Two aggregate-function-based algorithms for analysis of 3D frictional contact by linear complementarity problem formulation

Three dimensional frictional contact is formulated as linear complementarity problem (LCP) by using the parametric variational principle and quadratic programming method. Two aggregate-function-based algorithms, called respectively as self-adjusting interior point algorithm and aggregate function smoothing algorithm, are proposed for the solution of the LCP derived from the contact problems. A nonlinear finite element code is developed for numerical analysis of 3D multi-body contact problems. Four numerical examples are computed to demonstrate the applicability and computational efficiency of the methods proposed.     

Improved genetic algorithm with two-level approximation for truss topology optimization

Truss topology optimization using Genetic Algorithms (GAs) usually requires large computational cost, especially for large-scale problems. To decrease the structural analyses, a GA with a Two-level Approximation (GATA) was proposed in a previous work, and showed good computational efficiency with less structural analyses. However, this optimization method easily converges to sub-optimum points, resulting in a poor ability to search for a global optimum. Therefore, to address this problem, we propose an Improved GA with a Two-level Approximation (IGATA) which includes several modifications to the approximation function and simple GA developed previously. A Branched Multi-point Approximation (BMA) function, which is efficient and without singularity, is introduced to construct a first-level approximation problem. A modified Lemonge penalty function is adopted for the fitness calculation, while an Elite Selection Strategy (ESS) is proposed to improve the quality of the initial points. The results of numerical examples confirm the lower computational cost of the algorithm incorporating these modifications. Numerous numerical experiments show good reliability of the IGATA given appropriate values for the considered parameters.     

Analysis of factors influencing the solution of the consolidation problem by using an element-free Galerkin method

The meshless method is new type numerical method developed in recent years. There are no fewer than 20 variations published to-date, and some of them were successfully applied to solve Biot's consolidation problem. In the present paper, the system equations for the plain-strain consolidation problem using an element-free Galerkin method (EFGM) are presented on the basis of enforcing essential boundary conditions with a penalty method. Next, a large number of calculations and analyses of the displacement and excess pore-water pressure for nodes are carried out. It is shown that the accuracy of the calculations is influenced by many factors including the distribution mode of nodes, the shape and size of the domain of influence of nodes, the numerical integration scheme, and the adopted penalty factor. Some useful conclusions are drawn. The findings can be advantageous to improve the computational capability and accuracy of numerical solutions to the Biot's consolidation problem with EFGM.     

An augmented Lagrangian decomposition method for quasi-separable problems in MDO

Several decomposition methods have been proposed for the distributed optimal design of quasi-separable problems encountered in Multidisciplinary Design Optimization (MDO). Some of these methods are known to have numerical convergence difficulties that can be explained theoretically. We propose a new decomposition algorithm for quasi-separable MDO problems. In particular, we propose a decomposed problem formulation based on the augmented Lagrangian penalty function and the block coordinate descent algorithm. The proposed solution algorithm consists of inner and outer loops. In the outer loop, the augmented Lagrangian penalty parameters are updated. In the inner loop, our method alternates between solving an optimization master problem and solving disciplinary optimization subproblems. The coordinating master problem can be solved analytically; the disciplinary subproblems can be solved using commonly available gradient-based optimization algorithms. The augmented Lagrangian decomposition method is derived such that existing proofs can be used to show convergence of the decomposition algorithm to Karush–Kuhn–Tucker points of the original problem under mild assumptions. We investigate the numerical performance of the proposed method on two example problems.     

A constraint-guided method with evolutionary algorithms for economic problems

This paper presents an evolutionary algorithms based constrain-guided method (CGM) that is capable of handling both hard and soft constraints in optimization problems. While searching for constraint-satisfied solutions, the method differentiates candidate solutions by assigning them with different fitness values, enabling favorite solutions to be distinguished more likely and more effectively from unfavored ones.We illustrate the use of CGM in solving two economic problems with optimization involved: (1) searching equilibriums for bargaining problems; (2) reducing the rate of failure in financial prediction problems. The efficacy of the proposed CGM is analyzed and compared with some other computational techniques, including a repair method and a penalty method for the problem (1), a linear classifier and three neural networks for the problem (2), respectively. Our studies here suggest that the evolutionary algorithms based CGM compares favorably against those computational approaches.     

