AUTOMATING THE FINITE ELEMENT METHOD FOR THE THERMAL BUCKLING ANALYSIS OF PLATES - Choporov, S. V. (Computer Science and Applied Mathematics, 2017)
The finite element method is the most successful numerical method for simulation of mechanical problems. It can be viewed as a virtual machine that automates simulation taking as input geometry of a domain, meshing the domain into finite elements of the same shape and producing a system of discrete equations. Implementations of the finite element method are usually specialized. Implementations often use meshes as input and allow simulate a small set of variational problems. But only a little set of implementations allows carry out the thermal buckling analysis. This article reviews researches that devoted to an automation of the finite element method. In particular, this work discusses an approach for a representation of a domain, an algorithm for a meshing procedure and an approach for the thermal buckling analysis of a plate. As input, implicit functions are employed to represent a plate as a geometric object. Logical R-functions (conjunction, disjunction and negation) allow construct an implicit function for a complex domain in constructive manner. In the first step, the meshing routine uses a background mesh to generate a set of quadrilaterals. Obtained meshes are refined by local smoothing. In the next step, the second-order shear deformation theory for plates and shells is used in the discretization of differential equations. Finally, solving the generalized eigenvalue problem we get eigenvalues and eigenvectors. Eigenvalues correspond to critical temperature; eigenvectors correspond to a field of nodal displacements. In the article, developed approach is used to carry out the thermal buckling analysis of complex domains (for example, automotive clutches).