 1.59947E+02 9.00000E+00 1.10000E+01 1.00000E+00

19 9.05980E+01 9.00000E+00 1.10000E+01 1.00000E+01

20 1.10351E+02 9.00000E+00 1.30000E+01 6.00000E+00

21 1.63141E+02 9.00000E+00 1.30000E+01 1.00000E+00

22 1.15427E+02 9.00000E+00 1.30000E+01 1.00000E+01

23 1.46047E+02 9.00000E+00 1.50000E+01 6.00000E+00

24 1.48498E+02 9.00000E+00 1.50000E+01 1.00000E+00

25 1.15379E+02 9.00000E+00 1.50000E+01 1.00000E+01

26 3.85410E+01 4.00000E+00 1.30000E+01 1.00000E+00

27 3.54170E+01 4.00000E+00 1.30000E+01 1.00000E+01

Min 3.54170E+01 4.00000E+00 1.10000E+01 1.00000E+00

Max 1.63141E+02 9.00000E+00 1.50000E+01 1.00000E+01

Ž‘ = 7.599E+01 ‘ŠŽ = 4.165E+01 ‘Š’ = 27

---------------------------------------------------------------

3_

3.54E+01 6.10E+01 8.65E+01 1.12E+02 1.38E+02 1.63E+02

X Y YP KT 4.00E+00+---------+---------+---------+---------+---------+-

4.00000E+00 4.21030E+01 4.18644E+01 9! 122@12

! *

! *

! *

4.50E+00+ *

! *

! *

! *

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5.00E+00+ *

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! *

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5.50E+00+ *

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6.00E+00+ *

6.00000E+00 5.65394E+01 5.72698E+01 9! 2 3@* 2 1

! *

! *

! *

6.50E+00+ *

! *

! *

! *

! *

7.00E+00+ *

! *

! *

! *

! *

7.50E+00+ *

! *

! *

! *

! *

8.00E+00+ *

! *

! *

! *

! *

8.50E+00+ *

! *

! *

! *

! *

9.00E+00+ *

9.00000E+00 1.29318E+02 1.27827E+02 9! 1 1 3 @ 11 11

3$

‚ˆ„ 7 “�€‚�…�ˆŸ �Ž 1 ”€Š’Ž�“ Y = 1/ (A + B * X)

