Three-dimensional stability of a rectangular plate under uniaxial tension

Abstract

The paper studies the three-dimensional stability of an isotropic, linear elastic, rectangular plate under a uniform tensile load applied to its sides. The concept of free strains is used to reduce the three-dimensional problem to a two-dimensional one. It is solved using the three-dimensional linearized theory of stability. An approximate solution of the buckling problem is obtained by the finite-difference method. Numerical results are presented

Numerical solution to the buckling problem for a sandwich plate under uniaxial compression

“…Each of these methods is efficient with a mesh having N < 10 4 nodes. The experience of solving specific problems for thin plates suggests that solutions of a differential problem are practicable when the number of nodes is within the interval 10 5 ≤ N ≤ 10 6 [5,7,9]. When using such meshes to solve buckling problems, the need arises to accelerate the convergence of methods for solving finite-difference equations.…”

“…When using such meshes to solve buckling problems, the need arises to accelerate the convergence of methods for solving finite-difference equations. To enhance the efficiency of computation, use is made of an optimization procedure [5,[7][8][9] involving a variable mesh and both methods of solving finite-difference equations. The initial mesh is used to solve the global spectral algebraic problem by subspace iteration.…”

“…Let us determine base factors [2,5,[7][8][9]. We will use the following base scheme and base system of equations to represent the global discrete spectral problems in explicit form: …”