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Distortion Effects in Isoparametric Elements, an Analytic Approach

机译：等参元素中的失真效应，一种分析方法

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The effects of geometric distortion in isoparametric finite elements are investigated at the element formulation level, rather than the more usual level of numerical evaluation. This provides a more direct approach and avoids excessive testing or heuristic interpretation. The isoparametric finite element formulation is expressed in terms of parameters corresponding to polynomial orders of distortion. The response to polynomial strain fields is used to quantify the error in representing such fields. This error, together with that inherent in the numerical integration, is used to estimate stiffness and stress errors, according to the magnitudes and polynomial orders of the distortions and the strain fields. The effect of sampling at the optimal points, and its relation to reduced integration, is rationalized. The results can be used to give simple order-of-magnitude estimates of error. The procedure can also be implemented, in computer code, to give more detailed estimates for specific distortions and response requirements.

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