A higher‐order equilibrium finite element method

Summary In this paper, a mixed spectral element formulation is presented for planar, linear elasticity. The degrees of freedom for the stress are integrated traction components, ie, surface force components. As a result, the tractions between elements are continuous. The formulation is based on mini...

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Bibliographic Details
Published in:International journal for numerical methods in engineering Vol. 114; no. 12; pp. 1262 - 1290
Main Authors: Olesen, K., Gervang, B., Reddy, J. N., Gerritsma, M.
Format: Journal Article
Language:English
Published: Bognor Regis Wiley Subscription Services, Inc 22.06.2018
Subjects:
curvilinear coordinates
Elasticity
Energy conservation
Equilibrium
Finite element method
interelement continuity of the tractions
Lagrange multiplier
mixed finite element formulation
pointwise equilibrium of forces
stress singularity
ISSN:0029-5981, 1097-0207
Online Access:Get full text
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Summary:Summary In this paper, a mixed spectral element formulation is presented for planar, linear elasticity. The degrees of freedom for the stress are integrated traction components, ie, surface force components. As a result, the tractions between elements are continuous. The formulation is based on minimization of the complementary energy subject to the constraints that the stress field should satisfy equilibrium of forces and moments. The Lagrange multiplier, which enforces equilibrium of forces, is the displacement field and the Lagrange multiplier, which enforces equilibrium of moments, is the rotation. The formulation satisfies equilibrium of forces pointwise if the body forces are piecewise polynomial. Equilibrium of moments is weakly satisfied. Results of the method are given on orthogonal and curvilinear domains, and an example with a point singularity is given.
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ISSN:0029-5981
1097-0207
DOI:10.1002/nme.5785