A= 3.67374E-02 B= - 3.21271E-03

CKO= 1.49386E+01 CKO%= 35.9 CKO CP. = 9.87110E-01

3_

3.54E+01 6.10E+01 8.65E+01 1.12E+02 1.38E+02 1.63E+02

X Y YP KT 1.10E+01+---------+---------+---------+---------+---------+-

1.10000E+01 7.45396E+01 7.45746E+01 9! 21 11 1 @ 1 1 1

! *

! *

! *

1.14E+01+ *

! *

! *

! *

! *

1.18E+01+ *

! *

! *

! *

! *

1.22E+01+ *

! *

! *

! *

! *

1.26E+01+ *

! *

! *

! *

! *

1.30E+01+ *

1.30000E+01 7.62077E+01 7.61248E+01 9! 11 2 2 @ 1 1 1

! *

! *

! *

1.34E+01+ *

! *

! *

! *

! *

1.38E+01+ *

! *

! *

! *

! *

1.42E+01+ *

! *

! *

! *

! *

1.46E+01+ *

! *

! *

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! *

1.50E+01+ *

1.50000E+01 7.72137E+01 7.72615E+01 9! 1 12 2 @ 1 11

3$

‚ˆ„ 3 “�€‚�…�ˆŸ �Ž 2 ”€Š’Ž�“ Y = A + B / X

A= 8.46504E+01 B= - 1.10833E+02

CKO= 4.16392E+01 CKO%= 100.0 CKO CP. = 5.99823E-02

3_

3.54E+01 6.10E+01 8.65E+01 1.12E+02 1.38E+02 1.63E+02

X Y YP KT 1.00E+00+---------+---------+---------+---------+---------+-

1.00000E+00 8.23453E+01 8.30527E+01 9! 2 1 2 1 @* 1 11

! *

! *

! *

1.90E+00+ *

! *

! *

! *

! *

2.80E+00+ *

! *

! *

! *

! *

3.70E+00+ *

! *

! *

! *

! *

4.60E+00+ *

! *

! *

! *

! *

5.50E+00+ *

! *

! *

6.00000E+00 7.70738E+01 7.54823E+01 9! 1 2 1 1 1 @ 1 1 1

! *

6.40E+00+ *

! *

! *

! *

! *

7.30E+00+ *

! *

! *

! *

! *

8.20E+00+ *

! *

! *

! *

! *

9.10E+00+ *

! *

! *

! *

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1.00E+01+ *

1.00000E+01 6.85418E+01 6.94259E+01 9! 1 1 1 11 1 @ 1 2

3$

‚ˆ„ 1 “�€‚�…�ˆŸ �Ž 3 ”€Š’Ž�“ Y = A + B * X

A= 8.45668E+01 B= - 1.51408E+00

CKO= 4.12651E+01 CKO%= 99.1 CKO CP. = 1.14916E+00***********************************************************************************************************************

‘ŠŽ = 1.16635160E+01 R = 9.54656513E-01

***********************************************************************************************************************

Ž ’ Š ‹ Ž � … � ˆ Ÿ

11 4.64553E-01 9 - 6.47581E-01 13 - 7.14781E-01 22 - 1.57465E+00 27 - 2.90206E+00 25 - 3.36981E+00

5 - 3.62067E+00 14 4.23122E+00 12 5.33308E+00 7 5.40261E+00 1 5.75339E+00 16 5.77573E+00

10 6.43520E+00 24 6.44152E+00 26 - 7.29922E+00 6 - 8.42069E+00 15 - 9.17674E+00 17 - 1.01399E+01

3 1.18882E+01 4 1.29949E+01 2 - 1.48676E+01 8 - 1.50560E+01 20 - 1.68572E+01 23 1.69392E+01

18 2.28307E+01 21 2.31746E+01 19 - 2.40212E+01

***********************************************************************************************************************

‚ˆ„ Ž�Ž�™…��ŽƒŽ “P€‚�…�ˆŸ

Y (5) =Y (1) *Y (2) *Y (3) / 5.774019E+03

***********************************************************************************************************************

ƒ�€”ˆŠ ˆ‡Œ…�…�ˆŸ ‘ Š Ž

3_

0.00E+00 8.33E+00 1.67E+01 2.50E+01 3.33E+01 4.17E+01

OT ‘�…„�…ƒŽ ‡�€-…�ˆŸ ”“�Š-ˆˆ ‘ Š Ž = 4.16542733E+01+---------+---------+---------+---------+---------*

! 20 40 60 80 100%

!

�Ž‘‹… *** ”€Š’Ž�€ ‘ Š Ž = 1.16635160E+01+ *

3$

***********************************************************************************************************************

”ŽPŒ“‹ŸP ŒŽ„…‹ˆ

„€’€: 4/5/2008 Ž’P€�Ž’€�Ž 27 Ž�›’Ž‚ ‡€Š€‡-ˆŠ:

B=6; E=2; G=1; L=11; P=2;

5=F (1; 2;

3);

------------------------------------------------------------------------------------------------------------------

! N! N! KŽ�””ˆ-ˆ…�’› “P€‚�…�ˆ‰! CKO%!! ‘ŠŽ. ‘�%!

! €Pƒ! “P-Ÿ! - ----------------------------------------------------------! - -------------! R! - -------------!

!!! A! B! C! D! 100!! 100!

! - ---! - ---! - -------------! - -------------! - -------------! - -------------! - -------------! - -------------! - -------------!

!!!!!!!!!!

! 1! 7! 3.6737450E-02! - 3.2127082E-03!!! 35.9!! 2.5!

!!!!!!!!!!

! 2! 3! 8.4650388E+01! - 1.1083328E+02!!! 100.0!! 11.7!

!!!!!!!!!!

! 3! 1! 8.4566750E+01! - 1.5140801E+00!!! 99.1!! 224.5!

!!!!!!!!!!

! ***! ***!!!!! 28.0! 9.5465651E-01!!

!!!!!!!!!!

