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The purpose of this paper is to examine quadratic convergence of finite element analysis for hyperelastic material at finite strains via Abaqus‐UMAT as well as classification of the rates of convergence for iterative solutions in regular cases.

Different formulations for stiffness – Hessian form of the free energy functionals – are systematically given for getting the rate‐independent analytical tangent and the numerical tangent as well as rate‐dependent tangents using the objective Jaumann rate of Kirchoff stress tensor as used in Abaqus. The convergence rates for available element types in Abaqus are computed and compared for simple but significant nonlinear elastic problems, such as using the 8‐node linear brick (B‐bar) element – also with hybrid pressure formulation and with incompatible modes – further the 20‐node quadratic brick element with corresponding modifications as well as the 6‐node linear triangular prism element and 4‐node linear tetrahedral element with modifications.

By using the Jaumann rate of Kirchoff stress tensor for both, rate dependent and rate independent problems, quadratic or nearly quadratic convergence is achieved for most of the used elements using Abaqus‐UMAT interface. But in case of using rate independent analytical tangent for rate independent problems, even convergence at all is not assured for all elements and the considered problems.

First time the convergence properties of 3D finite elements available in Abaqus sre systematically treated for elastic material at finite strain via Abaqus‐UMAT.

Gives introductory remarks about chapter 1 of this group of 31 papers, from ISEF 1999 Proceedings, in the methodologies for field analysis, in the electromagnetic community. Observes that computer package implementation theory contributes to clarification. Discusses the areas covered by some of the papers ‐ such as artificial intelligence using fuzzy logic. Includes applications such as permanent magnets and looks at eddy current problems. States the finite element method is currently the most popular method used for field computation. Closes by pointing out the amalgam of topics.

The purpose of this paper is to research the interaction between multiple bubbles and their noise radiation considering the influence of compressibility. The influences of bubble spacing, initial inner pressure, buoyance and phase difference are presented with different bubbles arrangements.

Based on wave equation, the new boundary integral equation considering the compressibility is given by the matching between prophase and anaphase approximation of bubble motion and solved with boundary element method. The time-domain characteristics of noise induced by multiple bubbles are obtained by the moving boundary Kirchhoff integral equation. With the surface discretization and coordinate transformation, the bubbles surface is treated as a moving deformable boundary and noise source, and the integral is implemented on the surface directly.

Numerical results show the manner of jet generation will be affected by the phase difference between bubbles. With the increasing of phase difference, the directive property of noise becomes obvious. With the enlargement of initial inner pressure, the sound pressure will arise at the early stage of expanding, and the increasing of buoyance parameter will reduce the sound pressure after the generation of jet. Since the consideration of compressibility, the oscillation amplitude of bubbles will be weakened.

The paper could provide the reference for the research about the dynamics and noise characteristics of multiple bubbles in compressible fluid. And the new method based on boundary integral equation to simulate the multiple bubbles motion and noise radiation is presented.

This paper aims to propose a new approach on the problem of circuit optimisation by using the generalised optimisation methodology presented earlier. This approach is focused on the application of the maximum principle of Pontryagin for searching the best structure of a control vector providing the minimum central processing unit (CPU) time.

The process of circuit optimisation is defined mathematically as a controllable dynamical system with a control vector that changes the internal structure of the equations of the optimisation procedure. In this case, a well-known maximum principle of Pontryagin is the best theoretical approach for finding of the optimum structure of control vector. A practical approach for the realisation of the maximum principle is based on the analysis of the behaviour of a Hamiltonian for various strategies of optimisation and provides the possibility to find the optimum points of switching for the control vector.

It is shown that in spite of the fact that the maximum principle is not a sufficient condition for obtaining the global minimum for the non-linear problem, the decision can be obtained in the form of local minima. These local minima provide rather a low value of the CPU time. Numerical results were obtained for both a two-dimensional case and an N-dimensional case.

The possibility of the use of the maximum principle of Pontryagin to a problem of circuit optimisation is analysed systematically for the first time. The important result is the theoretical justification of formerly discovered effect of acceleration of the process of circuit optimisation.

The purpose of this paper is to identify a new and simple two‐end algorithm for fault location identification and characterization, in electrical distribution systems.

The developed diagnostic algorithm is based on a simple model of the network using a lumped parameters representation.

Test results have proved the approach to be efficient, allowing a precise fault identification and location while not requiring synchronized measures from the two ends.

There is a need for measurement systems at all MV/LV substations.

Applicability with limited investments is not possible where metering systems are not so diffused, although smart grids and DG units require such infrastructures. Moreover, utilities are quite interested in such issues, since the new required quality standards put severe constraints on faults management and clearance.

The paper presents a new and easier diagnostic algorithm for faults diagnosis in distribution systems.

The purpose of this paper is to use α‐dense curves for solving Boolean equations, 0‐1 integer programming problems such as the shortest path problem or the knapsack problem.

The paper's aim is to present the applications in Boolean algebra and 0‐1 integer programming of a new method based on α‐dense curves first developed at the beginning of the 1980s by Yves Cherruault and Arthur Guillez. The α‐dense curves generalize the space filling curves (Peanocurves,…) and fractal curves. The main idea consists in expressing n variables by means of a single one.

