Axisymmetric Large Deflections of Circular Plates Subjected to Thermal and Mechanical Loads

Abstract

Summary This paper is concerned with the nonlinear axisymmetric analysis of circular plates with in-plane edge restraint. Both temperature and mechanical loads are accommodated as an ex­ tension of investigations performed for the isothermal mechanical loading problem.1-4 An exact mathematical formulation within the framework of the von Karman large-strain displacement relations5 is developed. The equilibrium equations and boundary conditions are then derived by utilizing the calculus of variations for arbitrary axisymmetric temperatures and normal distributed loading. The satisfaction of equilibrium and compatibilhVy equations requires the solution of two simultaneous nonlinear ordinary differential equations subject to the prescribed boundar}^ conditions. Analytical solutions of such equations are apparently not possible and therefore numerical procedures must be em­ ployed. A finite-difference procedure utilizing relaxed iterations, developed by Keller and Reiss,4 and employed by them for the solution of isothermal problems with apparently unlimited loadparameter ranges, is used here for combined thermomechanical problems. Numerical results are presented for the special case of a simply supported circular plate with radially immovable boundaries, subject to a uniform pressure and an arbitrary tem­ perature variation through the thickness (no planform variation). These results have been obtained for a large range of temperature and load parameters. However, because of space limitations, only a limited number of data are presented in this paper.