Abstract
The paper presents the equilibrium finite element discretization of symmetrically loaded spherical flat shells. It is based on Castigliano principle. A new second-order equilibrium finite element is suggested, and the equilibrium and physical equations, obtained for it by using the Bubnov-Galiorkin method, are presented. A mathematical model for solving the problem of the elastic shell computation is created, based on the above equations. The methodology is illustrated by a numerical example. The results are obtained, using a computer-aided program developed by the authors. The calculation results, obtained using the mesh of the elements of various density, show that the accuracy of the created element and the convergence of the results are high.DOI: http://dx.doi.org/10.5755/j01.mech.18.3.1886
Highlights
Computer-aided analysis of structures requires the development of their discrete model with the finite number of the degrees of freedom
The problem of calculating the internal forces, displacements and strains under the given load is reduced to deriving the equations of the displacement method
These equations are derived by summing up the stiffness values of the elements according to the algorithm, regulated by equations of statics
Summary
Computer-aided analysis of structures requires the development of their discrete model with the finite number of the degrees of freedom. The problem of calculating the internal forces, displacements and strains under the given load is reduced to deriving the equations of the displacement method. These equations are derived by summing up the stiffness values of the elements according to the algorithm, regulated by equations of statics. The mathematical model and the calculation algorithm of the internal forces and displacements in the shell analysis are developed and formulated, using the equations of statics and geometry. The analysis and description of the method of shell discretization by equilibrium finite elements are still lacking in the scientific literature
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