MATHEMATICAL PROGRAMMING ANALYSIS OF BILINEAR RHEOLOGICAL LUBRICATION MECHANICS

Bilinear theological lubrication mechanics provides an important basis for the designs of re- cently developed electrorheological(ER)'smart'journal bearings and those lubricated by mixed fluid-solid lubri- cants.But there is not yet a reliable and efficient numerical method for such a problem of non-Newtonian flu- id mechanics.In the present paper,a finite element method(FEM)together with mat hematical programming solution is successfully used to solve such a problem.A reliable and generalized numerical method for the designs of electrorheological 'smart' journal bearings and the bearings lubricated by mixed fluid- solid lubri- cant is presented.

EXTENSION OF CONVEX MODELS AND ITS IMPROVEMENT ON THE APPROXIMATE SOLUTION

In this paper, by means of combining non-probabilistic convex modeling with perturbation theory, an improvement is made on the first order approximate solution in convex models of uncertainties. Convex modeling is extended to largely uncertain and non-convex sets of uncertainties and the combinational convex modeling is developed. The presented method not only extends applications of convex modeling, but also improves its accuracy in uncertain problems and computational efficiency. The numerical example illustrates the efficiency of the proposed method.

CRITERIA FOR FINITE ELEMENT ALGORITHM OF GENERALIZED HEAT CONDUCTION EQUATION

To eliminate oscillation and overbounding of finite element solutions of classical heat conduction equation, the author and Xiao have put forward two new concepts of monotonies and have derived and proved several criteria. This idea is borrowed here to deal with generalized conduction equation and finite element criteria for eliminating oscillation and overbounding are also presented. Some new and useful conclusions are drawn.

RIGID FINITE ELEMENT AND LIMIT ANALYSIS

According to the lower-bound theorem of limit analysis the Rigid Finite Element Meth-od(RFEM)is applied to structural limit analysis and the linear programmings for limit analysis are deducedin this paper.Moreover,the Thermo-Parameter Method(TPM)and Parametric Variational principles(PVP)are used to reduce the computational effort while maintaining the accuracy of solutions.A better solution isalso obtained in this paper.

PARAMETRIC QUADRATIC PROGRAMMING METHOD FOR VISCOPLASTICITY

Perzyna model in viscoplasticity has been studied by the parametric variational principle, which could be transformed into solving the parametric quadratic programming problem. The FEM form of this problem and its implementation have also been discussed in the paper.

NONLINEAR QUASI-CONFORMING FINITE ELEMENT METHOD

The nonlinear quasi-conforming FEM is presented based on the basic concept of the quasi- -conforming finite element. First, the incremental principle of stationary potential energy is discussed, Then, the formulation process of the nonlinear quasi-conforming FEM is given. Lastly, two computational examples of shells are given.

UNILATERAL CONTACT PROBLEMS USING QUASI-ACTIVE SET STRATEGY

The unilateral contact problem can be formulated as a mathematical programming with inequality constraints. To resolve the difficulty in dealing with inequality constraints, a quasi-active set strategy algorithm was presented. At each iteration, it transforms the problem into one without contact in terms of the solution obtained in last iteration and initiates the current iteration using the solution of the transformed problem, and updates a group of contact pairs compared with Lemke algorithm that uqdates only one pair of contact points. The present algorithm greatly enhances the efficiency and numerical examples demonstrate the effectiveness and robustness of the proposed algorithm.

FINITE ELEMENT ANALYSIS FOR CONSOLIDATION IN INTERACTION BETWEEN STRUCTURE AND SATURATED SOIL FOUNDATION

The consolidation analysis of interaction between structure and saturated soil foundation is discussed. With the use of substructure technique, the structure is condensed onto the interface of the soil, and then the consolidation governing equations to describe the interaction between soil and structure are derived, The solution with non-iterative algorithm is proposed in this paper. The pressure Master-Slave relation method is used to deal with the non-permeability conditions on soil boundaries. A numerical example is illustrated. Based on this paper, the interactive consolidation analysis between large structure and soil has been more practical.

THE PARAMETRIC VARIATIONAL PRINCIPLE FOR PERZYNA MODEL IN VISCOPLASTICITY

This paper presents the parametric variational principle for Perzyna model which is one of the main constitutive relations of viscoplasticity.The principle,by which the potential energy function is minimized under a constrained condition transformed by the constitutive relations of viscoplasticity, is free from the bound of Drucker's postulate of plastic flow and consequently suitable for solving the nonassociated plastic flow problems. Furthermore, the paper has proven the presented principle and discussed the creep problem.

THE TOPOLOGICAL OPTIMIZATION FOR TRUSS STRUCTURES WITH STRESS CONSTRAINTS BASED ON THE EXIST-NULL COMBINED MODEL

A new exist-null combined model is proposed for the structural topology optimization. The model is applied to the topology optimization of the truss with stress constraints. Satisfactory computational result can be obtained with more rapid and more stable convergence as compared with the cross-sectional optimization. This work also shows that the presence of independent and continuous topological variable motivates the research of structural topology optimization.

An Efficient Approach to a Class of Non-smooth Optimization Problems

This paper presents an entropy-based smoothing technique for solving a class of non-smooth optimization problems that are in some way related to the maximum function.Basic ideas concerning this approach are that we replace the non-smooth maximum function by a smooth one,called aggregate function,which is derived by employing the maximum entropy principle and its useful properties are proved.Wilh this smoothing technique,both unconstrained and constrained mimma.x problems are transformed into unconstrained optimization problems of smooth functions such that this class of non-smooth optimization problems can be solved by some existing unconstrained optimization softwares for smooth functions The present approach can be very easily implemented on computers with very fast and -.Inhie convergence.

AN AGGREGATE FUNCTION METHOD FOR NONLINEAR PROGRAMMING

This paper presents a new method, called the "aggregate function" method, for solvingnonlinear programming problems. At first, we use the "maximum" constraint in place of theoriginal constraint set to convert a multi-constrained optimization problem to a non-smoothbut singly constrained problem; we then employ the surrogate constraint concept and themaximum entropy principle to derive a smooth function, by which the non-smooth maximumconstraint is approximated and the original problem is converted to a smooth and singly con-strained problem; furthermore, we develop a multiplier penalty algorithm. The presentalgorithm has merits of stable and fast convergence and ease of computer implementation,and is particularly suitable to solving a nonlinear programming problem with a large num-ber of constraints.

A SMOOTH QUASI-EXACT PENALTY FUNCTION FOR NONLINEAR PROGRAMMING

To simplify the presentation, we consider here only the following inequality constrained nonlinear programming problem:

Variational principle with nonlinear complementarity for three-dimensional contact problems and its numerical method

Variational principles with nonlinear complementarity and finite-dimensional nonlinear complementarity models for three-dimensional frictional contact problems are established.The existence and uniqueness of the solutions to the finite-dimensional models are proved.A minimum principle is developed and a minimization algorithm is presented.Numerical calculation shows that the algorithm is highly efficient,reliable and promising.

AN EFFICIENT APPROACH TO NONLINEAR MINIMAX PROBLEMS

A nonlinear minimax problem is usually defined aswherefi(x), i=1,…,m, are generally smooth nonlinear functions of a vector x ∈ R^n. Since the objective φ(x) is a non-smooth function, (A) is then a non-smooth, unconstrained optimization problem and cannot be solved by standard unconstrained minimization algorithms. One normally transforms it into an equivalent nonlinear programming problem: