Formalismo de Integral Funcional en Elastodinámica
Abstract
We present a functional integral formalism for elastodyamics which provides a convenient framework for meshless computational implementation. Equilibrium is recovered by setting velocities to zero and enforcing a no-evolution condition.
The computational implementation, which we term Functional Integral Method (FIM) combines a simple least squares second degree polynomial fitting with an approximation of the exact equations. The error which is order h2, depends on a
non dimensional parameter ζ. The strong formulation corresponds to the limit ζ = O. When the first eight neighbors are used to fit the polynomial on a regular nodal array bilinear finite element equations are recovered exactly for ζ = 0.5 .
However, the use of the optimal parameter (which in this case is ζ = 0.75) provides better accuracy. Other'nodal arrays are also discussed. Finally, the FIM is applied to stationary vibrations and transient problems.
The computational implementation, which we term Functional Integral Method (FIM) combines a simple least squares second degree polynomial fitting with an approximation of the exact equations. The error which is order h2, depends on a
non dimensional parameter ζ. The strong formulation corresponds to the limit ζ = O. When the first eight neighbors are used to fit the polynomial on a regular nodal array bilinear finite element equations are recovered exactly for ζ = 0.5 .
However, the use of the optimal parameter (which in this case is ζ = 0.75) provides better accuracy. Other'nodal arrays are also discussed. Finally, the FIM is applied to stationary vibrations and transient problems.
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ISSN 2591-3522