Basis for isoparametric stress elements

Abstract The family of the so-called ‘isoparametric strain (displacement) elements’ is restricted to membranes and solids. The reason for this restriction has led to the development of a new family based on stress assumptions; these elements will be referred to as ‘isoparametric stress elements’. This family contains plates and solids but no membranes. The omission of a particular element in each family is consistent with the plate-membrane analogies. The basic flexibility matrix of an isoparametric stress element is singular since the zero stress state is directly included. The rank technique is adopted to automatically extract the zero stress modes such that the element can be completely interchangeable between any finite element system. The theory for stress assumed isoparametric “quadrilateral” plate bending elements with curved boundaries is given. A brief presentation of the theory for isoparametric stress solid elements is also included.