Abstract
In this paper, we present a simple, powerful, yet efficient and easily applicable technique based on the GDQ method for solving nonlinear problems. The proposed technique is implemented to some nonlinear engineering problems in structure analysis. The results reveal that the proposed technique is effective. Then, the proposed technique is used to explain the effects of the variation of cross section area on the nondimensional critical buckling loads for columns with and without elastic foundation for three sets of boundary conditions. Finally, the proposed technique is used to investigate the effect of the nonlinearity term of Winkler elastic foundation on the nondimensional critical buckling loads of nonuniform columns resting on elastic foundations. The effectiveness of the proposed technique is validated through comparing the present results with exact solutions and other numerical results available in references. The proposed method benefits the optimum design of columns against buckling in engineering applications. The most important conclusions from this paper can be summarized as follows. When the inertia ratio varies parabolically, the nondimensional critical buckling loads increase in comparison with varying linearly. Moreover, the nondimensional critical buckling loads increase in the presence of the elastic foundation.
Highlights
It is pivotal in structural analysis and its design to study the buckling behaviors and to determine the critical buckling loads for uniform and nonuniform structural members.Many types of structures and structural members for buckling analysis can be defined as a uniform and/or nonuniform with different end conditions widely used as columns in many engineering structure applications such as but not limited to columns, shells and plates, cranes, and other application fields
The third objective is to investigate the effect of the nonlinearity term of Winkler elastic foundation on the nondimensional critical buckling loads of nonuniform columns resting on elastic foundations (linear and nonlinear Winkler foundation and linear Pasternak foundation), under the three sets of boundary conditions. e validation of the proposed method has been approved by comparing our numerical results with the exact solutions and other available numerical results of uniform and nonuniform columns
A proposed approach of generalized differential quadrature (GDQ) method has been presented to study the buckling behaviors of nonuniform columns resting on the two-layer elastic foundations
Summary
It is pivotal in structural analysis and its design to study the buckling behaviors and to determine the critical buckling loads for uniform and nonuniform structural members.Many types of structures and structural members for buckling analysis can be defined as a uniform and/or nonuniform with different end conditions widely used as columns in many engineering structure applications such as but not limited to columns, shells and plates, cranes, and other application fields. It is pivotal in structural analysis and its design to study the buckling behaviors and to determine the critical buckling loads for uniform and nonuniform structural members. One of the very important branches of studied in the fields of structural, mechanical engineering, and aeronautical engineering is the buckling analysis of nonuniform columns. This field has become more and more systematic during the last decades. Several researchers have studied the buckling analysis of nonuniform columns that are closely related to the fields of structural, mechanical, and aeronautical engineering. A great deal of literature has been published on investigating the buckling of nonuniform columns. is is mainly due to the fact that it may provide an economical solution to carry the desired higher compressive loads in engineering structures
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