Quadrilateral Folded Plate Structure Elements of Reduced Trefftz Type Sulaiman Abo Diab Faculty of Civil Engineering, Tishreen University, Lattakia, Syria (Received April 30, 2003) General strategy for developing finite elements of general geometric shape explained on quadrilateral folded plate structure element ensuring invariance properties is presented in this paper. The basic idea of this strategy consists in using the natural coordinate system only for defining the element geometry and performing the element integration in a mapped biunit square. For defining the approximation functions a suitable local Cartesian coordinate system defined from the directions of the covariant base vectors and the perpendicular contravariant base vectors is used. The origin of the local coordinate system is located at the element centroid (centre of gravity). Hybrid and boundary finite elements of reduced Trefftz type for analysing the folded plate structures are also presented. The folded plate structure element is a combination of a plate bending element and a plane stress element. 1. INTRODUCTION The obstacles in formatting displacement and hybrid finite elements are reported in many publications [1-4]. Different suggestion has been made for selecting the element coordinate systems and constructing the approximation basis for various finite element types. For the hybrid quadrilateral Kirchhoff plate-bending element developed in [4], the element local coordinate system is selected in a skew (but not curvilinear) coordinate system located at the geometric center of the element and defined in the direction of the natural coordinate system. For the hybrid Trefftz elements developed in [3,5], the origin of the local coordinate system is located at the element centroid and the displacement functions are assumed in those coordinates but it seems that no attention is paid to the selection of their direction. The invariance properties are preserved through constructing the approximation basis in the local coordinates divided by an average distance between element centoid and element corners. In general, the most widely used strategy in formatting finite elements of general geometric form depends on an approximation basis selected directly in a natural coordinate system [6-10]. In this paper a general strategy for developing finite elements of general geometric shape explained on quadrilateral folded plate structure element ensuring invariance properties is presented. The basic idea of this strategy consists in using the natural coordinate system only for defining the element geometry and performing the element integration in a mapped biunit square. For defining the approximation functions a suitable local Cartesian coordinate system defined from the directions of the covariant base vectors and the perpendicular contravariant base vectors is used. The origin of the local coordinate system is located at the element centroid (centre of gravity). Such strategy enhances basically the application of complex formulations like the Trefftz method in the framework of the finite element method and enables preserving invariance properties as well as insensitivity to nodal point numbering for finite elements of general geometric shapes; see for example [11 - 14]. A slightly modified geometrical interpolation technique for constructing the finite element shape functions is also presented. The displacement approximation basis starts with approximation functions in parametric form involving a homogeneous part and a particular part. This modified technique leads to a constructed displacement basis with shape functions, which involve also in addition to the homogeneous part a particular part. The modified interpolation