Nonlinear axisymmetric thermomechanical response of FGM circular plates
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(2020) 42:360
TECHNICAL PAPER
Nonlinear axisymmetric thermomechanical response of FGM circular plates Weidong Zhao1 Received: 19 March 2020 / Accepted: 28 May 2020 © The Brazilian Society of Mechanical Sciences and Engineering 2020
Abstract Based on von Kármán plate theory, axisymmetric geometrically nonlinear governing equations of simple power-law type functionally graded material (FGM) circular plates are derived. Material properties are assumed to be temperature-independent, and thermal or/and mechanical loads are considered in the derivation. Considering clamped boundary conditions, the dimensionless critical (lowest) buckling temperature (temperature difference) 14.684 of the systems is obtained by analyzing linear-eigenvalue problem. With this constant and an analytical formula proposed in this paper, accurate dimensional critical (lowest) buckling temperature (temperature difference) of any specified clamped FGM circular plate can be easily calculated. Moreover, two-point boundary value problem posed by the governing equations and the clamped boundary conditions is solved using the shooting method. Thermal buckling response under thermal load and geometrically nonlinear mechanical behaviors under thermomechanical load of the system are discussed. When the temperature difference of the upper and lower surfaces of FGM plates exists, the solution of one-dimension Fourier heat conduction equation is an infinite series, which depicts a nonlinear temperature field (NLTF) along the thickness direction of plates. The effects of the initial terms of the series on the accuracy of solutions are examined. The results reveal it is necessary to take enough the initial terms of the series even for thinner FGM plates. Typical load–deflection curves of the clamped FGM circular plates with different temperature fields (along the thickness) are presented. For a given temperature field, the clamped FGM circular plates under transverse uniform load are a hard stiffness nonlinear system. When the values of thermal and mechanical load and their loading sequence meet certain combinations, the clamped circular plate will inevitably undergo secondary buckling (snap-through buckling). Keywords Functionally graded materials · Circular plates · Thermal buckling · Thermomechanical nonlinear response
1 Introduction With the development of modern aerospace technology, traditional homogeneous materials and laminated composite materials have been unable to bear the ultra-high temperature and large thermal gradient loads that aerospace equipment needs to bear. To meet the requirements of aerospace equipment for bearing ultra-high temperature and large thermal gradient materials, the concept of FGM was first proposed by Japanese scientists in 1984 [1]. FGM is one of the Technical Editor: João Marciano Laredo dos Reis. * Weidong Zhao [email protected] 1
School of Civil Engineering, Qinghai University, Xining 810016, China
novel graded composite materials which are a mixture of two or more constituent materials. Compared with homogene
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