Elastostatic inverse formulation
2002
In this paper an inverse method for solving elastostatic problems with incomplete boundary conditions is presented. In general, inverse problems are ill-posed boundary value problems whose stability and uniqueness of solution and sensitivity-based formulations require additional constraints. In the development we use the Betti-reciprocal theorem to represent the boundary traction field in terms of the boundary and field displacements in an integral form. Initially, we assume the unknown boundary conditions and deformations required to solve the problem. In this way we equate the work done by the exact solution (unknown) to the work done by an assumed solution. Discretizing the resulting equations and using an iterative procedure each step in the solution process becomes the solution to a well-posed problem. Thus, with sufficient perturbations the correct boundary conditions are reconstructed.
Keywords:
- Mathematical optimization
- Mathematical analysis
- Free boundary problem
- Method of fundamental solutions
- Boundary knot method
- Mathematics
- Mixed boundary condition
- Boundary value problem
- Cauchy boundary condition
- Different types of boundary conditions in fluid dynamics
- Singular boundary method
- Neumann boundary condition
- Robin boundary condition
- Correction
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