A unified formalism for various coupling analyses of composite laminates and its applications to crack problems

Abstract

In this paper, a unified formalism is proposed to deal with several different coupling analyses of composites. This formalism is established from the Stroh formalism for two‐dimensional problems and the Stroh‐like formalism for coupled stretching‐bending problems and their extensions to the magneto‐electro‐elastic coupling analysis. Since different coupling conditions can be represented by one unified formalism, if for particular problems the boundary conditions of different coupling problems can be written in one unified form, the final solution should also have the same form for different types of problems. To show the usefulness and powerfulness of this unified formalism, a typical example of crack problems is presented in this paper.     

Refrigeration and its influence on the world food supply now and in the future

There is a clear trend towards a lower rate of increase in world population. If the present trend continues the food supply will be sufficient for the foreseeable future. However, urbanization will also continue and distribution problems will become tremendous. Refrigeration, therefore, will continue to play an important role in solving the world food distribution problem. Mankind today is facing greater and greater problems with wealth distribution. As far as food is concerned we have a physical distribution problem. The technical distribution problems, however, are much easier to solve than the problems related to wealth distribution.

Résumé

There is a clear trend towards a lower rate of increase in world population. If the present trend continues the food supply will be sufficient for the foreseeable future. However, urbanization will also continue and distribution problems will become tremendous. Refrigeration, therefore, will continue to play an important role in solving the world food distribution problem. Mankind today is facing greater and greater problems with wealth distribution. As far as food is concerned we have a physical distribution problem. The technical distribution problems, however, are much easier to solve than the problems related to wealth distribution.     

Reshipments and overshipments in transportation problems with minimax objective

Summary In this paper transportation problems with minimax objective are studied. It is shown that it can be decided in linear time whether reshipments and overshipments can improve the solution. Moreover, new algorithms are stated which solve even the lexicographic version of the underlying minimax transportation, reshipment and overshipment problems. The first two problems can be solved by an algorithm of time complexityO(n ²), wheren is the number of origins and destinations, whereas the overshipment problem is solved in linear time. Moreover, some extensions of the problems are addressed.     

Direct determination of asymptotic structural postbuckling behaviour by the finite element method

Application of the finite element method to Koiter's asymptotic postbuckling theory often leads to numerical problems. Generally it is believed that these problems are due to locking of non-linear terms of different orders. A general method is given here that explains the reason for the numerical problems and eliminates these problems. The reason for the numerical problems is that the postbuckling stresses are inaccurately determined. By including a local stress contribution, the postbuckling stresses are calculated correctly. The present method gives smooth postbuckling stresses and shows a quick convergence of the postbuckling coefficients. © 1998 John Wiley & Sons, Ltd.     

Project Management Problems

ABSTRACT

Twelve hundred different problems, as described by project practitioners, are sorted according to an adaptation of the classic management functions first described by Henri Fayol: planning, scheduling, organizing, staffing, directing, and controlling. Observations include that planning problems are most prevalent, that some problems vary with project structure, and that some problems vary with success level. The most surprising lesson is that many types of problems are equally or even more prevalent on successful projects.     

H-Adaptive finite element methods for dynamic problems,with emphasis on localization

H-adaptive procedures for the finite element solution of transient solid mechanics problems are studied, with particular emphasis on problems involving localization due to material instability. Various types of error criteria are examined and it is shown that for problems involving plastic response or localization, an error criterion based on an L₂-projection of strains is the most effective for the constant strain elements considered here. Examples of one-dimensional and two-dimensional localization (shear band formation) problems are given.     

A convenient solver for solving optimal control problems

Abstract

This paper focuses on the development of a solver for solving optimal control problems. A developed numerical optimal control module integrated with the Sequential Quadratic Programming method is introduced. An optimal control problem solver based on the proposed method is implemented to solve optimal control problems efficiently in engineering applications. In addition, a systematic procedure for solving optimal control problems by using the optimal control problem solver is also proposed. A time‐optimal benchmark problem presented in the literature is used to illustrate for the capability and facility of solving optimal control problems. The numerical results demonstrate the proposed method and the procedure suggested in this paper are helpful to engineers in solving optimal control problems in a systematic and efficient manner.     

A new optimization algorithm for solving complex constrained design optimization problems

This article presents the performance of a very recently proposed Jaya algorithm on a class of constrained design optimization problems. The distinct feature of this algorithm is that it does not have any algorithm-specific control parameters and hence the burden of tuning the control parameters is minimized. The performance of the proposed Jaya algorithm is tested on 21 benchmark problems related to constrained design optimization. In addition to the 21 benchmark problems, the performance of the algorithm is investigated on four constrained mechanical design problems, i.e. robot gripper, multiple disc clutch brake, hydrostatic thrust bearing and rolling element bearing. The computational results reveal that the Jaya algorithm is superior to or competitive with other optimization algorithms for the problems considered.     

