Incremental Finite Element Matrices

by Sundaramoorthy Rajasekaran, Asst. Prof. of Civ. Engrg.; PSG Coll. of Tech., Coimbatore, India,
David W. Murray, (M.ASCE), Prof. of Civ. Engrg.; Univ. of Alberta, Edmonton, AB, Canada,

Serial Information: Journal of the Structural Division, 1973, Vol. 99, Issue 12, Pg. 2423-2438

Document Type: Journal Paper


A common technique in geometrically nonlinear finite element analysis is to express the total potential in terms of Lagrangian displacement coordinates, differentiate the potential to obtain the equilibrium equations, and form the differentials of the equilibrium equations to obtain linear incremental equilibrium equations. The geometric nonlinearities in the strain-displacement equations give rise to incremental matrices in the preceding equations. The form of these matrices is not unique in the expression for the total potential. The paper presents expressions for incremental matrices that remain valid in the equilibrium equations and in the linear incremental equilibrium equations. The construction of such matrices is illustrated for truss elements, in-plane bending elements, membrane elements, and plate flexural elements. An examination of some of the recent literature indicates that some investigators have used inappropriate forms of these incremental matrices.

Subject Headings: Matrix (mathematics) | Finite element method | Equilibrium | Linear analysis | Geometrics | Nonlinear finite element analysis | Lagrangian functions | Nonlinear analysis

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