Finite-element modelling and shear stress analysis of engineering structural elements

Abstract

This paper deals with the shear stress analysis of engineering beams with uniform cross-sections using finite-element method. The analysis is based on special finite elements whose properties, like stiffness matrices as well as load vectors, are derived on the basis of their axial nodal displacements. From geometrical point of view these elements are three-dimensional, but according to the strain or stress tensor, they are two-dimensional. The aforesaid stress analysis is independent of the cross-sectional shape and the material properties. These elements are subjected to shearing stress analysis due to St. Venant's torsion and due to loading of a beam by shear forces. Stiffness matrices and load vectors are derived in general forms and a closed form can be easily obtained. The material is assumed to be isotropic and linearly elastic. The proposed procedure can be applied in analysis, such as, marine, airplane, vessel structures, etc. Based on this procedure, a computer program has been developed. For justification of the proposed stress analysis as well as its accuracy, for examples are presented. A comparison with analytical and other numerical solutions is also provided.

Keywords

shearing stress analysis St. Venant's torsion loading of a beam by shear forces finite-element method new quadrilateral finite element

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