Total quality control for a surface mount technology process for the manufacture of printed circuit board assemblies

Surface mount technology is used widely nowadays in the manufacture of printed circuit board assemblies in the electronics industry. The occurrence of defective products when this technology is used is mostly caused by technological problems, but sometimes it is also caused by management problems or human errors. When technological problems are being tackled, human interactions will always be involved. This is because the quality of a product is related to the quality of the material, the design of the product and the manufacturing process, and as tasks are subdivided, problems occurring in production cannot be solved completely by the sole effort of a single individual. Hence improvement of product quality involes man, machine, and material. This article explains how quality problems arising from surface mount technology are tackled by team effort in an organization via the implementation of a process-oriented total quality control system.     

OPTIMAL DESIGN WITH DISCRETE VARIABLES: SOME NUMERICAL EXPERIMENTS

Continuous–discrete variable non-linear optimization problems are defined and categorized into six different types. These include a full range of problems from continuous to purely discrete and non-differentiable. Methods for solution of these problems are studied and their characteristics are catalogued. The branch and bound, simulated annealing and genetic algorithms are found to be the most general methods for solving discrete problems. After some enhancements, these and two other methods are implemented into a program for certain applications. Several example problems are solved to study performance of the methods. It is concluded that solution of the mixed variable non-linear optimization problems usually requires considerable more computational effort compared to the continuous variable optimization problems. In addition, there is no guarantee that the best solution has been obtained; however, good practical solutions are usually obtained. © 1997 by John Wiley & Sons, Ltd.     

Modified flux-vector-based Green element method for problems in steady-state anisotropic media

In this study we present a new numerical technique for solving problems in steady-state heterogeneous anisotropic media, namely the ‘flux-vector-based’ Green element method (‘$\mathit{q}$-based’ GEM) for anisotropic media. This method, which is appropriate for problems where the permeability has either constant or continuous components over the whole domain, is based on the boundary element method (BEM) formulation for direct, steady-state flow problems in anisotropic porous media, which is applied to finite element method (FEM) meshes. For situations involving media discontinuities, an extension of this ‘$\mathit{q}$-based’ GEM formulation is proposed, namely the modified ‘$\mathit{q}$-based’ GEM for anisotropic media. Numerical results are presented for various physical problems that simulate flow in an anisotropic medium with diagonal layers of different permeabilities or around faults and wells, and they show that the new method, with the extensions proposed, is very suitable for steady-state problems in such media.     

Performance of GEM2 on the ELLPACK problem population

The Pilot global element program GEM2 MK1.0 has been used to solve the two-dimensional problems in the ELLPACK population of partial differential equation test problems. The performance achieved is summarized in this paper; special attention is paid to those problems which are singular or near singular, and for which comparisons have been published by Houstis and Rice.¹²     

An axisymmetric infinite element

A parametric infinite element is presented for solving axisymmetric problems under non-axisymmetric forcing functions where the considered domain is assumed infinite. The element accuracy is compared against the exact solution for two classical problems: Boussinesq's and Cerruti's. Boussinesq's problem for a rigid circular plate is also presented. For these problems, using relatively simple displacement functions, the element provides a reasonable infinite domain representation.     

Adaptive mesh refinement of the boundary element method for potential problems by using mesh sensitivities as error indicators

This paper presents a novel method for error estimation and h-version adaptive mesh refinement for potential problems which are solved by the boundary element method (BEM). Special sensitivities, denoted as mesh sensitivities, are used to evaluate a posteriori error indicators for each element, and a global error estimator. A mesh sensitivity is the sensitivity of a physical quantity at a boundary node with respect to perturbation of the mesh. The element error indicators for all the elements can be evaluated from these mesh sensitivities. Mesh refinement can then be performed by using these element error indicators as guides.The method presented here is suitable for both potential and elastostatics problems, and can be applied for adaptive mesh refinement with either linear or quadratic boundary elements. For potential problems, the physical quantities are potential and/or flux; for elastostatics problems, the physical quantities are tractions/displacements (or tangential derivatives of displacements). In this paper, the focus is on potential problems with linear elements, and the proposed method is validated with two illustrative examples. However, it is easy to extend these ideas to elastostatics problems and to quadratic elements.The computing for this research has been supported by the Cornell National Supercomputer Facility.     

