Pikul A. Method of calculation of non-thin plates and shells on the basis of 3D-curvilinear finite elements

The thesis is dedicated to the research of the stress-strain state in problems of deformation of non-thin plates and shells of zero or positive Gaussian curvature with static loading. This paper shows the problems of analysis of thick-walled construc- tions and been shown new solid finite element constructed in a curvilinear coordinate system based on the vector approximation of the displace- ment function in the Maclaurin series. Displacements of a finite element are taken as a vector-function, which includes the rigid-body motions. The results of the research on the reliability and efficiency of the use of the finite element method on the basis of the curvilinear solid finite element on the problems of the Theory of Elasticity under the action of stationary load (the equilibrium of thick plates with different fixing con- ditions, the bending of transversally isotropic plates with different fixing conditions, the balance of the thick-walled cylinder under the influence of external and internal pressure, and also under the action of tension on the ends, the balance of the thick-walled sphere under the influence of an external and internal pressure) with different parameters and different size of mesh density are presented. There are a lot of tests solved to confirm the reliability. The results there are compared with well known analytical solutions and with the solutions that are obtained using other finite element schemes in the LIRA-SAPR and SCAD Office. In the process of FEM testing, the limits of the use of the solid curvilinear finite element for the modeling of non-thin plates and shells are defined. The demonstration of the possibilities offered by the proposed method has been demonstrated on practical cases - the modeling of the functioning of flanged connections of steel joints, the analysis of the base plate of the round pylon, the analysis of the thick foundation slab of a 30-storey reinforced concrete dwelling building.