Admissible matrix formulation - From orthogonal approach to explicit hybrid stabilization

Admissible matrix formulation is a patch test approach for efficient construction of multi-field finite element models. In hybrid stress and strain elements, the formulation employs the patch test to identify the constraints on, respectively, the flexibility and stiffness matrices which are most detrimental to the element efficiency. Admissible changes are introduced to the matrices so as to reduce the computational cost while the element accuracy remains virtually intact. In this paper, a comprehensive review of admissible matrix formulation is presented. Finite element techniques seminal to the formulation are also discussed.postprin

A six-node pentagonal assumed natural strain solid-shell element

In this paper, a six-node pentagonal solid-shell element is formulated. Particular attention is focused on alleviating shear, trapezoidal and thickness lockings that plagues the conventional element. While assumed natural strain method is employed to alleviate shear and trapezoidal lockings, a modified generalized laminate stiffness matrix is proposed to circumvent thickness locking. Unlike the commonly adopted plane stress assumption, the modified laminate stiffness matrix enables the element to reproduce the exact thickness stress and transverse displacement when the element is loaded by thickness stress. Numerical examples reveal that the element is close in accuracy with other state-of-the-art three-node degenerated shell elements. © 2001 Elsevier Science B.V.postprin

Transition finite element families for adaptive analysis of axisymmetric elasticity problems

In this paper, four transition element families that comprise five- to seven-node quadrilateral elements are developed based on the hybrid-stress and enhanced assumed strain (EAS) formulations for adaptive analyses of axisymmetric elasticity problems. For members in the first hybrid-stress family, a quasi-linear stress field with ten equilibrating stress modes is derived and employed. To study the effect of including more stress modes in the assumed stress field, another family with two additional stress modes is implemented. On the other hand, two EAS element families are constructed with respect to the incompatible displacement modes of two existing incompatible displacement transition element families. Several numerical examples are exercised. It can be seen that the first hybrid-stress family is the most accurate one among the proposed families. Moreover, the EAS families are close to the respective incompatible families in accuracy yet the former families are not only more efficient in computation but also more concise in formulation. © 2010 Elsevier B.V. All rights reserved.postprin

A simple assumed strain method for enhancing the accuracy of the cubic triangular C degree plate bending element

The conventional cubic triangular Mindlin/Reissner plate bending element, DISP10, is in general too stiff. To reduce the element stiffness, three of the strain sampling points are shifted from the integration stations to the element corners so as to reduce the number of shear constraints in the global level. The strain field is then obtained by interpolation. In this way, the constraint ratio of the element increases from 1.125 to 1.5 which is exactly equal to a postulated optimal value. However, the element does not appear to be more accurate than its conventional counterpart. While keeping the constraint ratio and interpolation pivots unchanged, two different ways of refining the sampled strains at the element corners are attempted and the pertinent elements are consistently more accurate than DISP10postprin

Hybrid-trefftz six-node triangular finite element models for helmholtz problem

In this paper, six-node hybrid-Trefftz triangular finite element models which can readily be incorporated into the standard finite element program framework in the form of additional element subroutines are devised via a hybrid variational principle for Helmholtz problem. In these elements, domain and boundary variables are independently assumed. The former is truncated from the Trefftz solution sets and the latter is obtained by the standard polynomial-based nodal interpolation. The equality of the two variables are enforced along the element boundary. Both the plane-wave solutions and Bessel solutions are employed to construct the domain variable. For full rankness of the element matrix, a minimal of six domain modes are required. By using local coordinates and directions, rank sufficient and invariant elements with six plane-wave modes, six Bessel solution modes and seven Bessel solution modes are devised. Numerical studies indicate that the hybrid-Trefftz elements are typically 50% less erroneous than their continuous Galerkin element counterpart.published_or_final_versionSpringer Open Choice, 01 Dec 201

An efficient rotation-free triangle for drape/cloth simulations - Part I: model improvement, dynamic simulation and adaptive remeshing

This series of two papers aim to improve the rotation-free (RF) triangle model previously developed by the authors and apply it for drape/cloth simulations. To avoid a previously un-observed drawback, the membrane strain obtained from the three-node displacement interpolation is replaced by the one obtained from the six-node interpolation. Dynamic simulations are made possible by explicit time integration. Instead of using dense structural meshes, the quality of draped patterns is improved by global adaptive remeshing. The works in this paper provide important and necessary techniques for practical applications of the RF triangle in the drape simulation. In part II, other techniques including collision handling and garment construction are further discussed and some practical applications of garments on still and moving human body model would be presented.postprin

On the relative merits of three-point integration rules for six-node triangles

There exist two three-point integration rules for triangular elements. Both rules are precise up to the second order and used for evaluating the six-node triangles. While one of rules has its sampling stations inside the triangle, that of the other coincide with the edge nodes. Though the former is commonly employed, it will be seen in this short paper that latter is indeed more favourable in view of element accuracy. © 1997 Elsevier Science B.V.postprin

Hybrid finite element models for piezoelectric materials

In this paper, hybrid variational principles are employed for piezoelectric finite element formulation. Starting from eight-node hexahedral elements with displacement and electric potential as the nodal d.o.f.s, hybrid models with assumed stress and electric displacement are devised. The assumed stress and electric displacement are chosen to be contravariant with the minimal 18 and seven modes respectively. The pertinent coefficients can be condensed at the element level and do not enter the system equation. A number of benchmark tests are exercised. The predicted results indicate that the assumed stress and electric displacements are effective in improving the element accuracy. © 1999 Academic Press.postprin

A twelve-node hybrid stress brick element for beam/column analysis

In this paper, a hybrid stress 12-node brick element is presented. Its assumed stress field is derived by first examining the deformation modes of a geometrically regular element and then generalizing to other element configurations using tensorial transformation. The total number of stress modes is 30 which is minimal for securing the element rank. To reduce the computational cost associated with the fully populated flexibility matrix, the admissible matrix formation is employed to induce high sparsity in the matrix. Popular beam bending benchmark problems are examined. The proposed elements deliver encouraging accuracy.postprin

Simple finite element formulation for computing stress singularities at bimaterial interfaces

By using the weak form of the governing equations for sectorial bimaterial domains and assuming that the displacement field is proportional to the (λ+1)th power of the distance from the singular stress point, a second-order characteristic matrix equation on λ is derived by a one-dimensional finite element formulation that only discretizes the domain circumferentially. Numerical examples covering a variety of interfacial singularities are presented to demonstrate the efficacy of the formulation. Accurate solutions are yielded by very few elements whereas convergence can be attained by either h- or p-refinement. The related procedures are programmed in a short MAPLE worksheet given in the appendix.postprin