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The purpose of this paper is to emphasise the analogies between variational and network formulations using geometrical forms, with the purpose of developing alternative but otherwise equivalent derivations of the finite element (FE) method.

FE equations for electromagnetic fields are examined, in particular nodal elements using scalar potential formulation and edge elements for vector potential formulation.

It is shown how the equations usually obtained via variational approach may be more conveniently derived using integral methods, employing a geometrical description of the interpolating functions of edge and facet elements. Moreover, the resultant equations describe the equivalent multi‐branch circuit models.

The approach proposed in the paper explores the analogy of the FE formulation to loop or nodal magnetic or electric networks and has been shown to be very beneficial in teaching, especially to students well familiar with circuit methods. The presented methods are also helpful when formulating classical network models. Finally, for the first time, the geometrical forms of edge and facet element functions have been demonstrated.

The purpose of this paper is to propose a new finite element method (FEM) solving strategy for efficient analysis of the challenging edge effect problem in plate structures. Its main ideas are to develop special-purpose plate element models to effectively simulate the behaviors in the plate’s edge zones near free/SS1 edges.

These new elements are developed based on the hybrid-Trefftz element method. During their construction procedures, the analytical solutions of the edge effect problem, which are in exponential forms, are used to enhance the interior displacement fields. Besides, the Lagrangian multipliers are introduced into the modified hybrid-Trefftz functional for considering the stress resultant constraints at free/SS1 edges. Thus, these elements theoretically possess the abilities to correctly capture the very steep gradients of the resultant distributions in the boundary layers.

These new specialized hybrid-Trefftz plate elements can very efficiently solve the edge effect problem with high accuracy, even when distorted meshes are used. Moreover, because these elements’ construction procedures contain only boundary integrals, the computation expense for accurately integrating the exponential trial functions can be considerably saved.

This work presents an alternative novel idea for using the FEM to more effectively handle the local stress problems by incorporating the use of the analytical trial functions.

The purpose of this paper is to enhance the feasibility of the edge-based smoothed triangular (EST) element, some modifications are made in this study.

First, an efficient strategy based on graph theory is proposed to construct the edge system. Second, the stress is smoothed in global coordinate system based on edge instead of strain, which makes the theory of EST more rigorous and can be easily extended to the situation of multi elements sharing the same edge. Third, the singular degree of freedoms (DOFs) of the nodes linked by edges are restrained in edge local coordinate system, which makes the global stiffness matrix non-singular and can be decomposed successfully.

First, an efficient edge constructing strategy can make EST element more standout. Second, some modifications should be made to EST element to extend it to the situation with multi elements sharing the same edge, so that EST element can deal with the geometrical models with this kind of features. Third, the way to restrain the singular DOFs of EST element must be different from normal isoparametric triangle element, because the stiffness matrix of the smoothing domain is not computed in local coordinate system.

The modified EST element performs stably in engineering analysis including large scale problems and the situation with multi elements sharing the same edge, and the efficiency of edge system constructing is no longer the bottleneck.

Introducing the concept of a design domain to truss topology optimization, this paper presents an algorithm generating geometrically admissible ground structures on possibly concave (or even disconnected) 3D design domains. That is a set of connections between nodal points actually respecting the geometry of the design domain. Since ground structures may be applied in other contexts the presentation does not assume any specifics of truss topology optimization. However, in the example section an application of ground structures in a truss topology optimization problem may be found.

The purpose of this paper is to set up a new framework to enable direct modifications of volume meshes enriched with semantic information associated to multiple partitions. An instance of filleting operator is prototyped under this framework and presented in the paper.

In this paper, a generic mesh modification operator has been designed and a new instance of this operator for filleting finite element (FE) sharp edges of tetrahedral multi-partitioned meshes is also pro-posed. The filleting operator works in two main steps. The outer skin of the tetrahedral mesh is first deformed to round user-specified sharp edges while satisfying constraints relative to the shape of the so-called Virtual Group Boundaries. Then, in the filleting area, the positions of the inner nodes are relaxed to improve the aspect ratio of the mesh elements.

The classical mainstream methodology for product behaviour optimization involves the repetition of four steps: CAD modelling, meshing of CAD models, enrichment of models with FE simulation semantics and FEA. This paper highlights how this methodology could be simplified by two steps: simulation model modification and FEA. The authors set up a new framework to enable direct modifications of volume meshes enriched with semantic information associated to multiple partitions and the corresponding fillet operator is devised.

The proposed framework shows only a paradigm of direct modifications of semantic enriched meshes. It could be further more improved by adding or changing the modules inside. The fillet operator does not take into account the exact radius imposed by user. With this proposed fillet operator the mesh element density may not be enough high to obtain wished smoothness.

