A Deformation Decomposition Method of Arbitrary Triangular Elements Based on Mathematical and Mechanical Conditions

Compared with the complete components, the stress and deformation of the components with holes (especially irregular holes) are more complex, which brings difficulties to the relevant analysis and design. In order to meet the quantitative analysis requirements of the basic deformation performance of open-hole components in engineering, this paper proposes a deformation decomposition method suitable for planar and spatial arbitrary triangular elements based on POD theory. This method satisfies the orthogonality of mathematics and the balance of mechanics, and can decompose the comprehensive deformation of triangular elements into macroscopic basic deformations such as tension, compression and shear. The quantitative information of each basic deformation can be obtained by performing deformation decomposition on the open-hole components discretized by arbitrary triangular elements. According to the decomposition results, the deformation decomposition diagram and cloud diagram are drawn, which can realize the quantitative and visual analysis of the macroscopic basic deformation performance, and then provide theoretical support for the preliminary design of the open-hole components. Finally, this paper uses the deformation decomposition method and the finite element strain analysis method to carry out a comparative analysis of the simply supported beam and the four-sided consolidation plate with a hole, and the comparison results prove the correctness and effectiveness of the deformation decomposition method.