------------------------------------------------------------------------------------------------------------------

DMAX = - 2.4021168E+01 ( 19)

CKO% = 28.00

ŠŽ�””ˆ-ˆ…�’ ”ˆ˜…P€ F = 12.75440; F (001) = 2.52846; F (005) = 1.92428

‚›�Ž‹�ˆ‹

***********************************************************************************************************************

Ïðèëîæåíèå Â

Ðåçóëüòàòû ANETR äëÿ σz

B=6; E=2; G=1; L=11; P=1;

6=F (1; 2;3);

1 1.07573E+02 6.00000E+00 1.30000E+01 6.00000E+00

2 9.66540E+01 6.00000E+00 1.30000E+01 1.00000E+00

3 9.77720E+01 6.00000E+00 1.30000E+01 1.00000E+01

4 1.08093E+02 6.00000E+00 1.10000E+01 6.00000E+00

5 1.06188E+02 6.00000E+00 1.50000E+01 6.00000E+00

6 1.07432E+02 6.00000E+00 1.10000E+01 1.00000E+00

7 1.05237E+02 6.00000E+00 1.10000E+01 1.00000E+01

8 1.08531E+02 6.00000E+00 1.50000E+01 1.00000E+00

9 9.76700E+01 6.00000E+00 1.50000E+01 1.00000E+01

10 8.10040E+01 4.00000E+00 1.30000E+01 6.00000E+00

11 8.24950E+01 4.00000E+00 1.10000E+01 6.00000E+00

12 8.09860E+01 4.00000E+00 1.50000E+01 6.00000E+00

13 9.56720E+01 4.00000E+00 1.10000E+01 1.00000E+00

14 9.11610E+01 4.00000E+00 1.10000E+01 1.00000E+01

15 9.55100E+01 4.00000E+00 1.50000E+01 1.00000E+00

16 9.13070E+01 4.00000E+00 1.50000E+01 1.00000E+01

17 1.31362E+02 9.00000E+00 1.10000E+01 6.00000E+00

18 1.25308E+02 9.00000E+00 1.10000E+01 1.00000E+00

19 1.26622E+02 9.00000E+00 1.10000E+01 1.00000E+01

20 1.20552E+02 9.00000E+00 1.30000E+01 6.00000E+00

21 1.18298E+02 9.00000E+00 1.30000E+01 1.00000E+00

22 1.20214E+02 9.00000E+00 1.30000E+01 1.00000E+01

23 1.27884E+02 9.00000E+00 1.50000E+01 6.00000E+00

24 1.29646E+02 9.00000E+00 1.50000E+01 1.00000E+00

25 1.29244E+02 9.00000E+00 1.50000E+01 1.00000E+01

26 9.37530E+01 4.00000E+00 1.30000E+01 1.00000E+00

27 9.45410E+01 4.00000E+00 1.30000E+01 1.00000E+01

Min 8.09860E+01 4.00000E+00 1.10000E+01 1.00000E+00

Max 1.31362E+02 9.00000E+00 1.50000E+01 1.00000E+01

Ž‘ = 1.063E+02 ‘ŠŽ = 1.588E+01 ‘Š’ = 27

---------------------------------------------------------------

3_

8.10E+01 9.11E+01 1.01E+02 1.11E+02 1.21E+02 1.31E+02

X Y YP KT 4.00E+00+---------+---------+---------+---------+---------+-

4.00000E+00 8.96032E+01 8.95875E+01 9! 21 @2 211

! *

! *

! *

4.50E+00+ *

! *

! *

! *

! *

5.00E+00+ *

! *

! *

! *

! *

5.50E+00+ *

! *

! *

! *

! *

6.00E+00+ *

6.00000E+00 1.03906E+02 1.03932E+02 9! 12 @1122

! *

! *

! *

6.50E+00+ *

! *

! *

! *

! *

7.00E+00+ *

! *

! *

! *

! *

7.50E+00+ *

! *

! *

! *

! *

8.00E+00+ *

! *

! *

! *

! *

8.50E+00+ *

! *

! *

! *

! *

9.00E+00+ *

9.00000E+00 1.25459E+02 1.25448E+02 9! 1 2 @1 12 1

3$

‚ˆ„ 1 “�€‚�…�ˆŸ �Ž 1 ”€Š’Ž�“ Y = A + B * X

A= 6.08987E+01 B= 7.17218E+00

CKO= 5.17057E+00 CKO%= 32.6 CKO CP. = 1.90567E-02 R= 9.432861E-01

***********************************************************************************************************************

3_

