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非线性本构关系下圆板的大挠度问题
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Abstract:
本文基于经典板理论和本构非线性关系，研究了周边固支和周边简支圆板在横向均布载荷的作用下的非线性静态响应。假设了材料弹性模量是应变的线性函数，利用能量法推导了本构关系非线性的情况下，圆板弯曲的基本方程和边界条件，对基本方程和边界条件进行了无量纲化处理，并采用打靶方法求解了周边固支和周边简支条件下，圆板轴对称弯曲的数值解。分析了本构非线性参数对圆板轴对称弯曲变形和中性层位置的影响。
In this paper, based on the classical plate theory and nonlinear constitutive relation, the nonlinear static response of circular plates with fixed and simply supported edges peripheries under laterally uniform load are studied. It is assumed that the elastic modulus of material is a linear function of strain. The basic equations and boundary conditions of circular plate bending under the condition of non-linear constitutive relation are derived by energy method. The equations and boundary conditions are nondimensionalized, and the numerical solutions of circular plate axisymmetric bending under the conditions of peripheral fixed support and simple support are solved by shooting method. The influence of constitutive nonlinear parameters on bending deformation and neutral layer is analyzed.
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