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An alternative stabilization approach has been developed for the 9‐node Lagrange plane and plate elements. In this approach, a stabilization stiffness is formulated using functions associated with the spurious zero‐energy modes. Efficiency has been increased by employing the same uniformly‐reduced integration scheme on the stabilization and underintegrated stiffness matrices. The results obtained using this rank‐sufficient element, termed the γ‐ψ element, appear to surpass those obtained with other rank‐sufficient 9‐node elements in accuracy.

A hexahedral 8‐node element based on the Hellinger—Reissner principle is formulated with the γ projection operator so that it can achieve engineering accuracy for plate and beam problems with a single layer of elements. It passes the patch test and is less sensitive to mesh shape since the local coordinates are used to describe the stress fields. The resulting element stiffness is simple and only 3×3 submatrix inversions are needed. Numerical results show that the new element is both accurate and efficient.

The numerical quadrature of the stiffness matrices and force vectors is a major factor in the accuracy and efficiency of the finite element methods. Even in the analysis of linear problems, the use of too many quadrature points results in a phenomenon called locking whereas the use of insufficient quadrature points results in a phenomenon called spurious singular mode. Therefore, efficient numerical quadrature schemes for structural dynamics are developed. It is expected that these improved finite elements can be used more reliably in many structural applications. The proposed developed quadrature schemes for the continuum and shell elements are straightforward and are modularized so that many existing finite element computer codes can be easily modified to accommodate the proposed capabilities. This should prove of great benefit to many computer codes which are currently used in structural engineering applications.

An enhanced L₂ projection method for recovering accurate derivatives such as moments, or shears, from finite element solutions for C° plates is presented. In the enhanced global and local projections, the square of the residuals in the equilibrium equations is included. Results are compared with those of standard global and local projection methods. Numerical examples show that in the global projection, the enhanced technique improves the accuracy of projected solution significantly. In the local projection, the enhanced projection technique circumvents the numerical ill‐conditioning which occurs in some meshes, and usually recovers derivatives with better accuracy. These techniques are effective for both thin and thick plate problems, and can provide more reliable error estimates for mesh adaptivity.

The total Lagrangian formulation and implementation of the element‐free Galerkin method (EFG) is presented for the analysis of contact‐impact problems with large deformations and for the simulation of metal forming processes. An integration scheme based on stress points is used, so no mesh is needed. A simple but general contact searching algorithm is used to treat the contact interface and an algorithm for the contact force is presented. Numerical results for Taylor bar impact are compared to finite element solutions and agree well. Solutions to upsetting, extrusion of metals with large material distortions are given to show the effectiveness of the algorithm. In particular, EFG is shown to be more capable of treating motions of the workpiece around corners of the punch than finite element methods.

The purpose of this paper is to discuss the linear solution of equality constrained problems by using the Frontal solution method without explicit assembling.

Re-written frontal solution method with a priori pivot and front sequence. OpenMP parallelization, nearly linear (in elimination and substitution) up to 40 threads. Constraints enforced at the local assembling stage.

When compared with both standard sparse solvers and classical frontal implementations, memory requirements and code size are significantly reduced.

Large, non-linear problems with constraints typically make use of the Newton method with Lagrange multipliers. In the context of the solution of problems with large number of constraints, the matrix transformation methods (MTM) are often more cost-effective. The paper presents a complete solution, with topological ordering, for this problem.

A complete software package in Fortran 2003 is described. Examples of clique-based problems are shown with large systems solved in core.

More realistic non-linear problems can be solved with this Frontal code at the core of the Newton method.

Use of topological ordering of constraints. A-priori pivot and front sequences. No need for symbolic assembling. Constraints treated at the core of the Frontal solver. Use of OpenMP in the main Frontal loop, now quantified. Availability of Software.

The rostrum of a paddlefish provides hydrodynamic stability during feeding process in addition to detect the food using receptors that are randomly distributed in the rostrum. The exterior tissue of the rostrum covers the cartilage that surrounds the bones forming interlocking star shaped bones.

The aim of this work is to assess the mechanical behavior of four finite element models varying the type of formulation as follows: linear-reduced integration, linear-full integration, quadratic-reduced integration and quadratic-full integration. The paper also presents the load transfer mechanisms of the bone structure of the rostrum. The base material used in the study was steel with elastic–plastic behavior as a homogeneous material before applying materials properties that represents the behavior of bones, cartilages and tissues.

Conclusions are based on comparison among the four models. There is no significant difference between integration orders for similar type of elements. Quadratic-reduced integration formulation resulted in lower structural stiffness compared with linear formulation as seen by higher displacements and stresses than using linearly formulated elements. It is concluded that second-order elements with reduced integration are the alternative to analyze biological structures as they can better adapt to the complex natural contours and can model accurately stress concentrations and distributions without over stiffening their general response.

The use of advanced computational mechanics techniques to analyze the complex geometry and components of the paddlefish rostrum provides a viable avenue to gain fundamental understanding of the proper finite element formulation needed to successfully obtain the system behavior and hot spot locations.

A generalized time finite element method is considered for time integration of non‐linear equations of motion arising from dynamic problems. A simple three‐time level family of schemes is obtained. Evaluation of the schemes shows that the proposed approach may lead to unconditionally stable algorithms for non‐linear problems. Numerical examples show the accuracy and efficiency of the proposed algorithm in comparison to Newmark's average acceleration method and four order accurate explicit algorithm.