27,002 research outputs found
Modal interaction in postbuckled plates. Theory
Plates can have more than one buckled solution for a fixed set of boundary conditions. The theory for the identification and the computation of multiple solutions in buckled plates is examined. The theory predicts modal interaction (which is also called change in buckle pattern or secondary buckling) in experiments on certain plates with multiple theoretical solutions. A set of coordinate functions is defined for Galerkin's method so that the von Karman plate equations are reduced to a coupled set of cubic equations in generalized coordinates that are uncoupled in the linear terms. An iterative procedure for solving modal interaction problems is suggested based on this cubic form
Lam\'e Parameter Estimation from Static Displacement Field Measurements in the Framework of Nonlinear Inverse Problems
We consider a problem of quantitative static elastography, the estimation of
the Lam\'e parameters from internal displacement field data. This problem is
formulated as a nonlinear operator equation. To solve this equation, we
investigate the Landweber iteration both analytically and numerically. The main
result of this paper is the verification of a nonlinearity condition in an
infinite dimensional Hilbert space context. This condition guarantees
convergence of iterative regularization methods. Furthermore, numerical
examples for recovery of the Lam\'e parameters from displacement data
simulating a static elastography experiment are presented.Comment: 29 page
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