Hybrid‐Trefftz stress elements for plate bending

• Published in: International journal for numerical methods in engineering Vol. 121; no. 9; pp. 1946 - 1976
• Main Authors: Teixeira de Freitas, João António, Tiago, Carlos
• Format: Journal Article
• Language: English
• Published: Hoboken, USA John Wiley & Sons, Inc 15.05.2020; Wiley Subscription Services, Inc
• Subjects: Approximation; Bending; classification of finite element formulations; emulation of conform finite elements; Euler-Lagrange equation; Finite element method; hybrid‐Trefftz finite elements; Interpolation; Kirchhoff and Mindlin‐Reissner plate bending; Locking; Mathematical analysis; Mindlin plates; Quadrilaterals; singular stress fields
• ISSN: 0029-5981; 1097-0207
• DOI: 10.1002/nme.6294

Summary The hybrid‐Trefftz stress element is used to emulate conventional finite elements for analysis of Kirchhoff and Mindlin‐Reissner plate bending problems. The element is hybrid because it is based on the independent approximation of the stress‐resultant and boundary displacement fields. The Trefftz variant is consequent on the use of the formal solutions of the governing Lagrange equation to approximate the stress‐resultant field. In order to emulate conventional elements, nodal functions are used to approximate the displacements on the boundary of the element. Duality is used to set up the element solving system. The associated variational statements and conditions for existence and uniqueness of solutions are recovered. Triangular and quadrilateral elements are tested and characterized in terms of convergence, sensitivity to shear‐locking, and shape distortion. Their relative performance is assessed using assumed strain Mixed Interpolation of Tensorial Components (MITC) elements and recently proposed Trefftz‐based elements. This relative assessment is extended to a hypersingular problem to illustrate the effect of enriching the domain and boundary approximation bases.