- ISSN 0258-2724
- CN 51-1277/U
- EI Compendex
- Scopus
- Indexed by Core Journals of China, Chinese S&T Journal Citation Reports
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- Chinese Science Citation Database
| Citation: | WANG Lijuan, ZHAO Lei, JIANG Ning, QIAO Junting, LIU Shizhong, ZHANG Jiangong. Matrix Analysis of Variable Cross-Section Curved Beam Elements Based on Energy Method[J]. Journal of Southwest Jiaotong University. doi: 10.3969/j.issn.0258-2724.20240256
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To obtain the analytical solution formula of the stiffness matrix of a 2-node 6-degree-of-freedom explicit variable cross-section curved beam element, the variable cross-section curved beam element was incorporated into the widely used finite element system of rod structures. Based on Castigliano’s second theorem, the stiffness matrix of the spatial variable cross-section curved beam element was derived, and the flexibility matrix of the variable cross-section curved beam element was deduced by using the principle of stationary potential energy of elastic bodies; then, the cantilever end stiffness matrix of the variable cross-section curved beam element was obtained through inverse calculation. According to the static equilibrium condition and the principle of virtual work, the element stiffness matrix of the overall variable cross-section curved beam was obtained. In addition, the finite element formulation of the variable cross-section curved beam element could be degenerated into the formulation of uniform cross-section and uniform curvature beam elements and the standard formulation of uniform cross-section straight beam elements. A static calculation program for variable cross-section curved beam bridges was developed using MATLAB, and it was compared with the ANSYS solid finite element model to verify the static analysis theory of variable cross-section curved beams. The results indicate that the developed theory analyzes the bending-torsion coupling of the variable cross-section curved beam based on the finite element theory. The maximum deflection error between the variable cross-section curved beam theory and the ANSYS solid finite element model is 3.72%, and the maximum error compared with the ANSYS beam element model is less than 0.5%; furthermore, the maximum deflection error between the variable cross-section straight beam degenerated from the developed theory and the ANSYS solid finite element beam model is 1.72%, and the maximum error compared with the ANSYS beam element model is less than 0.1%.
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