The Application of a Finite Element-Based Large Increment Method for Nonlinear Structural Problems
Amjad Aref Principal Investigator
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We present a new approach based upon the flexibility method to solve nonlinear structural problems using a large increment method (LIM). The idea is built upon using a nonlinear material model without the need for linearization and a step-by-step approach. This is accomplished by separating the physical equations from the equilibrium and compatibility equations, and utilizing the theory of the generalized inverse of a matrix.<br/>The proposed work consists of four main research initiatives to address the areas of investigation. The first initiative involves formulating the LIM within a finite element framework. Although emphasis will be placed on structural framing elements, formulations for plate and shell elements will also be developed. With this in place, the method will then be extended to incorporate inelastic behavior. Both time-dependent and thermally-dependent constitutive models will be considered. The third initiative relates to the extension of LIM to large displacement and large deformation problems. Finally, the fourth research thrust concerns development of the method for parallel computation. We emphasize that the methodology proposed is inherently suitable for parallel computations.<br/><br/>Since this represents a new approach for solving structural problems, there are significant technical challenges that must be met to accomplish the research objectives. However, the potential contribution is significant. One immediate application of LIM in civil engineering would be for analysis of 3-D frame structures undergoing plastic hinge formation at extreme loads.