A State Space Solution Approach for Problems of Cylindrical Tubes and Circular Plates

Tseng, W.-D.; Tarn, Jiann-Quo

doi:10.1017/jmech.2015.33

Cited by 2 publications

(2 citation statements)

References 14 publications

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“…erefore, the complex boundary conditions can be decomposed into a plurality of simple stress situations. e problem can be solved by accumulating each simple stress situation result [14]. Any one complicated boundary function can be decomposed into a simple regular trigonometric function system by Fourier decomposition.…”

Section: Special Solution For Nonhomogeneous Boundary Conditionsmentioning

confidence: 99%

Comparative Study of Wellhole Surrounding Rock under Nonuniform Ground Stress

Jiang

Zhou

2019

Advances in Civil Engineering

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The stress analysis of the wellhole surrounding rock and the regular failure of the wellhole has always been a concern for the well builders. Firstly, the Hamilton canonical equations are obtained by using the Hamiltonian variational principle in the sector domain, and the zero eigensolution and nonzero eigensolutions of the homogeneous equation are solved. According to the Hamiltonian operator matrix with the orthogonal eigenfunction system, the special solution form of the nonhomogeneous boundary condition equation is obtained. Then, according to the principle of the same coefficient being equal, the relationship equation between the direction eigenvalue and the angle coefficient is obtained, from which the specific expression of the special solution of the equation can be determined. Furthermore, the analytical solution of the wellhole surrounding rock problem under nonuniform ground stress is obtained by using the linear elastic accumulative principle. Finally, a concrete example is given to compare the finite element method and the symplectic algorithm. The results are consistent, which ensures the accuracy and the reliability of the symplectic algorithm. The relationship between the circumferential stress distribution around the hole and the lateral pressure coefficient is further analyzed.

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Section: Special Solution For Nonhomogeneous Boundary Conditionsmentioning

confidence: 99%

Comparative Study of Wellhole Surrounding Rock under Nonuniform Ground Stress

Jiang

Zhou

2019

Advances in Civil Engineering

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“…Horton et al [49] derived the solution for the radial stiffness of the rubber bush mounting. Tseng and Tarn [50] using the Hamiltonian state space approach derived the solution for the transversely isotropic circular cylindrical tubes and plates under axisymmetric torque. Chekurin and Postolaki [51] derived the solution for the cylinder with stress-free flat ends using the variational principle.…”

Section: Introductionmentioning

confidence: 99%

Analysis of axisymmetric hollow cylinder under surface loading using variational principle

Sirsat,

Padhee

2024

Mathematics and Mechanics of Solids

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In this work, a variational principle–based approach has been adopted to analyze one of the classical linear elasticity problem of the axisymmetric cylinder under surface loading. The use of variational principle results in a set of governing partial differential equations with associated boundary conditions. The equations have been solved using the separation of variable approach and the Frobenius method. A general solution has been derived and used to solve two test cases. The proposed solution is capable of meeting all the boundary conditions. The solution has been validated by comparing it with a finite element–based numerical solution and considering a special limiting condition of a solid cylinder, for which results are available in the literature. Further various studies have been carried out to understand the robustness and limitation of the presented solution.

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A State Space Solution Approach for Problems of Cylindrical Tubes and Circular Plates

Cited by 2 publications

References 14 publications

Comparative Study of Wellhole Surrounding Rock under Nonuniform Ground Stress

Comparative Study of Wellhole Surrounding Rock under Nonuniform Ground Stress

Analysis of axisymmetric hollow cylinder under surface loading using variational principle

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