Accurate Calculation of Stress Distributions in Multiholed Plates

Abstract

This paper discusses the application of the point-matching technique in obtaining the solution of many problems involving multiholed thin plates undergoing generalized plane stress. The stress functions appropriate to plates with symmetric groups of holes are described. A large number of problems solved by a computer program are described and compared with published results. Problems are solved also for which there are no known published results. Two interesting new problems are discussed in detail. The results show the power and flexibility of the technique. The extension of the methods to permit the solution of problems in the deflection of thin, multiholed plates and shallow shells is discussed.

Simple estimation of effective elastic constants for thin plates with regular perforations and an application to the vibration of distillation column trays

“…5 Previous theoretical methods usually require complex general solutions for the stress potentials, with the coefficient of each term found by applying appropriate boundary conditions such as far-field loadings and traction-free stress fields on free surfaces. The results from such an approach 6–8 compare very well to experimental data such as those in Nuno et al 9 and Duncan and Upfold 10 and are referred to as the ‘exact solutions’ in this article. However, the implementation of such methods is often complicated and may require new general solutions to be derived for different perforation arrangements.…”

“…The results are shown in dimensionless form in Figures 8–10, where E and D are Young’s modulus and bending stiffness of the plate material, respectively. Previous theoretical solutions summarised by O’Donnell 17 and based on the work of Bailey and Hicks 6 and Hulbert and Niedenfuhr 7 are also shown.…”

A review of least‐squares methods for solving partial differential equations

“…29-3 2.6 5. [72][73][74][75][76][77][78] Difficulties in implementing linear least squares include ill-conditioning and higher-order continuity. Equation (13) is in the sdme form as the normal equations of least-squares curvefitting, which tend to become ill-conditioned for large n. The problem can be reduced by scaling79 or by avoiding elimination algorithms in favour of more sophisticated linear least-squares codes based on Gram-Schmidt orthonormalization or orthogonal Householder transformations.80781 The second difficulty arises in the use of finite-element local approximators.…”