tailieunhanh - Finite Element Analysis - Thermomechanics of Solids Part 16

Tham khảo tài liệu 'finite element analysis - thermomechanics of solids part 16', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 16 Introduction to Nonlinear FEA OVERVIEW The previous section addressed finite-element methods for linear problems. Applications that linear methods serve to analyze include structures under mild loads disks and rotors spinning at modest angular velocities and heated plates. However a large number of problems are nonlinear. Plasticity is a nonlinear materials theory suited for metals in metal forming vehicle crash and ballistics applications. In problems with high levels of heat input mechanical properties such as the elastic modulus and thermal properties such as the coefficient of specific heat can be strongly temperature-dependent. Rubber seals and gaskets commonly experience strains exceeding 50 . Soft biological tissues typically are modeled as rubberlike. Many problems involve variable contact for example meshing gear teeth. Heat conducted across electrical contacts can be strongly dependent on normal pressures. Fortunately much of the linear finite-element method can be adapted to nonlinear problems as explained in this chapter. The next chapter focuses on isothermal problems. The extension to thermomechanical problems will be presented in a subsequent chapter. TYPES OF NONLINEARITY There are three major types of nonlinearity in thermomechanical boundary-value problems material nonlinearity geometric nonlinearity and boundary-condition nonlinearity. Nonlinearities can also be present if the formulation is referred to deformed coordinates possibly introducing stress fluxes and converted coordinates. Material nonlinearity can occur through nonlinear dependence of the stress on the strain or temperature including temperature dependence of the tangent modulus tensor. Metals undergoing plastic flow exhibit nonlinear material behavior. Geometric nonlinearity occurs because of large deformation especially in problems referred to undeformed coordinates. Rubber components typically exhibit large deformation and require nonlinear kinematic descriptions. In

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