Dynamic Finite Element Analysis of Cracked Bodies

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Abstract
Application of the finite element method to problems involving finite cracked bodies subjected to impact loadings is discussed. Mass matrices for a particularly simple, well-established singular element have been developed and applied to the problem of a centrally cracked strip whose ends are loaded by a step tensile stress. The results agree extremely well with those obtained by using a higher order singular element. Results are also presented for this problem employing an equally coarse finite element mesh with no singular element at all, and again good agreement is demonstrated. The problems of an edge cracked strip suddenly pulled at its ends and of a cracked cylinder subjected to sudden internal pressure are also analyzed using these two approaches. The response of these examples, like the majority of cracked finite bodies, are dominated by their vibrational modes. Results indicate that for the purpose of determining the maximum amplification of the stress intensity factor due to dynamic loading, the use of a singular element is unnecessary.

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