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| Moving least squares meshless method for static bending of reinforced folded shells |
| Received:August 28, 2023 Revised:September 27, 2023 |
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| DOI：10.7511/jslx20230828001 |
| KeyWord:3D continuous shell theory moving-least square approximation stiffened shell folded shell static bending |
| Author | Institution |
| 陈卫 |
南华大学 土木工程学院, 衡阳 |
| 彭林欣 |
广西大学 土木建筑工程学院, 南宁 ;广西大学 广西防灾减灾与工程安全重点实验室 工程防灾与结构安全教育部重点实验室, 南宁 |
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| Abstract: |
| A folded plate structure in a deployable structure system has been widely used in practical structural engineering due to its high stiffness to weight ratio and easy splicing.Compared to folded plates,folded shells have the characteristics of variable geometric shapes and beautiful appearance.In addition,the reinforcement bars in reinforced plate and shell structures can be calculated using methods based on the Euler-Bernoulli beam(EBT) and Timoshenko beam theoretical(TBT) frameworks.However,when the span-depth ratio of the reinforcement reaches a certain limit,the EBT and TBT no longer meet the engineering accuracy requirements.This article proposes a moving least-squares meshless method for solving the static bending problem of reinforced folded shells by treating the ribs as elongated or curved plates based on 3D continuous shell theory.Firstly,based on the 3D continuous shell theory,the two-dimensional meshless node information on the following coordinate system is mapped into the 3D shell using a mapping technique.The moving least-squares approximation is used to fit the surface geometry and displacement field.Based on the principle of minimum potential energy,the meshless discrete equation for static bending of the shell is derived;Secondly,the discrete equation is modified using the complete transformation method.Then,the modified Stiffness matrix and load array of each shell are converted to the overall coordinate system.Finally,the discrete equation of the entire reinforced folded shell structure is obtained by using the substructure method.At the end of the article,the convergence and accuracy of the method in calculating the static bending of reinforced folded shells were verified by comparing the calculation results of this paper with the ABAQUS finite element solutions of four numerical examples:a folded plate and a folded shell,a reinforced plate,and a reinforced shell. |
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