Body force method

The body force method is based on the principle of superposition. The solution in the body force method is obtained by the superposition of fundamental solutions so as to satisfy a given boundary condition. By means of these fundamental solutions all problems can be solved in principle. In this paper, first the fundamental principle of the body force method is illustrated and then its application to crack problems, elastic–plastic problems and elastodynamic problems are shown. This revised version was published online in July 2006 with corrections to the Cover Date.     

Geometrically non-linear enhanced strain mixed methods and the method of incompatible modes

A class of ‘assumed strain’ mixed finite element methods for fully non-linear problems in solid mechanics is presented which, when restricted to geometrically linear problems, encompasses the classical method of incompatible modes as a particular case. The method relies crucially on a local multiplicative decomposition of the deformation gradient into a conforming and an enhanced part, formulated in the context of a three-field variational formulation. The resulting class of mixed methods provides a possible extension to the non-linear regime of well-known incompatible mode formulations. In addition, this class of methods includes non-linear generalizations of recently proposed enhanced strain interpolations for axisymmetric problems which cannot be interpreted as incompatible modes elements. The good performance of the proposed methodology is illustrated in a number of simulations including 2-D, 3-D and axisymmetric finite deformation problems in elasticity and elastoplasticity. Remarkably, these methods appear to be specially well suited for problems involving localization of the deformation, as illustrated in several numerical examples.     

Optimal subgradient methods: computational properties for large-scale linear inverse problems

This paper studies the computational properties of the optimal subgradient algorithm (OSGA) for applications of linear inverse problems involving high-dimensional data. First, such convex problems are formulated as a class of convex problems with multi-term composite objective functions involving linear mappings. Next, an efficient procedure for computing the first-order oracle for such problems is provided and OSGA is equipped with some prox-functions such that the OSGA subproblem is solved in a closed form. Further, a comprehensive comparison among the most popular first-order methods is given. Then, several Nesterov-type optimal methods (originally proposed for smooth problems) are adapted to solve nonsmooth problems by simply passing a subgradient instead of the gradient, where the results of these subgradient methods are competitive and totally interesting for solving nonsmooth problems. Finally, numerical results with several inverse problems (deblurring with isotropic total variation, elastic net, and \(\ell _1\)-minimization) show the efficiency of OSGA and the adapted Nesterov-type optimal methods for large-scale problems. For the deblurring problem, the efficiency measures of the improvement on the signl-to-noise ratio and the peak signal-to-noise ratio are used. The software package implementing OSGA is publicly available.     

A meshless numerical method based on the local boundary integral equation (LBIE) to solve linear and non-linear boundary value problems

Meshless methods for solving boundary value problems have been extensively popularized in recent literature owing to their flexibility in engineering applications, especially for problems with discontinuities, and because of the high accuracy of the computed results. A meshless method for solving linear and non-linear boundary value problems, based on the local boundary integral equation method and the moving least squares (MLS) approximation, is discussed in the present article. In the present article, the implementation of the LBIE formulation for linear and non-linear problems with the linear part of the differential operator being the Helmholtz type, is developed. For non-linear problems, the total formulation and a rate formulation are developed for the implementation of the presently proposed method. The present method is a true meshless one, as it does not need domain and boundary elements to deal with the volume and boundary integrals, for linear as well as non-linear problems. The “companion solution” is employed to simplify the present formulation and reduce the computational cost. It is shown that the satisfaction of the essential as well as natural boundary conditions is quite simple, and algorithmically very efficient in the present LBIE approach, even when the non-interpolative MLS approximation is used. Numerical examples are presented for several linear and non-linear problems, for which exact solutions are available. The present method converges fast to the final solution with reasonably accurate results for both the unknown variable and its derivatives in solving non-linear problems. No post processing procedure is required to compute the derivatives of the unknown variable [as in the conventional boundary element method and field/boundary element method, as the solution from the present method, using the MLS approximation, is already smooth enough. The numerical results in these examples show that high rates of convergence with mesh refinement for the Sobolev norms 6·6₀ and 6·6₁ are achievable, and that the values of the unknown variable and its derivatives are quite accurate.     

Industrial statistics: The challenges and the research

ABSTRACT

Industrial problems have stimulated an enormous amount of valuable statistical research, from the t-test to advanced statistical tools for quality. Industry continues to generate challenging problems for statistical design, modeling, and analysis. Useful articles are published in our journals, often stimulated by industrial applications. Nonetheless, there is concern that research in industrial statistics is falling well short of its potential for providing interesting problems, that some of the most exciting problems are not getting space in our journals, and that few statisticians working in industry are publishing research. This article endeavors to map out the current state of research in industrial statistics, to describe major issues that need to be addressed, and to discuss whether the research is on target to meet those challenges.