The Nonlinear Thermo-Hyperelastic Analysis of Functionally Graded Incompressible Hollow Sphere with Temperature Dependent Material Using Finite Element Method
محورهای موضوعی : Mechanics of Solids
Ali Zargaripoor
1
(دانشگاه خواجه نصیرالدین طوسی)
Mohammad Shariyat
2
(KNT University of tehran)
کلید واژه: Hyperelastic, Functionally graded material, Temperature dependent material, ,
چکیده مقاله :
In this paper, a nonlinear finite element formulation is presented for analysis of the stress, displacement, and temperature distributions of thermo hyperelastic hollow spheres subjected to mechanical and thermal forces. It is assumed that the hollow sphere is made of functionally graded and temperature-dependent material. The coupled nonlinear equations are derived from the concept of multiplicative decomposition of the deformation gradient. Mechanical and thermal parts are considered for studying the thermo-hyperelastic behavior.An appropriate strain energy function is considered and by exchange the invariants of strain tensors in the modified model, the governing equations are extended to an incompressible model. The governing equations are found by considering Mooney-Rivlin hyperelastic model. Distribution of displacement, stress components, and temperature through the thickness of the hollow sphere are plotted for different constitutive, temperature dependency, and inhomogeneity parameters. The obtained results indicate that the temperature dependency of the material and inhomogeneity properties have a considerable influence on displacement, stress components, and temperature distribution along the radial direction.
In this paper, a nonlinear finite element formulation is presented for analysis of the stress, displacement, and temperature distributions of thermo hyperelastic hollow spheres subjected to mechanical and thermal forces. It is assumed that the hollow sphere is made of functionally graded and temperature-dependent material. The coupled nonlinear equations are derived from the concept of multiplicative decomposition of the deformation gradient. Mechanical and thermal parts are considered for studying the thermo-hyperelastic behavior.An appropriate strain energy function is considered and by exchange the invariants of strain tensors in the modified model, the governing equations are extended to an incompressible model. The governing equations are found by considering Mooney-Rivlin hyperelastic model. Distribution of displacement, stress components, and temperature through the thickness of the hollow sphere are plotted for different constitutive, temperature dependency, and inhomogeneity parameters. The obtained results indicate that the temperature dependency of the material and inhomogeneity properties have a considerable influence on displacement, stress components, and temperature distribution along the radial direction.
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