8.10E+01 9.11E+01 1.01E+02 1.11E+02 1.21E+02 1.31E+02

X Y YP KT 1.10E+01+---------+---------+---------+---------+---------+-

1.10000E+01 1.08154E+02 1.08147E+02 9! 1 12@ 2 2

! *

! *

! *

1.14E+01+ *

! *

! *

! *

! *

1.18E+01+ *

! *

! *

! *

! *

1.22E+01+ *

! *

! *

! *

! *

1.26E+01+ *

! *

! *

! *

! *

1.30E+01+ *

1.30000E+01 1.03373E+02 1.03377E+02 9! 1212 @ 21

! *

! *

! *

1.34E+01+ *

! *

! *

! *

! *

1.38E+01+ *

! *

! *

! *

! *

1.42E+01+ *

! *

! *

! *

! *

1.46E+01+ *

! *

! *

! *

! *

1.50E+01+ *

1.50000E+01 1.07441E+02 1.07444E+02 9! 1 1 @21211

3$

‚ˆ„ 11 “�€‚�…�ˆŸ �Ž 2 ”€Š’Ž�“ Y = A * X**2 + B * X + C

A= 1.10477E+00 B= - 2.88999E+01 C= 1.86047E+02

CKO= 4.70435E+00 CKO%= 29.6 CKO CP. = 4.40933E-03 R= 9.512971E-01

***********************************************************************************************************************

3_

8.10E+01 9.11E+01 1.01E+02 1.11E+02 1.21E+02 1.31E+02

X Y YP KT 1.00E+00+---------+---------+---------+---------+---------+-

1.00000E+00 1.07867E+02 1.07860E+02 9! 2 1 @121 1

! *

! *

! *

1.90E+00+ *

! *

! *

! *

! *

2.80E+00+ *

! *

! *

! *

! *

3.70E+00+ *

! *

! *

! *

! *

4.60E+00+ *

! *

! *

! *

! *

5.50E+00+ *

! *

! *

6.00000E+00 1.05126E+02 1.05130E+02 9! 11 1 1@ 21 1 1

! *

6.40E+00+ *

! *

! *

! *

! *

7.30E+00+ *

! *

! *

! *

! *

8.20E+00+ *

! *

! *

! *

! *

9.10E+00+ *

! *

! *

! *

! *

1.00E+01+ *

1.00000E+01 1.05974E+02 1.05978E+02 9! 1 11 @1 1 1

3$

‚ˆ„ 11 “�€‚�…�ˆŸ �Ž 3 ”€Š’Ž�“ Y = A * X**2 + B * X + C

A= 8.42139E-02 B= - 1.13545E+00 C= 2.58845E+00

CKO= 4.55717E+00 CKO%= 28.7 CKO CP. = 5.29090E-03 R= 9.523351E-01

***********************************************************************************************************************

Ž ’ Š ‹ Ž � … � ˆ Ÿ

14 9.33221E-02 6 1.38079E-01 7 - 1.75046E-01 19 - 3.06599E-01 20 - 7.57778E-01 16 9.43032E-01

24 1.53924E+00 8 1.94079E+00 22 - 1.94367E+00 5 2.32755E+00 23 2.50700E+00 13 2.72245E+00

3 - 2.86911E+00 25 3.01911E+00 15 3.26416E+00 18 - 3.50247E+00 4 3.52884E+00 10 - 4.44486E+00

17 5.28129E+00 26 5.57438E+00 21 - 5.74154E+00 2 - 5.86899E+00 9 - 7.03834E+00 11 - 7.72479E+00

1 7.77977E+00 27 8.24425E+00 12 - 8.53008E+00

***********************************************************************************************************************

‚ˆ„ Ž�Ž�™…��ŽƒŽ “P€‚�…�ˆŸ

Y (6) =Y (1) +Y (2) +Y (3)

***********************************************************************************************************************

ƒ�€”ˆŠ ˆ‡Œ…�…�ˆŸ ‘ Š Ž

3_

0.00E+00 3.18E+00 6.35E+00 9.53E+00 1.27E+01 1.59E+01

OT ‘�…„�…ƒŽ ‡�€-…�ˆŸ ”“�Š-ˆˆ ‘ Š Ž = 1.58833364E+01+---------+---------+---------+---------+---------*

! 20 40 60 80 100%

!

�Ž‘‹… 1 ”€Š’Ž�€ ‘ Š Ž = 5.17056730E+00+ *

!

!

�Ž‘‹… 2 ”€Š’Ž�€ ‘ Š Ž = 4.70435362E+00+ *

!

!

