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The purpose of this paper is to present a two-dimensional (2D) model of the base force element method (BFEM) based on the complementary energy principle. The study proposes a model of the BFEM for arbitrary mesh problems.

The BFEM uses the base forces given by Gao (2003) as fundamental variables to describe the stress state of an elastic system. An explicit expression of element compliance matrix is derived using the concept of base forces. The detailed formulations of governing equations for the BFEM are given using the Lagrange multiplier method. The explicit displacement expression of nodes is given. To verify the 2D model, a program on the BFEM using MATLAB language is made and a number of examples on arbitrary polygonal meshes and aberrant meshes are provided to illustrate the BFEM.

A good agreement is obtained between the numerical and theoretical results. Based on the studies, it is found that the 2D formulation of BFEM with complementary energy principle provides reliable predictions for arbitrary mesh problems.

Due to the use of Lagrange multiplier method, there are more basic unknowns in the control equation. The proposed method will be improved in the future.

This paper presents a new idea and a new numerical method, and to explore new ways to solve the problem of arbitrary meshes.

The paper presents a 2D model of the BFEM using the complementary energy principle for arbitrary mesh problems.

Based on the base force element method, a two-dimensional random circle aggregate model with Monte Carlo principle is proposed to carry out research on softening curve in meso-level.

The meso-level structure of recycled concrete is considered as the five-phase materials composed of aggregate, old interfacial transition zone, old mortar, new interfacial transition zone and new mortar. A multi-polyline damage model is adopted to describe the nonlinear mechanical behavior of recycled concrete material. The destruction state of the element is determined by the first strength theory. The research studies on damage process of recycled concrete under the loading conditions of uniaxial tension were established using the base force element method.

The softening curves of recycled concrete are obtained, which are in good agreement with experiment results. Simulation results show that the macroscopic mechanical properties and failure mechanism can analyze more reasonably from mesoscopic structure. Besides that, it can be investigated from the numerical results of the size effect in recycled concrete through the mesoscopic heterogeneity. Furthermore, the form of aggregate distribution has influence on the crack path but little effect on the tensile strength of recycled concrete.

The results show that the base force element method has been successfully applied to the study of softening curve of recycled concrete under uniaxial tension.

This paper aims to propose the five-phase sphere equivalent model of recycled concrete, which can be used to deduce the theoretical formulas for the Poisson’s ratio and effective elastic modulus.

At a mesoscopic level, the equivalent model converts the interfacial layer, which consists of the new interfacial transition zone (ITZ), the old mortar and the old (ITZ), into a uniform equivalent medium. This paper deduces a strength expression for the interfacial transition zone at the microscopic level using the equivalent model and elastic theory. In addition, a new finite element method called the base force element method was used in this research.

Through numerical simulation, it was found that the mechanical property results from the five-phase sphere equivalent model were in good agreement with those of the random aggregate model. Furthermore, the proposed model agree on quite well with the available experimental data.

The equivalent model can eliminate the influence of the interfacial layer on the macroscopic mechanical properties, thereby improving the calculation accuracy and computational efficiency. The proposed model can also provide a suitable model for multi-scale calculations.

Based on the random aggregate model of recycled aggregate concrete (RAC), this paper aims to focus on the effect of loading rate on the failure pattern and the macroscopic mechanical properties.

RAC is regarded as a five-phase inhomogeneous composite material at the mesoscopic level. The number and position of the aggregates are modeled by the Walraven formula and Monte–Carlo stochastic method, respectively. The RAC specimen is divided by the finite-element mesh to establish the dynamic base force element model. In this model, the element mechanical parameters of each material phase satisfy Weibull distribution. To simulate and analyze the dynamic mechanical behavior of RAC under axial tension, flexural tension and shear tension, the dynamic tensile modes of the double-notched specimens, the simply supported beam and the L specimens are modeled, respectively. In addition, the different concrete samples are numerically investigated under different loading rates.

The failure strength and failure pattern of RAC have strong rate-dependent characteristics because of the inhomogeneity and the inertial effect of the material.

