Torsion problem: stress statement and solution by the boundary element method
Journal: Structural Mechanics of Engineering Constructions and Buildings (Vol.19, No. 4)Publication Date: 2023-11-27
Authors : Vladimir Lalin; Daniil Semenov;
Page : 339-348
Keywords : Elastic Rod Torsion; Poisson’s equation; Integral Representation of Stresses; Boundary Integral Equation; Integral Equation of the second kind;
- Torsion problem: stress statement and solution by the boundary element method
- GENERATING FINITE-ELEMENT MODEL OF THE SHAFT AND SETTLEMENT BOUNDARY VALUE PROBLEM OF STRESS-STRAIN STATE
- Solution of the axisymmetric problem of thermoelasticity of a radially inhomogeneous cylindrical shell by numerical-analytical method and the finite element method
- B-spline wavelet discrete-continual finite element method for the local solution to the two-dimensional problem of the theory of elasticity
- Temperature Profile on the Boundary of Solution Domain for a Potential Problem Using BEM
Abstract
The formulation of the problem of torsion regarding stresses and its solution by the boundary elements method are described. The main advantage of the problem formulation in stresses is direct determination of stresses in the cross-section, unlike the classical formulation, when the result of the approximate solution is the Prandtl stress function values, and the determination of stresses is brought down to numerical differentiation. The boundary integral equation of the second kind is obtained to formulate the problem with respect to stresses. The procedure for solving the problem by the boundary elements method is described, the system of solving equations is compiled. Solutions of test problems on torsion of rods with rectangular and channel cross-sections are presented. Comparison of the calculation results with known analytical solutions illustrates the reliability and permissible engineering accuracy of the obtained solutions.
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