THREE-DIMENSIONAL BASIC FORMULATIONS OF ADDITIONAL INCOMPATIBLE DISPLACEMENT ON INTERNAL PARAMETERS

The additional incompatible displacement terms on internal parameters for plane elasticity problems were given in a previous publication¹². With reference to the general formulas in12, new incompatible displacement elements can be constructed directly, avoiding the previous tedious trial and error process. This paper aims to extend the previous work 12 to three-dimensional cases. Formulations of the additional incompatible displacement terms are established in terms of isoparametric coordinates and Cartesian coordinates, respectively. Taking H8 and H20 solid elements as examples, two new incompatible elements are developed. To illustrate the feasibility of the present approach, numerical examples are provided. It is shown that the two new elements produce convergent and highly accurate results.