Abstract
By constructing the compressive bar element and developing the stiffness matrix, most issues about the compressive bar can be solved. In this paper, based on second derivative to the equilibrium differential governing equations, the displacement shape functions are got. And then the finite element formula of compressive bar element is developed by using the potential energy principle and analytical shape function. Based on the total potential energy variation principle, the static and geometrical stiffness matrices are proposed, in which the large deformation of compressive bar is considered. To verify the accurate and validity of the analytical trial function element proposed in this paper, a number of the numerical examples are presented. Comparisons show that the proposed element has high calculation efficiency and rapid speed of convergence.
Highlights
Compressive bar element analysis is essential in structural engineering design
Results show that the present method has many advantages including accuracy, efficiency, and simplicity compared to the direct stiffness method and the interpolation shape function element
The comparison shows that there is no need to divide the bar into multiple elements but only one element to get the accurate buckling load for the proposed finite element method, and only three iterations are needed to get this exact solution, which means that the iterative convergence speed is fast and the efficiency is high
Summary
Compressive bar element analysis is essential in structural engineering design. It can be used to calculate the static and stability problem. Direct stiffness method can accurately solve differential equation of static but has low efficiency affected by the number of meshes [5]. For elements which seem to be ideal from a numerical and a theoretical perspective, it may fail in the large deformation range, due to the high compression states and many interesting methods [23,24,25,26,27,28] have been developed to solve the problem. In the present paper, using the differential equations of equilibrium, and considering the effect of large deformation, the displacement shape function is derived. Results show that the present method has many advantages including accuracy, efficiency, and simplicity compared to the direct stiffness method and the interpolation shape function element
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