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<p>A new formulation is proposed for linearized elastic solids, which can be used for the analysis of boundary value problems. This formulation is based on considering both the displacement field and the stress tensor as main variables for the problem, solving in parallel the equation of motion and the constitutive equation (expressing the linearized strain as a function of the stresses) to find such unknown variables. Some boundary value problems are solved using separation of variables for the fully dynamic case for isotropic bodies. The application of the above method is briefly considered for anisotropic bodies, and also for a relatively new class of constitutive equation, wherein the linearized strain is a nonlinear function of the stress.</p>

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Some New Methods of Solving Boundary Value Problems in Linearized Elasticity and for a Class of Nonlinear Elastic Body

  • 期刊论文

  • 发表日期：

    2026年1月27日

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  • R. Bustamante,
  • O. Orellana

摘要

A new formulation is proposed for linearized elastic solids, which can be used for the analysis of boundary value problems. This formulation is based on considering both the displacement field and the stress tensor as main variables for the problem, solving in parallel the equation of motion and the constitutive equation (expressing the linearized strain as a function of the stresses) to find such unknown variables. Some boundary value problems are solved using separation of variables for the fully dynamic case for isotropic bodies. The application of the above method is briefly considered for anisotropic bodies, and also for a relatively new class of constitutive equation, wherein the linearized strain is a nonlinear function of the stress.