3-D beam element of composite cross section including warping and shear deformation effects
In this paper a boundary element method is developed for the construction of the 1414 stiffness matrix and the nodal load vector of a member of arbitrary homogeneous or composite cross section taking into account both warping and shear deformation effects. The composite member consists of materials in contact each of which can surround a finite number of inclusions. To account for shear deformations, the concept of shear deformation coefficients is used. In this investigation the definition of these factors is accomplished using a strain energy approach. Seven boundary value problems are formulated and solved employing a pure BEM approach, that is only boundary discretization is used. The evaluation of the shear deformation coefficients is accomplished from stress functions using only boundary integration. Numerical results are presented to illustrate the method and demonstrate its efficiency and accuracy. The influence of the warping effect especially in composite members of open form cross section is analyzed through examples demonstrating the importance of the inclusion of the warping degrees of freedom in the analysis of a space frame. Moreover, the discrepancy of both the deflections and the internal forces of a member of a spatial structure arising from the ignorance of the shear deformation effect necessitates the inclusion of this additional effect, especially in thick walled cross section members.
beam composite warping shear deformation boundary element method stiffness matrix nonuniform torsion bar twist