�Ž‘‹… 3 ”€Š’Ž�€ ‘ Š Ž = 4.55717450E+00+ *

3$

***********************************************************************************************************************

”ŽPŒ“‹ŸP ŒŽ„…‹ˆ

„€’€: 4/5/2008 Ž’P€�Ž’€�Ž 27 Ž�›’Ž‚ ‡€Š€‡-ˆŠ:

B=6; E=2; G=1; L=11; P=1;

6=F (1; 2;

3);

------------------------------------------------------------------------------------------------------------------

! N! N! KŽ�””ˆ-ˆ…�’› “P€‚�…�ˆ‰! CKO%!! ‘ŠŽ. ‘�%!

! €Pƒ! “P-Ÿ! - ----------------------------------------------------------! - -------------! R! - -------------!

!!! A! B! C! D! 100!! 100!

! - ---! - ---! - -------------! - -------------! - -------------! - -------------! - -------------! - -------------! - -------------!

!!!!!!!!!!

! 1! 1! 6.0898722E+01! 7.1721842E+00!!! 32.6! 9.4328610E-01! 0.1!

!!!!!!!!!!

! 2! 11! 1.1047693E+00! - 2.8899930E+01! 1.8604702E+02!! 29.6! 9.5129706E-01! 3.1!

!!!!!!!!!!

! 3! 11! 8.4213889E-02! - 1.1354500E+00! 2.5884491E+00!! 28.7! 9.5233506E-01! 3.7!

!!!!!!!!!!

------------------------------------------------------------------------------------------------------------------

DMAX = - 8.5300788E+00 ( 12)

CKO% = 28.69

ŠŽ�””ˆ-ˆ…�’ ”ˆ˜…P€ F = 12.14765; F (001) = 2.52846; F (005) = 1.92428

‚›�Ž‹�ˆ‹

***********************************************************************************************************************

Ïðèëîæåíèå Ã

Êîìàíäíûé ôàéë

/filnam, massiv! Îïðåäåëåíèå èìåíè ôàéëà

/title,lab_3! Îïðåäåëåíèå çàãîëîâêà çàäà÷è

/prep7 ! Âõîä â ïðåïðîöåññîð

a=6! h

b=13! R

c=6! r

et,1,92! Çàäàíèå òèïà ýëåìåíòà

mp,ex,1, 200000Çàäàíèå ñâîéñòâ ìàòåðèàëà

mp,ey,1, 200000

mp,ez,1, 200000

mp,nuxy,1,0.3

mp,nuxz,1,0.3

mp,nuyz,1,0.3

k,1,0,0,0! Ïîñòðîåíèå òî÷åê

k,2,60,0,0

k,3,60,-50,0

k,4,15,-50,0

k,5,15,-40,0

k,6,0,-40,0

L,1,2! Ïîñòðîåíèå ëèíèé

L,2,3

L,3,4

L,4,5

L,5,6

L,6,1

al,all! Îáúåäèíåíèå â îáëàñòü

voffst,1,25! Âûòÿãèâàíèå íà âûñîòó

local,100,0,0,0,-25,0,0,0,0,,! Ñìåùåíèå ñèñòåìû êîîðäèíàò

wpcsys,1,100

k,13,0,0,0

k,14,25,0,0

k,15,0,-25,0

L,13,14

L,14,15

L,15,13

al, 19, 20,21

voffst,9,35

local,100,0,0,0,-60,0,0,0,0,,

wpcsys,1,100

k, 19,0,-13,0

k, 20,13,0,0

L,16, 19

L,16, 20

larc, 19, 20,16,13! Ïîñòðîåíèå äóãè

al,28,29,30

voffst,14,6

vsbv,2,3! Âû÷èòàíèå îáúåìîâ

local,100,0,0,0,-54,0,0,0,0,,

wpcsys,1,100

k,24,0,-6,0

k,25,6,0,0

L,21,24

L,21,25

larc,24,25,21,6

al,22,24,25

voffst,10,54

vadd,1,4! Îáúåäèíåíèå îáúåìîâ

vsbv,3,2

smrtsize,all,5! Çàäàíèå ðàçìåðà êîíå÷íîãî ýëåìåíòà

vmesh,all! Ðàçáèåíèå íà êîíå÷íûå ýëåìåíòû

/solu! Âõîä â ïðîöåññîð

da,26,all! Çàêðåïëåíèå îáëàñòåé

da,8,uy

da,21,uy

da,3,ux

da, 20,ux

sfa,9,,pres,100! Ïðèëîæåíèå íàãðóçêè

solve! Çàïóñê çàäà÷è íà ðåøåíèå

/post1! Âõîä â ïîñòïðîöåññîð

plnsol,u,sum,0,1! ïðîñìîòð íàïðÿæåíèé