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3D steady heat conduction analysis considering heat source is conducted on the fundamental of the fast multipole method (FMM)-accelerated line integration boundary element method (LIBEM).

Due to considering the heat source, domain integral is generated in the traditional heat conduction boundary integral equation (BIE), which will counteract the well-known merit of the BEM, namely, boundary-only discretization. To avoid volume discretization, the enhanced BEM, the LIBEM with dimension reduction property is introduced to transfer the domain integral into line integrals. Besides, owing to the unsatisfactory performance of the LIBEM when it comes to large-scale structures requiring massive computation, the FMM-accelerated LIBEM (FM-LIBEM) is proposed to improve the computation efficiency further.

Assuming N and M are the numbers of nodes and integral lines, respectively, the FM-LIBEM can reduce the time complexity from O(NM) to about O(N+ M), and a full discussion and verification of the advantage are done based on numerical examples under heat conduction.

(1) The LIBEM is applied to 3D heat conduction analysis with heat source. (2) The domain integrals can be transformed into boundary integrals with straight line integrals by the LIM. (3) A FM-LIBEM is proposed and can reduce the time complexity from O(NM) to O(N+ M). (4) The FM-LIBEM with high computational efficiency is exerted to solve 3D heat conduction analysis with heat source in massive computation successfully.

The purpose of this paper is to present a novel eddy-current modeling technique of volumetric defects embedded in conducting plates. This problem is of great interest in electromagnetic non-destructive evaluation and has already been exhaustively studied.

The defect is modeled by a volumetric current dipole density which satisfies an integral equation. The latter is solved by the classical method of moments. The authors propose the use of globally defined, continuous basis functions for the expansion of the current dipole density.

The proposed global expansion provides an improvement of the numerical stability and the performance of the simulation, over classical approaches. The proposed method is tested against both measured and synthetic data obtained by a different defect model.

The new discretisation scheme – in contrast to the classical approaches – does not need the discretisation of the defect volume. This involves numerous advantages that are discussed in the paper.

The librarian and researcher have to be able to uncover specific articles in their areas of interest. This Bibliography is designed to help. Volume IV, like Volume III, contains features to help the reader to retrieve relevant literature from MCB University Press' considerable output. Each entry within has been indexed according to author(s) and the Fifth Edition of the SCIMP/SCAMP Thesaurus. The latter thus provides a full subject index to facilitate rapid retrieval. Each article or book is assigned its own unique number and this is used in both the subject and author index. This Volume indexes 29 journals indicating the depth, coverage and expansion of MCB's portfolio.

An efficient boundary element method (BEM) formulation for three‐dimensional elastoplasticity is presented in this paper. The BEM formulation for nonlinear problems requires discretization of the surface as well as part of the volume. In this paper nine‐noded quadrilateral elements are used for modelling the surface and 27‐noded brick elements for the volume. Particular attention is paid to the accurate evaluation of the Cauchy principal value volume integrals appearing in the interior stress calculations. An explicit initial strain formulation is used to satisfy the non‐linearity. The accuracy of the proposed method is demonstrated by solving a number of benchmark problems.

This paper aims to develop a multidomain boundary element method (BEM) for modeling 2D complex turbulent thermal flow using low Reynolds two‐equation turbulence models.

The integral boundary domain equations are discretised using mixed boundary elements and a multidomain method also known as a subdomain technique. The resulting system matrix is an overdetermined, sparse block banded and solved using a fast iterative linear least squares solver.

The simulation of a turbulent flow over a backward step is in excellent agreement with the finite volume method using the same turbulent model. A grid consisting of over 100,000 elements could be solved in the order of a few minutes using a 3.0 Ghz P4 and 1 GB memory indicating good efficiency.

The paper shows, for the first time, that the BEM is applicable to thermal flows using k‐ε.

The aim of this paper is to model time‐harmonic problems in unbounded domains with coils of complex geometry and ferromagnetic materials.

The approach takes the form of a coupling between two integrals methods: the magnetic moment method (MMM) and the partial element equivalent circuit (PEEC) method. The modeling of conductor system is achieved thanks to PEEC method while the MMM method is considered for the magnetic material.

The paper shows how to use the MMM/PEEC coupled method to model a problem comprising conductors and ferromagnetic materials and compare its results with the FEM and the FEM/PEEC coupling.

The two methods PEEC and MMM are well‐known. The innovation here is coupling these methods in order to take advantages from both methods. Moreover, the performances of this coupling are studied in comparison with others (FEM, FEM/PEEC coupling).

