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This paper presents a new hybrid element approach and applies it to plate bending. In contrast to more conventional models, the formulation is based on displacement fields which fulfil a priori the non‐homogeneous Lagrange equation (Trefftz method). The interelement continuity is enforced by using a stationary principle together with an independent interelement displacement. The final unknowns are the nodal displacements and the elements may be implemented without any difficulty in finite element libraries of standard finite element programs. The formulation only calls for integration along the element boundaries which enables arbitrary polygonal or even curve‐sided elements to be generated. Where relevant, known local solutions in the vicinity of a singularity or stress concentration may be used as an optional expansion basis to obtain, for example, particular singular corner elements, elements presenting circular holes, etc. Thus a high degree of accuracy may be achieved without a troublesome mesh refinement. Another important advantage of the formulation is the possibility of generating by a single element subroutine a large number of various elements (triangles, quadrilaterals, etc.), presenting an increasing degree of accuracy. The paper summarizes the results of numerical studies and shows the excellent accuracy and efficiency of the new elements. The conclusions present some ideas concerning the adaptive version of the new elements, extension to nonlinear problems and some other developments.
International Journal for Numerical Methods in Engineering – Wiley
Published: Apr 1, 1986
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