The dynamic base force element method has been successfully applied to the study of recycled concrete.

The purpose of this paper is to give a review on the newest developments of high-performance finite element methods (FEMs), and exhibit the recent contributions achieved by the authors’ group, especially showing some breakthroughs against inherent difficulties existing in the traditional FEM for a long time.

Three kinds of new FEMs are emphasized and introduced, including the hybrid stress-function element method, the hybrid displacement-function element method for Mindlin–Reissner plate and the improved unsymmetric FEM. The distinguished feature of these three methods is that they all apply the fundamental analytical solutions of elasticity expressed in different coordinates as their trial functions.

The new FEMs show advantages from both analytical and numerical approaches. All the models exhibit outstanding capacity for resisting various severe mesh distortions, and even perform well when other models cannot work. Some difficulties in the history of FEM are also broken through, such as the limitations defined by MacNeal’s theorem and the edge-effect problems of Mindlin–Reissner plate.

These contributions possess high value for solving the difficulties in engineering computations, and promote the progress of FEM.

To achieve a full understanding of the role of marketing from plan to profit requires a knowledge of the basic building blocks. This textbook introduces the key concepts in the art or science of marketing to practising managers. Understanding your customers and consumers, the 4 Ps (Product, Place, Price and Promotion) provides the basic tools for effective marketing. Deploying your resources and informing your managerial decision making is dealt with in Unit VII introducing marketing intelligence, competition, budgeting and organisational issues. The logical conclusion of this effort is achieving sales and the particular techniques involved are explored in the final section.

Discusses the 27 papers in ISEF 1999 Proceedings on the subject of electromagnetisms. States the groups of papers cover such subjects within the discipline as: induction machines; reluctance motors; PM motors; transformers and reactors; and special problems and applications. Debates all of these in great detail and itemizes each with greater in‐depth discussion of the various technical applications and areas. Concludes that the recommendations made should be adhered to.

The efficiency of the finite element analysis via force method depends on the overall flexibility matrix of the structure, while this matrix is directly affected from null bases vectors. As the null bases for an indeterminate structure are not unique, for an optimal analysis, the selected null bases should be sparse and banded corresponding to sparse, banded and well-conditioned flexibility matrix. This paper aims to present an efficient method for the formation of optimal flexibility matrix of finite element models comprising tetrahedron elements via mathematical optimization technique.

For this purpose, a linear mixed integer programming model is presented for finding sparse solution of underdetermined linear system, which is correspond to sparse null vector. The charged system search algorithm is improved and used to find the best generator for formation of null bases.

The efficiency of the present method is illustrated through some examples. The proposed method leads to highly sparse, banded and accurate null basis matrices. It makes an efficient force method feasible for the analysis of finite element model comprising tetrahedron elements.

The force method, in which the member forces are used as unknowns, can be appealing to engineers. The main problem in the application of the force method is the formation of a self-stress matrix corresponding to a sparse flexibility matrix. In this paper, the highly sparse, banded and accurate null basis matrices gains by using mathematical optimization technique.

Gives a bibliographical review of the finite element methods (FEMs) applied for the linear and nonlinear, static and dynamic analyses of basic structural elements from the theoretical as well as practical points of view. The range of applications of FEMs in this area is wide and cannot be presented in a single paper; therefore aims to give the reader an encyclopaedic view on the subject. The bibliography at the end of the paper contains 2,025 references to papers, conference proceedings and theses/dissertations dealing with the analysis of beams, columns, rods, bars, cables, discs, blades, shafts, membranes, plates and shells that were published in 1992‐1995.

Introduces papers from this area of expertise from the ISEF 1999 Proceedings. States the goal herein is one of identifying devices or systems able to provide prescribed performance. Notes that 18 papers from the Symposium are grouped in the area of automated optimal design. Describes the main challenges that condition computational electromagnetism’s future development. Concludes by itemizing the range of applications from small activators to optimization of induction heating systems in this third chapter.