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      for both element types, integration in closed form is used to evaluate the contribution of normal and shear strains over the cross section of the element. A numerical integration method with one Gauss point is used for the proposed element to evaluate the contribution of strains in the axial direction.
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zchunhua3120: ½ð±Ò+5, ¡ï¡ï¡ïºÜÓаïÖú 2017-03-23 14:17:32
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3Â¥: Originally posted by Mr__Right at 2017-02-07 17:16:59
integration in closed form »ý·ÖµÄ½âÎöÐÎʽ£¬Ïà¶ÔÓ¦µÄÊǺóÃæ
numerical integration  »ý·ÖµÄÊýÖµÐÎʽ

In mathematics, a closed-form expression is a mathematical expression that can be evaluated in a finite number of operations. It may contain constants, variables, certain "well-known" operations (e.g., + − ¡Á ¡Â), and functions (e.g., nth root, exponent, logarithm, trigonometric functions, and inverse hyperbolic functions), but usually no limit. The set of operations and functions admitted in a closed-form expression may vary with author and context.


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Then, by the contour integration technique, the basic solution in space-time domain to the plane elastodynamic problem of the layered media and the second kind of singular integral equations for crack propagating in layered media are given in a closed form.
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