Adaptive, Small-Rotation-Based, Corotational Technique for Analysis of 2D Nonlinear Elastic Frames

Abstract EN

This paper presents an efficient and accurate numerical technique for analysis of two-dimensional frames accounted for both geometric nonlinearity and nonlinear elastic material behavior.

An adaptive remeshing scheme is utilized to optimally discretize a structure into a set of elements where the total displacement can be decomposed into the rigid body movement and one possessing small rotations.

This, therefore, allows the force-deformation relationship for the latter part to be established based on small-rotation-based kinematics.

Nonlinear elastic material model is integrated into such relation via the prescribed nonlinear moment-curvature relationship.

The global force-displacement relation for each element can be derived subsequently using corotational formulations.

A final system of nonlinear algebraic equations along with its associated gradient matrix for the whole structure is obtained by a standard assembly procedure and then solved numerically by Newton-Raphson algorithm.

A selected set of results is then reported to demonstrate and discuss the computational performance including the accuracy and convergence of the proposed technique.