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Mathematical Problems in Engineering
Volume 2012, Article ID 974023, 23 pages
Research Article

Static and Vibrational Analysis of Partially Composite Beams Using the Weak-Form Quadrature Element Method

Department of Civil Engineering, Tsinghua University, Beijing 100084, China

Received 29 August 2011; Revised 7 November 2011; Accepted 21 November 2011

Academic Editor: Trung Nguyen Thoi

Copyright © 2012 Zhiqiang Shen and Hongzhi Zhong. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Deformation of partially composite beams under distributed loading and free vibrations of partially composite beams under various boundary conditions are examined in this paper. The weak-form quadrature element method, which is characterized by direct evaluation of the integrals involved in the variational description of a problem, is used. One quadrature element is normally sufficient for a partially composite beam regardless of the magnitude of the shear connection stiffness. The number of integration points in a quadrature element is adjustable in accordance with convergence requirement. Results are compared with those of various finite element formulations. It is shown that the weak form quadrature element solution for partially composite beams is free of slip locking, and high computational accuracy is achieved with smaller number of degrees of freedom. Besides, it is found that longitudinal inertia of motion cannot be simply neglected in assessment of dynamic behavior of partially composite beams.