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The hybrid‐Trefftz finite element model and its application to plate bending
Author(s) -
Jirouseka J.,
Guex Lan
Publication year - 1986
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620230410
Subject(s) - finite element method , quadrilateral , subroutine , singularity , mixed finite element method , displacement (psychology) , mathematics , nonlinear system , a priori and a posteriori , extended finite element method , degree (music) , basis (linear algebra) , element (criminal law) , bending , bending of plates , mathematical analysis , geometry , computer science , structural engineering , engineering , physics , psychology , philosophy , epistemology , quantum mechanics , acoustics , law , political science , psychotherapist , operating system
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.