بررسی سه بعدی رفتارهای مکانیکی غیرخطی وابسته به دمای ورق‌های مستطیلی مدرج تابعی روی پایه الاستیک وینکلر-پسترناک

غلامی, یوسف; انصاری خلخالی, رضا

بررسی سه بعدی رفتارهای مکانیکی غیرخطی وابسته به دمای ورق‌های مستطیلی مدرج تابعی روی پایه الاستیک وینکلر-پسترناک

نویسندگان

یوسف غلامی ¹

رضا انصاری خلخالی ²

¹ دانشجوی کارشناسی، مهندسی‌ مکانیک، دانشگاه گیلان

² دانشیار دانشگاه گیلان

چکیده

در این مقاله به بررسی رفتار مکانیکی غیرخطی ورقهای مستطیلی مدرج تابعی در جهت ضخامت وابسته به دما با استفاده از تئوری الاستیسیته سه بعدی روی پایه های الاستیک وینکلر-پسترناک پرداخته شده است. فرض میشود خواص مواد سازنده وابسته به دما می باشند و براساس یک قانون توانی در راستای ضخامت تغییر می کنند. با در نظر گرفتن رابطه کرنش غیرخطی گرین-لاگرانژ، اثرات غیرخطی هندسی در محاسبات منظور شده است. پس از بدست آوردن انرژی‌های کرنشی و جنبشی و کار ناشی از نیروی خارجی و در نظر گرفتن اثرات دما و بستر الاستیک، از اصل همیلتون برای بدست آوردن معادلات حاکم سه بعدی استفاده می شود. برای حل مسائل مربوط به رفتار مکانیکی سیستم، ابتدا از روش تربیع دیفرانسیلی تعمیم یافته برای گسسته سازی معادلات کوپل غیرخطی در فضای مکان استفاده میشود. سپس، با استفاده از روش گلرکین عددی برای حل مساله ارتعاشات آزاد، معادلات تبدیل به معادلات دیفرانسیل معمولی تابع زمان می شوند و با استفاده از روش گسسته سازی متناوب زمانی در حوزه زمان گسسته می‌شود. در نهایت، از الگوریتم طول کمان برای یافتن پاسخ فرکانسی سیستم بهره گرفته می‌شود. برای حل مساله خمش غیرخطی، با صرف نظر کردن از اثر اینرسی و استفاده از الگوریتم طول کمان، ماکزیمم خمش بر حسب نیرو به دست می آید. اثرات پارامترهای مانند نسبت طول به ضخامت، ثابت های وینکلر و پسترناک، تغییر دمای یکنواخت و خطی و شاخص کسر حجمی بر پاسخ فرکانسی و ماکزیمم خمش ورقهای مدرج تابعی با شرایط مرزی مختلف به تفضیل مورد بررسی قرار گرفته است.

کلیدواژه‌ها

ورق مدرج تابعی

رفتار مکانیکی غیرخطی

تئوری الاستیسیته سه بعدی

حل عددی

20.1001.1.10275940.1397.18.7.12.1

موضوعات

سازه های هوا فضا

عنوان مقاله English

Three dimensional analysis of temperature-dependent nonlinear mechanical behaviors of functionally graded rectangular plates resting on WinklerâPasternak elastic foundation

نویسندگان English

Y. Gholami ¹

Reza Ansari ²

¹ Department of Mechanical Engineering, University of Guilan, Rasht, Iran

چکیده English

The temperature-dependent nonlinear mechanical behaviors of functionally graded rectangular plates in the thickness direction resting on Winkler–Pasternak elastic foundation are investigated using the three-dimensional theory of elasticity. The material properties are temperature-dependent and varied in the thickness direction based on a power-law. Considering the nonlinear Green-Lagrange strain relation, the geometric nonlinearity is taken into account. After obtaining the potential strain, kinetic energies, taking into account the effects of the temperature and the elastic foundation, the Hamilton’s principle is used to derive the nonlinear three-dimensional governing equations and corresponding boundary conditions. To solve the nonlinear free vibration problem, first, the generalized differential quadrature (GDQ) method is used to discretize the nonlinear coupled governing equations in the space domain. Then, the obtained equations are converted to the time-dependent ordinary differential equations using the numerical-based Galerkin scheme and the time periodic discretization (TPD) are used to discretize them in the time domain. Finally, the arc-length method is employed to find the frequency-response of system. Also, to solve the nonlinear bending problem, by neglecting the effect of inertia and using the arc length algorithm, the maximum deflection versus the applied load is obtained. The effects of different parameters such as length-to-thickness ratio, Winkler–Pasternak elastic foundation coefficients, uniform and linear temperature rises and volume fraction index on the frequency response and maximum deflection of functionally graded plates with various edge conditions are studied.

کلیدواژه‌ها English

Functionally graded plate

Nonlinear mechanical behaviors

3D theory of elasticity

Numerical solution procedure

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