Advanced 3D beam element of arbitrary composite cross section including generalized warping effects

What is it about?

In this paper an advanced 20x20 stiffness matrix and the corresponding nodal load vector of a member of arbitrary composite cross section is developed taking into account shear lag effects due to both flexure and torsion (the case of the 3-D beam element of arbitrary homogeneous cross section is treated as a special one). The composite member consists of materials in contact each of which can surround a finite number of inclusions. Nonuniform warping distributions are taken into account by employing four independent warping parameters multiplying a shear warping function in each direction and two torsional warping functions. Ten boundary value problems with respect to the kinematical components are formulated and solved employing the Analog Equation Method, a Boundary Element Method based technique. The aforementioned boundary value problems are formulated employing either an improved stress field arising from the correction of shear stress components or the stress field arising directly from displacement considerations. The warping functions and the geometric constants including the additional ones due to warping are evaluated employing a pure BEM approach, i.e. only boundary discretization of the cross section is used. Numerical results are presented to illustrate the method and demonstrate its efficiency and accuracy. The deviations arising from the use of the advanced 20x20 stiffness matrix and the classical 12x12 or 14x14 ones employed in commercial software packages are illustrated through examples of great practical interest. Moreover, the influence of nonuniform warping effects necessitating the use of the aforementioned “advanced” stiffness matrix is also demonstrated.

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