Methods of finite element analysis of arbitrary buckling forms of sandwich plates and shells

Abstract

1o IntroductionBased on the results presented in [1][2][3][4][5][6][7], the following basic conclusions can be formulated: 1) the buckling forms (CBFs) realized in sandwich structural elements depend both on the type of the precritical stress-strain state (SSS) in load-carrying layers and filler and on the values of some defining parameters of the structure (the complex of defining parameters entering in the equations given in [8,9] for mixed flexural and flexural-shear BFs was defined, in particular, in [10]),.2) the tangential membrane forces in load-carrying layers and the transverse tangential stresses in the filler are the main parameters of the precritical SSS, which determine the critical loads and BFs, 3) the main defining parameters of a sandwich structure, which govern the BFs, are the transverse compression coefficient, the ratio of the filler thickness to the thickness of the load-carrying layer, and the ratio between the shear modulus of the load-carrying layer material and the normal elastic modulus in the plane tangential to the midsurface of the load-carrying layer, whose particular combinations lead to jumplike changes in the BF, 4) to ensure the necessary degree of accuracy in determining the critical parameters of external loading and particularly the BF, the problem of determination of the precritical SSS, as a rule, must be formulated based on equations having a degree of accuracy no smaller than that of the equations of neutral equilibrium, 5) within rather wide ranges of defming parameters describing the actual sandwich structures, the degree of accuracy of the equations given in [2,8,9] and constructed in terms of the model era transversely soft core, is quite sufficient for the statement and solution of problems on mixed flexural and flexural-shear BFs, 6) when investigating arbitrary BFs, where, of all parameters of the precritical SSS, prevailing are the membrane tangential internal forces in load-carrying layers made of composite materials with small shear moduii in the tangential plane, it is necessary to use equations with regard to all geometrically nonlinear summands in kinematic relations, and