Fast Co-Clustering by Ranking and Sampling

Co-clustering treats a data matrix in a symmetric fashion that a partitioning of rows can induce a partitioning of columns, and vice versa. It has been shown advantageous over tradition clustering. However, the computational complexity of most co-clustering algorithms are costly, and thus limit their e?ectiveness on large datasets. A recently proposed sampling-based matrix decomposition method can achieve a linear computational complexity, but selected rows and columns can not effectively represent a large sparse dataset, and many unselected rows and columns can not be mapped to the selected rows and columns because they do not share features in common, thus its performance is impaired. To address this problem, we propose a fast co-clustering framework by ranking and sampling that only representative samples are selected for co-clustering, and the remaining samples can be easily labeled by their neighbors in clustered samples. Extensive experiments on large text datasets show that our approach is able to use very few samples to achieve comparable results in linear time compared to state-of-the-art co-clustering algorithms of nonlinear computational complexity.     

求解最优控制问题的Chebyshev-Gauss伪谱法

提出了一种求解最优控制问题的Chebyshev-Gauss伪谱法, 配点选择为Chebyshev-Gauss点. 通过比较非线性规划问题的Kaursh-Kuhn-Tucker条件和伪谱离散化的最优性条件, 导出了协态和Lagrange乘子的估计公式. 在状态逼近中, 采用了重心Lagrange插值公式, 并提出了一种简单有效的计算状态伪谱微分矩阵的方法. 该法的独特优势是具有良好的数值稳定性和计算效率. 仿真结果表明, 该法能够高精度地求解带有约束的复杂最优控制问题.     

A numerical analysis of contact and limit-point behavior in a class of problems of finite elastic deformation

Finite element methods for the analysis of bifurcations, limit-point behavior, and unilateral frictionless contact of elastic bodies undergoing finite deformation are presented. Particular attention is given to the development and application of Riks-type algorithms for the analysis of limit points and exterior penalty methods for handling the unilateral constraints. Applications focus on the problem of finite axisymmetric deformations, snap-through, and inflation of thick rubber spherical shells.     

A mixed interface finite element for cohesive zone models

The phenomena of crack initiation, propagation and ultimate fracture are studied here under the following assumptions: (i) the crack law is modelled by means of a cohesive zone model and (ii) the crack paths are postulated a priori. In this context, a variational formulation is proposed which relies on an augmented Lagrangian. A mixed interface finite element is introduced to discretise the crack paths, the degrees of freedom of which consist in the displacement on both crack lips and the density of cohesive forces. This enables an exact treatment of multi-valued cohesive laws (e.g. initial adhesion, contact conditions, possible rigid unloading, etc.), without penalty regularisation.A special attention is paid to the convergence with mesh-refinement, i.e. the well-posedness of the problem, on the basis of theoretical results of contact mechanics and some complementary numerical investigations. Fulfilment of the LBB condition is the key factor to gain the desired properties. Moreover, it is shown that the integration of the constitutive law admits a unique solution as soon as some condition on the augmented Lagrangian is enforced. Finally, a 3D simulation shows the applicability to practical engineer problems, including in particular the robustness of the formulation and its compatibility with classical solution algorithms (Newton method, line-search, path-following techniques).     

Analysis and applications of elasto-plastic contact problems considering large deformation

A numerical procedure for the analysis of the elasto-plastic contact problems under large deformation is presented. The contact surface is assumed unbonded and frictionless. Considering large strain and large displacement, a minimization problem with suitable contact conditions is proposed and the equivalence to the governing equations is shown. A recursive quadratic programming problem based on the finite element technique is adopted for solution method. The method is illustrated by two numerical examples and the results are compared with existing experimental results.     

An augmented Lagrangian optimization method for contact analysis problems, 2: numerical evaluation

The ALM2 solution procedure is evaluated by solving two simple contact analysis problems for different friction conditions. These example problems are devised to have closed form solutions. This way there is no uncertainty about the target solution for evaluation of the proposed algorithm as well as existing algorithms. The numerical results with ALM2 are compared with the analytical solutions as well as with the penalty, Lagrange multiplier and existing augmented Lagrangian methods. All the algorithms are analysed for stick and slip friction conditions. The example problems are used to show clearly the dependence of the existing solution methods on the number of load steps and penalty values. It is concluded that convergence of incremental solution schemes employed in these methods does not guarantee accuracy of the contact solution even with the use of solution enhancement schemes such as automatic load stepping and contact load prediction. The example problems are also used to demonstrate solution independence of the proposed ALM2 procedure from penalty values, and from the number of load steps. The proposed formulation for calculation of frictional forces and the ALM solution algorithm have worked quite well for the example problems. However, the algorithm needs to be developed and evaluated for more complex contact analysis problems.     

