温度変化を伴う棒, 板の非線形挙動

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Structural members and machinery parts are often subjected to various kinds of heat treatment, such as welding, gas-cutting, quenching, etc. during the process of production. The heat treatment produces thermal stresses which may result in residual deformation and cracks in the members and parts. Similarly, those parts which are used at high temperature or steel structures at fires pose the problem on their critical strength.The thermal stress and deformation are produced by the change in the temperature distribution, and high temperature influences the mechanical properties of the material to a great extent. In order to investigate the mechanism of thermal stress and deformation, a thermal elastic-plastic analysis is required with consideration of the mechanical properites dependent upon temperature and the thermal history of the material. Furthermore, the deformation of a slender column or thin plate is usually large, so that the analysis should include nonlinearities in both geometrical and material relations.Concerning thermal stress analysis, the analytical solutions are limited especially when the problem involves the plastic strains, even though the fundamental relations have been established.To deal with general problems, the finite element method is a powerful tool. The authors have developed a basic theory for thermal elastic-plastic analysis based on the finite element method using the incremental procedure and have shown the usefulness of the method on problems of welding.In this paper, the theory is extended to the analysis of combined nonlinear problems considering the influence of temperature upon the properties of the material with the aid of the principle of virtual work. The basic equilibrium equations are obtained for a plate from which those for beams or columns are readily derived. In the equations, there are many additional terms appeared due to the nonlinearity of problem, such as load correction vector, equivalent nodal forces due to temperature changes, temperature stiffness matrix, initial stress stiffness matrix, initial deflection stiffness matrix, plastic stiffness matrix, etc. The functions of these matrices are clarified in examples of one dimensional members.
社団法人日本船舶海洋工学会の論文

温度変化を伴う棒, 板の非線形挙動

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