Large Deflection Analysis of Thin Elastic Structures by the Assumed Stress Hybrid Finite Element Method.
MASSACHUSETTS INST OF TECH CAMBRIDGE AEROELASTIC AND STRUCTURES RESEARCH LAB
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Two models for analyzing the large deflection, linear elastic, static behavior of structures have been developed. They are the consistent and inconsistent assumed stress hybrid finite element models. The consistent model satisfies the entire stress equilibrium equation while the inconsistent model satisfies only the linear portion of this equation. These models are consistently derived from the Principle of Virtual Work for two separate coordinate frames a stationary system and a convected moving, updated system. Throughout the development correction terms are maintained in all the functionals to minimize the approximate solution drifting away from the true solution. These correction terms correspond to checks on the stress equilibrium and compatibility in the reference state. The former check is recast into a more convenient form, for these models, than is usually used. Using a tangent stiffness approach updated at every solution step various incremental and incremental-iterative solution procedures are used. When used the check conditions are represented as equivalent loads. Careful attention is given to properly define various coordinate systems and reference frames. In conjunction with this the various definitions of stress and strain are discussed. Energy and work terms consistent with each system is considered in detail. The proper statements of the Principle of Virtual Work are defined.