This paper fulfils an identified industry need to speed up the product behaviour analysis process by directly modifying the simulation semantic enriched meshes.

A boundary element method in terms of the field variables is applied to three‐dimensional electromagnetic scattering problems. Especially, the influence of a dipole excited field on low conducting materials situated very close to the antenna will be discussed. We use higher order edge elements of quadilateral shape for the field approximation on curved surfaces. The tangential components of the unknown field variables are interpolated by vector element functions. The Galerkin method is implemented to obtain a set of linear equations. The applicability of the proposed edge element is investigated by the comparison of different BEM‐formulations and FEM‐results.

The aim of the present work is to find an efficient solution concerning the computational effort of quasi‐static electric field (QSEF) problems involving anisotropic conductivity and permittivity in the frequency domain.

Numerical simulations are carried out with tetrahedral nodal finite elements of first‐ and second‐order and with Withney elements. The solution of the boundary value problem with the aid of the electric scalar potential approximated by nodal finite elements is compared with those by the electric current vector potential represented by edge finite elements.

The simulation with an electric current vector potential approximated by the edge elements of first‐order prevail over that by the electric scalar potential approximated by nodal elements of second‐order concerning the memory requirements and the computation time at comparable accuracy.

The application of edge finite elements to solve QSEF problems considering an anisotropic complex conductivity in 3D.

A finite element formulation for the solution of 3D eddy current problems in terms of the electric intensity E is presented. A weak formulation, based on a Galerkin weighted residual procedure, is presented and edge elements, that impose only tangential continuity across element interfaces of the approximated field, are employed for the discretization of the problem with the finite element method. The reliability and validity of the suggested method is verified by its application to the calculation of the 3D eddy current distribution in two conducting systems.

Numerical simulation of the single point incremental forming (SPIF) processes can be very demanding and time consuming due to the constantly changing contact conditions between the tool and the sheet surface, as well as the nonlinear material behaviour combined with non-monotonic strain paths. The purpose of this paper is to propose an adaptive remeshing technique implemented in the in-house implicit finite element code LAGAMINE, to reduce the simulation time. This remeshing technique automatically refines only a portion of the sheet mesh in vicinity of the tool, therefore following the tool motion. As a result, refined meshes are avoided and consequently the total CPU time can be drastically reduced.

SPIF is a dieless manufacturing process in which a sheet is deformed by using a tool with a spherical tip. This dieless feature makes the process appropriate for rapid-prototyping and allows for an innovative possibility to reduce overall costs for small batches, since the process can be performed in a rapid and economic way without expensive tooling. As a consequence, research interest related to SPIF process has been growing over the last years.

In this work, the proposed automatic refinement technique is applied within a reduced enhanced solid-shell framework to further improve numerical efficiency. In this sense, the use of a hexahedral finite element allows the possibility to use general 3D constitutive laws. Additionally, a direct consideration of thickness variations, double-sided contact conditions and evaluation of all components of the stress field are available with solid-shell and not with shell elements. Additionally, validations by means of benchmarks are carried out, with comparisons against experimental results.

It is worth noting that no previous work has been carried out using remeshing strategies combined with hexahedral elements in order to improve the computational efficiency resorting to an implicit scheme, which makes this work innovative. Finally, it has been shown that it is possible to perform accurate and efficient finite element simulations of SPIF process, resorting to implicit analysis and continuum elements. This is definitively a step-forward on the state-of-art in this field.

The purpose of this paper is to demonstrate successful use of least-squares finite element method (LSFEM) with h-type mesh refinement and coarsening for the solution of two-dimensional, inviscid, compressible flows.

Unsteady Euler equations are discretized on meshes of linear and quadratic triangular and quadrilateral elements using LSFEM. Backward Euler scheme is used for time discretization. For the refinement of linear triangular elements, a modified version of the simple bisection algorithm is used. Mesh coarsening is performed with the edge collapsing technique. Pressure gradient-based error estimation is used for refinement and coarsening decision. The developed solver is tested with flow over a circular bump, flow over a ramp and flow through a scramjet inlet problems.

Pressure difference based error estimator, modified simple bisection method for mesh refinement and edge collapsing method for mesh coarsening are shown to work properly with the LSFEM formulation. With the proper use of mesh adaptation, time and effort necessary to prepare a good initial mesh reduces and mesh independency control of the final solution is automatically taken care of.

LSFEM is used for the first time for the solution of inviscid compressible flows with h-type mesh refinement and coarsening on triangular elements. It is shown that, when coupled with mesh adaptation, inherent viscous dissipation of LSFEM technique is no longer an issue for accurate shock capturing without unphysical oscillations.