The method of enhanced assumed strains (EAS) is a popular tool for avoiding locking phenomena, e.g., a remedy for shear locking in plane elasticity. We consider bending-dominated problems on thin bodies which can be treated as beams and prove that the degree of approximation of the EAS method is at least as good as that of a beam model. The hypercircle method is combined with arguments of nonco...

In a recent paper of Arnold et al. [D.N. Arnold, F. Brezzi, L.D. Marini, A family of discontinuous Galerkin finite elements for the Reissner–Mindlin plate, J. Sci. Comput. 22 (2005) 25–45], the ideas of discontinuous Galerkin methods were used to obtain and analyze two new families of locking free finite element methods for the approximation of the Reissner–Mindlin plate problem. By following t...

In a recent paper of Arnold, Brezzi, and Marini [4], the ideas of discontinuous Galerkin methods were used to obtain and analyze two new families of locking free finite element methods for the approximation of the Reissner–Mindlin plate problem. By following their basic approach, but making different choices of finite element spaces, we develop and analyze other families of locking free finite ...

We consider an elastic model for a curved rod with arbitrary threedimensional geometry, incorporating shear and membrane as well as bending and torsion effects. We define an approximation procedure based on a discretization by linear Timoshenko beam elements. Introducing an equivalent mixed problem, we establish optimal error estimates independent of the thickness, thereby proving that shear an...

We presented in Ko et al. (2016) an MITC4+ shell element that shows a much improved convergence behavior when compared to the widely used MITC4 (Dvorkin and Bathe, 1984) shell element. However, the element does still not show optimal convergence behavior when used in distorted meshes in the analysis of some shell problems. In the present paper, we establish a new MITC4+ shell element which show...

Displacement finite element models of various beam theories have been developed using traditional finite element interpolations (i.e., Hermite cubic or equi-spaced Lagrange functions). Various finite element models of beams differ from each other in the choice of the interpolation functions used for the transverse deflection w, total rotation φ and/or shear strain γxz, or in the integral form u...

BACKGROUND Comminuted fractures of the proximal humerus are generally treated with the locking plate system, and clinical results are satisfactory. However, unstable support of the medial column results in varus malunion and screw perforation. We designed a novel medial anatomical locking plate (MLP) to directly support the medial column. Theoretically, the combined application of locking plate...

In this paper, we propose two lower order nonconforming rectangular elements for the Reissner-Mindlin plate. The first one uses the conforming bilinear element to approximate both components of the rotation, and the modified nonconforming rotated Q1 element to approximate the displacement, whereas the second one uses the modified nonconforming rotated Q1 element to approximate both the rotation...

The finite element method (FEM) can be applied to practically analyze the tall buildings in which the shear walls are used to resist the lateral loads. Accordingly, a variety of displacement and strain-based as well as frame macro elements have been proposed for analysis of the tall buildings. With respect to application of the lower order plane stress elements, analytical problems may arise wi...