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The formulation of finite elements with incompatible discontinuous modes is examined rigorously. Both weak and strong discontinuities are considered. Starting from a careful elaboration of the kinematics for both types of discontinuities a comprehensive finite element formulation is derived based on a three‐field variational statement. Similarities and differences are highlighted between the various formulations which ensue.

A particular feature that makes foresight powerful is its capability to learn from past trends to help guide decision‐making for future policy. However, in studying both past and future trends, network perspectives are often missing. Since networks are capable of revealing the structure that underpins relationships between stakeholders, key issues and actions in the past, they are powerful to help envisage the future. The purpose of this paper is to propose a methodological framework to incorporate network analysis in foresight.

The paper develops a generic framework to incorporate network analysis into foresight's five stages. Trends identified by respondents of the Big Picture Survey are used to demonstrate how we operationalize this framework.

A network perspective can enrich foresight analysis in that it helps reveal structural linkages between trends and thus can better identify emerging future issues, both of which are critical in foresight.

The inclusion of network analysis can shed light on the process of understanding complex data and assist in building a model based on links and relationships. Network analysis can reveal otherwise unobservable structural features of the data and can help boundary setting discussions in foresight.

Network concepts and measures could usefully enrich the interpretation of foresight data for further analysis, or plausible scenarios.

Network analysis offers a new way of looking at the foresight data by disentangling complicated issue webs. As shaping the future becomes more essential because of the complexity of science, technology and society interrelationships, the incorporation of network perspectives in foresight might be one of the ways to propel future studies.

This paper proposes to extend the combination of Extended Finite Element Method (XFEM) and Level Set Method (LSM) from structural mechanics to electromagnetics. Based on this approach, the actual stage of the research work, dedicated to the investigation, development, implementation and validation of a shape optimization methodology, particularly tailored for 2D electric structures is described.

The proposed numerical approach is based on the efficiency of the XFEM and the flexibility of the LSM, to handle moving material interfaces without remeshing the whole studied domain at each optimization step.

This approach eliminates the conventional use of discrete finite elements and provides efficient, stable, accurate and faster computation schemes in comparison with other methods.

This research is limited to shape optimization of two‐dimensional electric structures, however, the work can be extended to 3D ones too.

The implementation of the proposed numerical approach for the shape optimization of a planar resistor is hereby described.

The main value of the proposed approach is a powerful and robust numerical shape optimization algorithm that demonstrates outstanding suppleness of handling topological changes, fidelity of boundary representation and a high degree of automation in comparison with other methods.

The purpose of this paper is to propose a new elemental enrichment technique to improve the accuracy of the simulations of thermal problems containing weak discontinuities.

The enrichment is introduced in the elements cut by the materials interface by means of adding additional shape functions. The weak form of the problem is obtained using Galerkin approach and subsequently integrating the diffusion term by parts. To enforce the continuity of the fluxes in the “cut” elements, a contour integral must be added. These contour integrals named here the “inter-elemental heat fluxes” are usually neglected in the existing enrichment approaches. The proposed approach takes these fluxes into account.

It has been shown that the inter-elemental heat fluxes cannot be generally neglected and must be included. The corresponding method can be easily implemented in any existing finite element method (FEM) code, as the new degrees of freedom corresponding to the enrichment are local to the elements. This allows for their static condensation, thus not affecting the size and structure of the global system of governing equations. The resulting elements have exactly the same number of unknowns as the non-enriched finite element (FE).

It is the first work where the necessity of including inter-elemental heat fluxes has been demonstrated. Moreover, numerical tests solved have proven the importance of these findings. It has been shown that the proposed enrichment leads to an improved accuracy in comparison with the former approaches where inter-elemental heat fluxes were neglected.

Difference schemes for hyperbolic systems of conservation laws occasionally converge to an unphysical weak solution, i.e. a weak solution containing discontinuities for which the entropy condition is violated. These unphysical discontinuities, when they exist as solutions of the difference scheme, tend to exhibit a surprising stability under perturbations. We point out here that this can be explained by an energy inequality, which is valid for the discrete approximation but which is not valid as applied to the differential equation itself. In spite of this difficulty, many simple difference schemes are highly successful at converging to the physically correct weak solution. A mechanism for this is given; we show that for shocks of moderate strength, there are numerous quadratic forms in the dependent variables which can serve effectively as entropy functions, i.e. for which an inequality exists determining the physically correct weak solution. It is shown how the limits of the solutions of a difference scheme will often necessarily satisfy such an inequality; as they are generally weak solutions of the given system, they must thus be the correct weak solutions.

