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Problems with numerical integration of discontinuous functions

Hi everybody,

 I am a beginner in doing research :-) and my topic is about "Micro Indentation Analysis using Continuum Dislocation Theory". I am applying high-order finite element method for this nonlinear problem.

 My plan is first writing a subroutine for the element. However, when I intend to compute the internal force  by using Gauss Integration, I see a problem with the integrand function of some components of the internal force vector. This integrand is discontious function. It is therefore, I cannot get a good approximation with the standard Gauss integration.

 Does anybody have idea on how to deal with this problem? I attached two images: one of the integrand function before and one of the integrand function after using standard Gauss integration in order to clarify my question. Thank you very much.

Best Regards,


Image icon 3InternalFNoGauss.png30.39 KB
Image icon 3InternalFGauss.png42.55 KB
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