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Symmetry Reduction of Structures for Large Rotations

The reduction of the number of unknowns while capturing the essential physical features in a nonlinear analysis of large spatial structures has long been a challenging task for researchers. We approach the problem of large displacement and large rotation analysis of space frame structures by means of group theory and substructuring technique. An accurate nonlinear analysis requires an element that accurately reflects the nonlinear behavior of the structure being modeled. Therefore details of the element formulations and updating procedure for large rotation will be given. The present formulation is capable of modeling a structure (with small to moderate axial force in its members) using one element per member, so that the number of degrees of freedom could be kept to minimum. The present methodology is based on the approach in a paper by Healey and Treacy. Axial deformation only was considered and matrix-iteration was used. We extend their idea to deal with the analysis of symmetry structures under going large displacement and large rotation in bending. Instead of matrix-iteration, we find that the basis vectors required to project the solution space into its symmetry subspace can be easily determined from the projection matrix. Excellent reduction can be obtained using the present method. The reduction efficiency depends on the symmetry of the structures. The higher the degree of symmetry the structure possesses, the greater the reduction will be.