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A co‐rotational weak‐form quadrature planar beam element for geometric nonlinear static and dynamic analysis
Author(s) -
Yuan Zhangxian,
Wang Xinwei,
Kardomateas George A.
Publication year - 2019
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.6183
Subject(s) - tangent stiffness matrix , numerical integration , quadrature (astronomy) , mathematical analysis , stiffness matrix , mathematics , finite element method , rigid body , gaussian quadrature , nonlinear system , tanh sinh quadrature , geometry , classical mechanics , physics , nyström method , boundary value problem , optics , quantum mechanics , thermodynamics
Summary The co‐rotational formulation of quadrature planar beam element undergoing large displacement and large rotation is presented. A local frame co‐rotates with the differential element and decomposes the motion into a rigid body movement and a strain‐producing deformation. General explicit formulations of elemental vectors and matrices, including internal force vector, external force vector, tangent stiffness matrix, and mass matrix, are derived via the numerical integration together with the differential quadrature law. Thus, the element nodes and numerical integration method can be chosen arbitrarily based on the accuracy requirement and problem type. A number of case studies on the static, postbuckling, and dynamic response of beams and frame structures are conducted. The convergence study shows that the co‐rotational quadrature element has an exponential rate of convergence and the reduced Gauss integration yield the highest accuracy. It is seen that the proposed co‐rotational quadrature beam element is simple in formulations, computationally efficient, and capable of capturing the complex nonlinear behavior of beam and frame structures with high precision.