Solving Large-Deflection Problem of Spatial Beam with Circular Cross-Section Using an Optimization-Based Runge–Kutta Method
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Geng Li
Abstract
Based on the Bernoulli–Euler beam theory, the nonlinear governing differential equations (GDEs) for a spatially deflected beam with circular cross-section are formulated, which are then reduced to first-order differential equations to be compatible with Runge–Kutta method. With the boundary conditions of a spatial beam, the governing equations are treated as an initial value problem (IVP) of ordinary differential equations. A Runge–Kutta method combined with an unconstrained optimization algorithm (RKUO) is presented to solve the IVP. The approach for determining the orientation of the cross-section plane at any position on the deflected beam is also provided. Finally, the comparison between the RKUO results and those achieved using nonlinear finite element (NFE) analysis and spatial pseudo-rigid-body model validate the accuracy and effectiveness of RKUO. The results also demonstrated the unique capabilities of RKUO to solve large spatial deflection problems that are outside the range of nonlinear finite element model.
Funding statement: Funding: Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant/Award Number: No. 20120203110015), Fundamental Research Funds for the Central Universities (Grant/Award Number: No. K5051204021), Shaanxi Coordinating Project for Science and Technology (Grant/Award Number: No. 2014KTCQ01-27), National Natural Science Foundation of China (Grant/Award Number: No. 51175396).
Acknowledgment
The authors gratefully acknowledge the financial support from the National Natural Science Foundation of China under Grant No. 51175396, the Specialized Research Fund for the Doctoral Program of Higher Education of China under Grant No. 20120203110015, the Shaanxi Coordinating Project for Science and Technology under Grant No. 2014KTCQ01-27, and the Fundamental Research Funds for the Central Universities under No. K5051204021.
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Articles in the same Issue
- Frontmatter
- Fundamental Sources of Economic Complexity
- Healing of the Carbuncle Phenomenon for AUSMDV Scheme on Triangular Grids
- Periodic and Quasi-periodic Responses of Van der Pol–Mathieu System Subject to Various Excitations
- Application of Bat Algorithm to Optimize Scaling Factors of Fuzzy Logic-Based Power System Stabilizer for Multimachine Power System
- Investigation on Electrothermoelastic Behavior of FGPM Cylindrical Shells
- Solving Large-Deflection Problem of Spatial Beam with Circular Cross-Section Using an Optimization-Based Runge–Kutta Method
