Process of estimating relationship between element distortion and analysis error

A computer-readable storage encoded with a computer program, wherein the program, when executed by a processor, causes the processor to perform a process for estimating an analysis error expected to occur during deformation analysis of an object by a finite element method, with regard to an element which is used for approximately representing a shape of the object, from geometric distortion of an original shape of the element, the process comprising:

• assuming at least one deformation mode occurring in the element upon deformation of the object, in the form of at least one of tension, bending, shear, and torsion;
• and
• estimating, with the processor, the analysis error as a function of a degree of the geometric distortion of the original shape of the element, prior to the deformation analysis by the finite element method, for each of the at least one assumed deformation mode,
• wherein the element is formed as a plane-like element having a plane thereof, and
• wherein the estimating comprises a first calculation of:
• (a) coordinate-transforming the plane-like element into an isoparametric element by expressing skew and trapezoid of the plane-like element with a plurality of basic distortion parameters which are defined so as to deal with the skew and the trapezoid independently of each other, wherein the skew and the trapezoid are the geometric distortion of the plane-like element;
• (b) decomposing the deformation mode of the plane-like element into a plurality of basic deformation modes including tension, shear, and bending, by dealing with the plane-like element as the isoparametric element;
• (c) calculating strain energy of the plane-like element by formulating normal strains and shear strain of the plane-like element, with the plurality of basic distortion parameters and the plurality of basic deformation modes, by dealing with the plane-like element as the isoparametric element;
• and
• (d) calculating the analysis error associated with a value of each of the plurality of basic distortion parameters, for each of the plurality of basic deformation modes, based on the calculated strain energy of the plane-like element.