This paper presents a computationally efficient numerical solution scheme to solve transient heat conduction problems using the boundary element method (BEM) without volume discretization. Traditionally, a transient solution using BEM is very computer intensive due to the excessive numerical integration requirements at each time increment. In the present work a numerical solution scheme based on the separation of time and space integrals in the boundary integral equation through the use of an appropriate series expansion of the integrand (incomplete gamma function) is presented. The space integrals are evaluated only once in the beginning and within each time increment the additional integrals are obtained from the previously evaluated space integrals by a simple calculation. Three‐dimensional applications are provided to compare the proposed strategy with that used traditionally. The CPU requirements are reduced substantially. The solution scheme presented allows for dynamically changing the time step size as the solution evolves. This feature is not practical in the traditional schemes based on boundary discretization only.

Orientation determination is an essential planning task in additive manufacturing (AM) because it directly affects the part quality, build time, geometric tolerance, fabrication cost, etc. This paper aims to propose a negative feedback decision-making (NFDM) model to realize the personalized design of part orientation in AM process.

NFDM model is constructed by integrating two sub-models: proportional–integral–derivative (PID) negative feedback control model and technique for order preference by similarity to an ideal solution (TOPSIS) decision-making model. With NFDM model, a desired target is first specified by the user. Then, the TOPSIS decision model calculates the “score” for the current part orientation. TOPSIS decision model is modified for ease of control. Finally, the PID controller automatically rotates the part based on the error between the user-specified target and the calculated “score”. Part orientation adjustment is completed when the error is eliminated. Five factors are considered in NFDM model, namely, surface roughness, support structure volume, geometric tolerance, build time and fabrication cost.

The case studies of turbine fan and dragon head indicate that the TOPSIS model can be perfectly integrated with the PID controller. This work extends the proposed model to different AM processes and investigates the feasibility of combining different decision-making models with PID controller and the effects of including various evaluation criteria in the integrated model.

The proposed model innovatively takes the TOPSIS decision-making model and the PID control model as a whole. In this way, the uncontrollable TOPSIS model becomes controllable, so the proposed model can control the TOPSIS model to achieve the user-specified targets.

The purpose of this paper is to present a new special element model for thermal analysis of composites.

A hybrid finite element formulation taking the fundamental solution as kernel function is presented in this work for analyzing the thermal behavior and predicting the effective thermal conductivity of fiber‐reinforced composites. A representative volume cell containing single or multiple fibers (or inclusions) is considered to investigate the overall temperature distribution affected by the inclusions and the interactions among them, and to evaluate the effective thermal conductivity of the composites using the presented algorithm with special‐purpose inclusion elements. Numerical examples are presented to demonstrate the accuracy and applicability of the proposed method in analyzing fiber‐reinforced composites.

The independent intra‐element field and frame field, as well as the newly‐developed hybrid functional, make the algorithm versatile in terms of element construction, with the result that the related variational functional involves the element boundary integral only. All numerical results are compared with the solutions from ABAQUS and good agreement is observed for all cases, clearly demonstrating the potential applications of the proposed approach to large‐scale modeling of fiber‐reinforced composites. The usage of special inclusion element can significantly reduce model meshing effort and computing cost, and simultaneously avoid mesh regeneration when the fiber volume fraction is changed.

Due to the fact that the established special elements exactly satisfy the interaction of matrix and fiber within the element, only element boundary integrals are involved, thus the algorithm can significantly reduce modeling effort and computing cost with less elements, and simultaneously avoid mesh regeneration when the fiber volume fraction is changed.

Based on the special fundamental solution, a newly‐constructed inclusion element is applied to a number of test problems involving unit RVCs with multiple fibers to access the accuracy of the model. The effective thermal conductivity of the composites is evaluated for cases of single and multiple fibers using the average temperatures at certain points on a data‐collection surface. A new algorithm for evaluating effective properties with special elements is presented.

The development of an interactive software tool, EQNWRITE, to help in the setup and manipulation of engineering mass, momentum and energy equations, is discussed. This software is a building tool for building mathematical models of process systems. For a given problem, EQNWRITE enables the user to interactively derive and simplify the governing equations in the desired reference frame and coordinate system. At the user's request, specified mathematical transformations are performed automatically and resulting equations are displayed. EQNWRITE allows the user to better perceive the physical significance of each term in the symbolic mathematical equations, which describe the dominant properties of a system, as they are being derived and simplified, while leaving the detailed mathematical transformations to the computer. EQNWRITE was programmed in the symbol manipulation language, MUSIMP and developed using some of the capabilities of the microcomputer based computer algebra system, MUMATH. Major programming features and capabilities of MUSIMP and MUMATH are briefly reviewed, followed by a discussion of the specific automatic transformations implemented in EQNWRITE. Finally, engineering examples are given showing the use of the transformation functions and operators.