The purpose of this paper is to present a finite element model capable of describing both the diffuse damage mechanism which develops first during the loading of massive brittle structures and the failure process, essentially due to the propagation of a macro‐crack responsible for the softening behaviour of the structure. The theoretical developments for such a model are presented, considering an isotropic damage model for the continuum and a Coulomb‐type criterion for the localized part.

This is achieved by activating subsequently diffuse and localized damage mechanisms. Localized phenomena are taken into account by means of the introduction of a displacement discontinuity at the element level.

It was found that, with such an approach, the final crack direction is predicted quite well, in fact much better than the prediction made by the fracture mechanics type of models considering combination of only elastic response and softening.

The presented model has the potential to describe complex damage phenomena in a cyclic and/or non‐proportional loading program, such as crack closing and re‐opening, cohesive resistance deterioration due to tangential sliding, by using only a few parameters compared to the traditional models for cyclic loading.

The purpose of this study is to develop an elasto-plastic multi-material shell model by which finite element analysis of laser welded joints is carried out at the interface of the heat-affected zone and base material.

The multi-material shell model is implemented on the simple cantilever and double cantilever welded plates to examine the efficiency of the developed model.

By reducing the computational time approximately 20 times with the developed model, the results obtained in the form of von Mises stress and equivalent plastic strain are found in good agreement as compared with the reference solid model.

The accurate and fast prediction of the stresses and strains in the laser welded joints, and the developed multi-material model is helpful to simulate complex industrial welded structures.

The purpose of this paper is to analyse of structures made in rock mass with multiple intersecting discrete discontinuities such as joint, fault, shear plane.

In this study, a numerical method is proposed for analyzing multiple intersecting joints with varying dip angles, spacing and roughness in eXtended Finite Element Method platform. A procedure is also outlined to treat excavated enhanced (jointed) elements for analysing the effect of excavation sequences.

The proposed method is compared with the existing interface element methods (Phase-2 model) by considering the stress and displacement distributions of a multiple intersecting jointed rock sample under uniaxial loading conditions. A circular tunnel in rock mass having intersecting joints is also analyzed for the distribution of mobilised friction angle of joints and results are compared with a derived analytical solution.

Nucleation and propagation of cracks should be incorporated into the proposed framework in future studies.

The proposed method is a useful tool for rock mechanics and geotechnical engineering problems to analyse strength and deformability of jointed rock masses.

The paper enumerates concepts and detail implementation procedures of the proposed method in three-noded triangular elements. The intersection of joints is formulated in such a way that no additional (junction) enrichment is required in model. The method has been improved for inclusion of Dirichlet and Neumann boundary conditions to be applied in the enhanced part of a problem domain.

The purpose of this paper is to present the composite finite element method (CFEM), with Cⁿ(n≥0) continuity so it improves the accuracy of the finite element method (FEM) for solving second‐order partial differential equations (PDEs) and also, can be used for solving higher order PDEs.

In this method, the nodal values in the conventional FEM have been replaced by the appropriate nodal functions. Based on this idea, a procedure has been proposed for obtaining the CFEM−Cⁿ shape functions based on the CFEM−Cⁿ⁻¹ shape functions as follows: the nodal values in the CFEM−Cⁿ⁻¹ have been replaced by deliberately selected nodal functions so that the smoothness of the CFEM−Cⁿ⁻¹ shape functions increase.

The proposed method has the following properties: first, its shape functions have simple explicit forms with respect to the natural coordinates of elements and consequently, the required integrals for calculation of stiffness matrix can be evaluated numerically by low‐order Gauss quadratures; second, numerical investigations show that the CFEM with Cⁿ(n>1) continuity leads to more accurate results in comparison with the FEM; third, in multi‐dimensional problems, the curved boundaries are modeled more accurately by the proposed method in comparison with the FEM; fourth, this method can treat with the weak discontinuities such as the interface between different materials, as simple as the FEM does; and fifth, this method can successfully model Kirchhoff plate problems.

This method is an improvement of the moving particle FEM and reproducing kernel element method. Despite these two methods, CFEM shape functions have simple explicit forms with respect to the natural coordinates of elements.

Connection boundary conditions are studied with the finite element method using different types of mixed finite elements, i.e. nodal, edge and facet elements of different shapes and degrees, used in both b‐ and h‐conform formulations. The developed associated tools are first applied to periodicity boundary conditions before being applied to the treatment of the moving band in 2D and 3D. This step by step approach enables their validation before pointing out the effect of the considered elements on the accuracy of the moving band method. A special attention is given to the consistency of these boundary conditions with gauge conditions and source magnetic fields.