Abstract
A new approach to solve plate constructions using combined analytical and numerical methods has been developed in this paper. It is based on an exact solution of an equilibrium equation. The proposed mathematical model is implemented as a computer program in which known analytical formulae are rewritten as wrapper functions of two arguments. Partial derivatives are calculated using automatic differentiation. A solution of a system of linear equations is substituted to these functions and evaluated using the Einstein summation convention. The calculated results are presented and compared to other analytical and numerical ones. The boundary conditions are satisfied with high accuracy. The effectiveness of the present method is illustrated by examples of rectangular plates. The model can be extended with the ability to solve plates of any shape.
Highlights
Thin plates are widely used as elements of building and engineering structures
Symmetry of the plate geometry, mechanical properties, boundary conditions and outer load are taken into account in this paper
Rectangular plate with two opposite edges supported and the other free, Rectangular plate supported at the contour, Plate clamped at the contour
Summary
Thin plates are widely used as elements of building and engineering structures. The Kirchhoff plate theory is the basis of engineering design and calculation of such elements. It is an approximate zeroth-order shear deformation plate theory. Discrepancy between order of basic differential equation and number of boundary conditions is the main disadvantage of the Kirchhoff theory. There are considered only three from six physical equations. Shearing and normal transverse stresses are not taken into account. They are determined from equation of equilibrium. The higher-order shear deformation plate theories are free from this discrepancy
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