Apply the method to Boolean algebra and 0‐1 integer programming.

The paper presents a new method based on α‐dense curves for solving Boolean equations and 0‐1 integer programming problems.

In this study, a modeling method for a clamped deformable cable simulation based on Kirchhoff theory is proposed. This methodology can be used to describe the physical deformation configuration of any constrained flexible cable in a computer-aided design/manufacturing system. The modeling method, solution algorithm, simulation and experimental results are presented to prove the feasibility of the proposed methodology. The paper aims to discuss these issues.

First, Kirchhoff equations for deformable cables are proposed based on the nonlinear mechanics of thin elastic rods, and the general solution of the equations described by the Euler angles is given in the arc coordinate system. The parametric form solution of the Kirchhoff equations, which is easy to use, is then obtained in a cylindrical coordinate form based on Saint Venant’s theory. Finally, mathematical expressions that reflect the clamped cable configuration are given, and the deformable process is simulated based on an open source geometry kernel and is then tested by a 3D laser scanning technology.

The method presented in this paper can be adapted to any boundary condition for constrained cables as long as the external force and torque are known. The experimental results indicate that both the model and algorithm are efficient and accurate.

A more comprehensive study must be executed for the physical simulation of more complicated constrained cables, such as the helical spring and asymmetric constraint. The influence of the material properties of the cable on the calculation efficiency must be considered in future analysis.

The semi-analytical algorithm of the cable simulation in cylindrical coordinates is a novel topic and is more accurate and efficient than the common numerical solution.

In this paper, a novel and unified method for geometry configuration simulation of flexible cable under certain boundary conditions is presented. This methodology can be used to realize cable assembly verification in any computer-aided design/manufacturing system. The modeling method, solution algorithm, geometry configuration simulation and experimental results are presented to prove the feasibility of this proposed methodology. The paper aims to discuss these issues.

Considering the gravity, bending and torsion, modeling of cable follows the Kirchhoff theory. For this purpose, Euler quaternions are used to describe its spatial geometry configuration by a carefully chosen set of coordinates. Then the cable is discretized by the FEM, and the equilibrium condition per element is computed. In this way, the global static behavior is independent of the discretization. The static evolution of the cable is obtained by numerical integration of the resulting Kirchhoff equations. Then the manner is demonstrated, in which this system of equations can be decoupled and efficiently solved. Geometry configuration simulation examples with different boundary conditions are presented. Finally, experiment validation are given to describe the effectiveness of the models and algorithms.

The method presented in this paper can be adapted to computer-aided assembly verification of flexible cable. The experimental results indicate that both of the model and algorithm are efficient and accurate.

The method should be extended to flexible cables with multiple branches and more complex constraints (holes, curved surfaces and clamps) and non-circular sections. Dynamic assembly process simulation based on the Kirchhoff theory must be considered in the future.

Unlike in previous approaches, the cable behavior was independent of the underlying discretization, and the finite element approach enables physically plausible cable assembly verification.

Different axiomatizations of network theory are considered. Kirchhoff networks are regarded with priority. Multipole and multiport networks are introduced as alternative variants. Additionally, Minty and Paynter networks, which are always dualizable are discussed briefly. The latter are special cases of Kirchhoff as well as of multiport networks. This paper seeks to discuss these issues.

The paper develops network theory inside of set theory, i.e. networks, multipoles, etc. are defined as objects of set theory. As such objects we use preferably ordered pairs, ordered triples, etc. The objects of network theory are then separated from the class of all these set theoretical objects by means of some defining conditions. These conditions are the axioms of our approaches to network theory.

It is shown that all presented variants of axiomatizations can be developed on the basis of a uniform representation for the time functions for voltages and currents. All these variants allow interdisciplinary applications of network theory and they can be generalized to multidimensional networks. An interesting byproduct is the relationship between multiport networks, networks in Belevitch normal form, Paynter networks, and bond graphs.

For applications it is essential that Kirchhoff and multipole networks are with respect to their modeling capability of equal value. But from the foundational point of view the multipole terminology has a number of crucial disadvantages compared with that based on Kirchhoff networks. This fact is important both for the conception of circuit simulation software packages and for the development of basic circuit theory curricula.

The purpose of this paper is to develop a hybrid‐Trefftz (HT) finite element model (FEM) for simulating heat conduction in nonlinear functionally graded materials (FGMs) which can effectively handle continuously varying properties within an element.

In the proposed model, a T‐complete set of homogeneous solutions is first derived and used to represent the intra‐element temperature fields. As a result, the graded properties of the FGMs are naturally reflected by using the newly developed Trefftz functions (T‐complete functions in some literature) to model the intra‐element fields. The derivation of the Trefftz functions is carried out by means of the well‐known Kirchhoff transformation in conjunction with various variable transformations.

The study shows that, in contrast to the conventional FEM, the HT‐FEM is an accurate numerical scheme for FGMs in terms of the number of unknowns and is insensitive to mesh distortion. The method also performs very well in terms of numerical accuracy and can converge to the analytical solution when the number of elements is increased.

The value of this paper is twofold: a T‐complete set of homogeneous solutions for nonlinear FMGs has been derived and used to represent the intra‐element temperature; and the corresponding variational functional and the associated algorithm has been constructed.