有限元法
非线性系统
灵敏度(控制系统)
计算
曲率
状态变量
插值(计算机图形学)
数学
应用数学
趋同(经济学)
计算机科学
数学分析
结构工程
帧(网络)
算法
几何学
工程类
物理
热力学
电信
量子力学
经济增长
经济
电子工程
作者
Michael H. Scott,Vahid Jafari Azad
摘要
Summary Response sensitivity is an essential component to understanding the complexity of material and geometric nonlinear finite element formulations of structural response. The direct differentiation method (DDM), a versatile approach to computing response sensitivity, requires differentiation of the equations that govern the state determination of an element and it produces accurate and efficient results. The DDM is applied to a force‐based element formulation that utilizes curvature‐shear‐based displacement interpolation (CSBDI) in its state determination for material and geometric nonlinearity in the basic system of the element. The response sensitivity equations are verified against finite difference computations, and a detailed example shows the effect of parameters that control flexure–shear interaction for a stress resultant plasticity model. The developed equations make the CSBDI force‐based element available for gradient‐based applications such as reliability and optimization where efficient computation of response sensitivities is necessary for convergence of gradient‐based search algorithms. Copyright © 2016 John Wiley & Sons, Ltd.
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