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Open AccessArticle

Unified Fundamental Formulas for Static Analysis of Pin-Jointed Bar Assemblies

by Pei Zhang 1,2,*, Huiting Xiong 3,* and Junsheng Chen 2
1
College of Civil and Transportation Engineering, Hohai University, Nanjing 210098, China
2
State Key Laboratory of Subtropical Building Science, South China University of Technology, Guangzhou 510640, China
3
JSTI Group, Nanjing 210019, China
*
Authors to whom correspondence should be addressed.
Symmetry 2020, 12(6), 994; https://doi.org/10.3390/sym12060994
Received: 9 March 2020 / Revised: 27 May 2020 / Accepted: 4 June 2020 / Published: 10 June 2020
The initial axial forces of members—whatever caused by prestress or external loads—may strongly change the mechanical properties of pin-jointed bar assemblies, to enhance, or even establish their structural stiffness. The structural responses under external disturbance cannot be calculated accurately if the influence of initial axial forces has not been considered appropriately. In this paper, an analytic theory considering the effect of initial internal forces is developed on the basis of linear elasticity hypothesis. The fundamental formulas proposed finally include generalized equilibrium equations and generalized compatibility equations, both of which have square coefficient matrices of full rank being transposed with each other. Generally, this method can be regarded as an extended version of a traditional force method considering the stiffening effect of initial internal forces. Compared with the matrix force method, it has a wider application scenario since few redundant simplifications are employed in the derivation of the formulas. In comparison with the displacement-based algorithm, the proposed method has the inherent advantages of the force method—the physical concepts of each item in equations are fairly explicit; and the combination coefficients of self-stress states and mechanisms are determined simultaneously in solving the structural responses. Thus, it is very helpful for us to essentially comprehend the principle that the pin-jointed bar assemblies resist the external loads. View Full-Text
Keywords: pin-jointed bar assemblies; static analysis; initial axial forces; matrix force method; displacement based method; moore–penrose generalized inverse pin-jointed bar assemblies; static analysis; initial axial forces; matrix force method; displacement based method; moore–penrose generalized inverse
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Zhang, P.; Xiong, H.; Chen, J. Unified Fundamental Formulas for Static Analysis of Pin-Jointed Bar Assemblies. Symmetry 2020, 12, 994.

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