1988•TRANSACTIONS OF THE JAPAN SOCIETY OF MECHANICAL ENGINEERS Series AOpen access

A study on the accuracy of J-integral calculation by finite element method.

Kikuo KISHIMOTO, Noriyasu TAKEUCHI, Shigeru Aoki, Masaru SAKATA

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Abstract

The accuracy of the finite element calculation of the J^^-integral, which represents the dynamic energy release rate for propagating cracks, is studied. The main error is found to be caused by the calculation of the singular area integral. In order to reduce the error, a new method for evaluating the singular area integral. In order to reduce the error, a new method for evaluating the singular area integral is developed. In this method, the integrand in the singular area integral is developed. In this method, the integrand in the singular area integral is approximated by a certain function which is transformable into a line integral. The line integral is then evaluated analytically. The usefulness of the present method is demonstrated by an elastodynamic example.

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The accuracy of the finite element calculation of the J^^-integral, which represents the dynamic energy release rate for propagating cracks, is studied. The main error is found to be caused by the calculation of the singular area integral. In order to reduce the error, a new method for evaluating the singular area integral. In order to reduce the error, a new method for evaluating the singular area integral is developed. In this method, the integrand in the singular area integral is developed. In this method, the integrand in the singular area integral is approximated by a certain function which is transformable into a line integral. The line integral is then evaluated analytically. The usefulness of the present method is demonstrated by an elastodynamic example.

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Available abstract

The accuracy of the finite element calculation of the J^^-integral, which represents the dynamic energy release rate for propagating cracks, is studied. The main error is found to be caused by the calculation of the singular area integral. In order to reduce the error, a new method for evaluating the singular area integral. In order to reduce the error, a new method for evaluating the singular area integral is developed. In this method, the integrand in the singular area integral is developed. In this method, the integrand in the singular area integral is approximated by a certain function which is transformable into a line integral. The line integral is then evaluated analytically. The usefulness of the present method is demonstrated by an elastodynamic example.

Key concepts: Line integral, Singular integral, Mathematics, Mathematical analysis, Integral equation, Function (biology), Line (geometry), Finite element method

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