COMPLAS 2025

Thermal Stress in Finite Displacement and Axisymmetric Problem

  • Natsumeda, Chikako (Yokohama National University)
  • Matsui, Kazumi (Yokohama National University)
  • Yamada, Takahiro (Yokohama National University)

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This study investigates the stress generation mechanism in finite displacement, axisymmetric and thermal stress problem. Given a disk with linear temperature distribution through its thickness, it obviously bends due to thermal expansion. Considering this situation as finite displacement problem, tensile stress in radial direction occurs on the inside of the curvature, that is on the low temperature side. On the other hand, this stress cannot be evaluated in infinitesimal displacement problem, which outputs zero stress throughout the disk. The mechanism of stress in thermal stress problem is commonly explained by mechanical strain that compensates for thermal strain difference, as often discussed in context of thermal shock and layered materials. However, this mechanism can be evaluated in infinitesimal displacement problem. Therefore, this stress should be accounted by some other mechanisms. To identify the mechanism of this stress generation, simulations are performed starting with simple problems. There are two factors to complicate understanding this stress, “dimension of the problem (3D problem)” and “geometric nonlinearity”. New problems are defined with simplified conditions for each factor. In particular, “dimension of the problem” is addressed in two steps: first, 2D problem neglecting depth (circumferential) effects, and then 3D (axisymmetric) problem. “Geometric nonlinearity” is also addressed in two steps: from infinitesimal to finite displacement problem. By examining the problem at each step, it is clarified that the stress does not arise in the simplified steps, but only appears when both factors, 3D (axisymmetric) problem and finite displacement, are considered. Based on this analysis, it is further discovered that the stress is imposed to prevent the disk from curving freely. This constraint arises from reduced distance from the central axis and the geometric effect in the circumferential direction, which is exactly captured in finite displacement formulation that considers equilibrium for forces in deformed configuration.