Consideration of Stress Stiffening and Material Reorientation in Modal Space Based Finite Element Solutions

Structural deformations are an important aspect of many engineering tasks. They are typically resolved as “off-line” finite element computations with accuracy set as the primary objective. Though high computational efficiency is always an important aspect, in certain applications its priority is of equal or similar importance as the accuracy itself. This paper tackles the problem of proper extension of linear models with the objective of keeping high numerical efficiency and covering moderate geometric nonlinearities. Modal-space based approach is addressed as one of the standard techniques for robust model reduction. Two extensions are proposed to account for moderate geometric nonlinearities in modal-space based solutions, one accounting for stress stiffening effect and the other for moderate material rigid-body rotations during deformation. Examples are provided to demonstrate the applicability and discuss the aspects of proposed techniques.