A new approach to reduce membrane and transverse shear locking for one-point quadrature shell elements: linear formulation

• Published in: International journal for numerical methods in engineering 2006-04, Vol.66 (2), p.214-249
• Main Authors: Cardoso, Rui P. R., Yoon, Jeong Whan, Valente, Robertt A. Fontes
• Format: Article
• Language: English
• Subjects: area coordinates; Computational techniques; Computer simulation; enhanced assumed strain; Exact sciences and technology; Finite element method; Fundamental areas of phenomenology (including applications); Locking; Mathematical analysis; Mathematical methods in physics; Mathematical models; Matrices; membrane locking; Physics; Quadratures; reduced integration; Shells; Solid mechanics; Static elasticity (thermoelasticity...); Structural and continuum mechanics; transverse shear locking
• ISSN: 0029-5981; 1097-0207
• DOI: 10.1002/nme.1548

In the last decade, one‐point quadrature shell elements attracted many academic and industrial researchers because of their computational performance, especially if applied for explicit finite element simulations. Nowadays, one‐point quadrature finite element technology is not only applied for explicit codes, but also for implicit finite element simulations, essentially because of their efficiency in speed and memory usage as well as accuracy. In this work, one‐point quadrature shell elements are combined with the enhanced assumed strain (EAS) method to develop a finite element formulation for shell analysis that is, simultaneously, computationally efficient and more accurate. The EAS method is formulated to alleviate locking pathologies existing in the stabilization matrices of one‐point quadrature shell elements. An enhanced membrane field is first constructed based on the quadrilateral area coordinate method, to improve element's accuracy under in‐plane loads. The finite element matrices were projected following the work of Wilson et al. (Numerical and Computer Methods in Structural Mechanics, Fenven ST et al. (eds). Academic Press: New York, 1973; 43–57) for the incompatible modes approach, but the present implementation led to more accurate results for distorted meshes because of the area coordinate method for quadrilateral interpolation. The EAS method is also used to include two more displacement vectors in the subspace basis of the mixed interpolation of tensorial components (MITC) formulation, thus increasing the dimension of the null space for the transverse shear strains. These two enhancing vectors are shown to be fundamental for the Morley skew plate example in particular, and in improving the element's transverse shear locking behaviour in general. Copyright © 2005 John Wiley & Sons, Ltd.