A Method of “Exact” Numerical Differentiation for Error Elimination in Finite-Element-Based Semi-Analytical Shape Sensitivity Analyses*
A Method of “Exact” Numerical Differentiation for Error Elimination in Finite-Element-Based Semi-Analytical Shape Sensitivity Analyses*
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DOI：
10.1080/08905459308905180
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发表时间：
1993
期刊：
影响因子：
--
通讯作者：
N. Olhoff;J. Rasmussen;E. Lund
中科院分区：
文献类型：
--
作者：
N. Olhoff;J. Rasmussen;E. Lund
ABSTRACT The traditional, simple numerical differentiation of finite-element stiffness matrices by a forward difference scheme is the source of severe error problems that have been reported recently for certain problems of finite-element-based, semi-analytical shape design sensitivity analysis. In order to develop a method for elimination of such errors, without a sacrifice of the simple numerical differentiation and other main advantages of the semi-analytical method, the common mathematical structure of a broad range of finite-element stiffness matrices is studied in this paper. This study leads to the result that element stiffness matrices can generally be expressed in terms of a class of special scalar functions and a class of matrix functions of shape design variables that are defined such that the members of the classes admit “exact” numerical differentiation (exact up to round-off error) by means of very simple correction factors to upgrade standard computationally inexpensive first-order finite di...
