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非线性力学应用广泛,研究它的求解方法日益重要。求解方法的基础是变分原理。本文将求解方法分成两类,一种是采用Gurtin的卷积形式,另一种是谱分解形式。作者曾对非线性力学的变分原理进行研究,建立了各种变分原理,其中较多地采用了谱分解形式。本文介绍了作者的一些工作,包括悬挂结构、薄壳、土力学和随机振动方面的变分原理,其中有关弹性-孔隙介质固结的动力学和随机振动的原理首次在本文中发表。根据变分原理可用有限元法求解。
Non-linear mechanics are widely used and it is increasingly important to study its solution methods. The basis of the solution method is the variational principle. In this paper, the solution methods are divided into two categories. One is the convolution of Gurtin, and the other is the spectral decomposition. The author once studied the variational principle of nonlinear mechanics and established various variational principles, among which the spectral decomposition form was used more often. This article describes some of the author’s work, including the variational principles of suspension structures, thin shells, soil mechanics, and random vibrations. The principles concerning the dynamics and random vibration of elastic-porosity media consolidation are first published in this paper. The variational principle can be solved using the finite element method.