Date of Award

Fall 1995

Document Type

Thesis

Degree Name

Master of Science (MS)

Department

Mechanical & Aerospace Engineering

Program/Concentration

Engineering Mechanics

Committee Director

Mohammad A. Aminpour

Committee Member

Chuh Mei

Committee Member

Norman F. Knight, Jr.

Call Number for Print

Special Collections; LD4331.E57 P316

Abstract

A three-node curved and twisted beam element is developed for linear analysis of structures modeled with curved and pre-twisted beams. A set of governing equations consisting of kinematic relations, constitutive relations, and equilibrium equations is derived. The beam element has three rotational and three displacement degrees of freedom at each node. The differential equations of kinematics are solved exactly for linearly varying longitudinal strains, constant transverse shear strains, linearly varying twist, and quadratically varying curvature changes to obtain the description of rotation and displacement modes. These rotation and displacement modes are then used as the basis functions for development of the finite element model. Constitutive relations for the beam are developed for general anisotropic materials and then specialized for isotropic materials. The results of the present element are compared with theoretical solutions available in the literature. Due to compatible assumptions for rotations and displacements and exact representation of rigid-body modes, the beam element is free from spurious modes and exhibits fast convergence to theoretical solutions.

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DOI

10.25777/1j2j-mh45

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