Numerical analysis of the stressed-deformed state of a tubular element under thermal loading
DOI:
https://doi.org/10.32347/2410-2547.2023.110.199-206Keywords:
semi-analytical finite element method, stress-strain state, plastic and thermoplastic deformation, tubular element, planar and spatial formulation, convergence of results, thermoforce loadingAbstract
In articles [2-5] solving relations and the block iteration method algorithm for solving linear and nonlinear equations by the semi-analytical finite element method for curvilinear heterogeneous prismatic bodies are implemented. In article [1], a numerical study of the convergence of the solution was performed, a wide range of test problems for bodies with smoothly and abruptly changing physical and geometric characteristics in elastic and elastic-plastic settings were considered. In [6], to confirm the reliability of the results obtained on the basis of the semi-analytical method of finite elements, the effectiveness of the application of this approach for the calculation of curvilinear inhomogeneous prismatic objects is shown. Solving control problems of the theory of elasticity, thermoelasticity, and thermoplasticity, as well as shape change problems, makes it possible to draw a conclusion about the reliability of the results of the research of a selected class of objects based on the developed methodology and implements its application program package.
In this paper, using the methodology outlined in the above works, the results of the numerical solution of the problem, which have an applied value, were presented. The stress-strain state of a tubular element with a rectangular cutout under conditions of thermoforce loading was studied. As a rule, solving similar problems is carried out in a flat setting without taking into account the bending load. This approach greatly simplifies the formulation of the problem, but leads to very significant errors in the results. At zero value of the bending load, a good agreement of the planar and spatial solutions is observed. The presence of a bending load leads to deviation of the curves from their initial position. The maximum discrepancy of the results is almost 50%.
The analysis of this structure from the standpoint of the spatial problem of thermoplasticity, which ensures taking into account the dependence of the physical and mechanical characteristics of the material on temperature and taking into account the bending load on the section of the cut, allowed us to reveal the real features of its deformation.
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