Buckling of Rectangular Plates under Nonlinear Creep

Abstract

Introduction. The task of analyzing the stability of plates and shells under creep conditions is critical for structural elements made of materials with the property of aging, which are under the action of long-term loads, since the loss of stability can occur abruptly and long before the exhaustion of the strength resource of the material. Currently, the issues of joint consideration of geometric nonlinearity and creep in the problems of buckling plates remain poorly studied, existing software systems do not provide such calculations. The objective of this work is to develop an algorithm for calculating the stability of rectangular plates with initial deflection, which are subjected to loads in the middle plane, taking into account geometric nonlinearity and creep.Materials and Methods. When obtaining the resolving equations, the geometric and static equations of the theory of flexible elastic plates were taken as the basis. Physical equations were derived from the assumption that total strains were equal to the sum of elastic strains and creep deformations. Finally, the problem was reduced to a system of two differential equations, in which the desired functions were the stress and deflection functions. The resulting system of equations was solved numerically using the finite-difference method in combination with the method of successive approximations and the Euler method. As the boundary conditions for the stress function, the frame analogy was used, as in the case of a plane problem of elasticity theory.Results. The solution to the problem for a plate compressed in one direction by a uniformly distributed load has been presented. The nature of the growth of displacements at different load rates and initial deflection was studied. It has been established that when the vertical displacements reach values comparable to the thickness of the plate, their growth rate begins to decay even at a load greater than the long-term critical one.Discussion and Conclusion. The results of stability analysis using the developed algorithm show that the growth of plate deflection under the considered boundary conditions is limited, stability loss is not observed at any load values not exceeding the instantaneous critical one. This indicates the possibility of long-term safe operation of such structures with a load less than instant critical one.