Fixed-point algorithms for stationary flow in porous media

We study from the theoretical and experimental points of view some fixed-point algorithms for solving steady-state filtration problems through porous media. The method used applies to a wide class of problems (no restrictions are made on the geometry of the domain or on the boundary conditions; capillarity effects can be treated, the medium can be inhomogeneous and anisotropic). It does not require any previous knowledge on the free boundary, it works on a fixed domain, and the computational cost is slightly more than the cost of solving a linear problem with the overrelaxation method. Moreover, it can be easily implemented in a finite element code. Many numerical tests are presented.     

A cooperative recurrent neural network for solving L(1) estimation problems with general linear constraints

The constrained L(1) estimation is an attractive alternative to both the unconstrained L(1) estimation and the least square estimation. In this letter, we propose a cooperative recurrent neural network (CRNN) for solving L(1) estimation problems with general linear constraints. The proposed CRNN model combines four individual neural network models automatically and is suitable for parallel implementation. As a special case, the proposed CRNN includes two existing neural networks for solving unconstrained and constrained L(1) estimation problems, respectively. Unlike existing neural networks, with penalty parameters, for solving the constrained L(1) estimation problem, the proposed CRNN is guaranteed to converge globally to the exact optimal solution without any additional condition. Compared with conventional numerical algorithms, the proposed CRNN has a low computational complexity and can deal with the L(1) estimation problem with degeneracy. Several applied examples show that the proposed CRNN can obtain more accurate estimates than several existing algorithms.     

Optimal simultaneous stabilization of linear single-input systems via linear state feedback control

Simultaneous stabilization of a collection of linear time-invariant systems is considered. The aim is to develop a practical method for the design of a single feedback controller such that all the systems involved are stabilized with good transient responses. Hurwitz's necessary and sufficient conditions are used as the required set of constraints for simultaneous stability. For transient behaviour, we introduce the usual quadratic objective function as performance index for each system. Their sum is the objective function for the collection of systems and the problem is to minimize it by choosing a feedback gain vector subject to boundedness and the Hurwitz stability constraints. A computational technique is proposed for solving this problem. The results obtained give good transient behaviour. For illustration, two numerical examples are solved.     

Iterative algorithms for the linear complementarity problem

Direct complementary pivot algorithms for the linear complementarity problem with P-matrices are known to have exponential computational complexity. The analog of Gauss-Seidel and SOR iteration for linear complementarity problems with P-matrices has not been extensively developed. This paper extends some work of van Bokhoven to a class of nonsymmetric P-matrices, and develops and compares several new iterative algorithms for the linear complementarity problem. Numerical results for several hundred test problems are presented. Such indirect iterative algorithms may prove useful for large sparse complementarity problems.     

An improved computationally efficient identification method for errors-in-variables models based on v-gap optimisation

A v-gap optimisation-based frequency-domain identification method is proposed to estimate a nominal normalised right graph symbol for errors-in-variables models. The proposed method follows the similar identification idea from a previous research work but with improved computational efficiency using interior-point (IP) algorithms. By imposing an inner function constraint instead of frequency point-wise constraints to normalise the graph symbol, the number of involved equality constraints for the v-gap optimisation is related to the nominal model order instead of the data length. As a consequence, the computational complexity of the proposed IP-based identification algorithm is much lower than that of linear matrix inequalities-based algorithms. Due to the fact that the data length is typically much larger than the finite nominal model order, the number of saved equality constraints is close to that of the employed data points. Finally, two numerical simulation examples are given to verify the proposed identification method.     

A new method for modelling and simulation of the dynamic behaviour of the wheel-rail contact

This paper presents a new method for modelling and simulation of the dynamic behaviour of the wheel-rail contact. The proposed dynamic wheel-rail contact model comprises wheel-rail contact geometry, normal contact problem, tangential contact problem and wheelset dynamic behaviour on the track. This two-degree of freedom model takes into account the lateral displacement of the wheelset and the yaw angle. Single wheel tread rail contact is considered for all simulations and Kalker s linear theory and heuristic non-linear creep models are employed. The second order differential equations are reduced to first order and the forward velocity of the wheelset is increased until the wheelset critical velocity is reached. This approach does not require solving mathematical equations in order to estimate the critical velocity of the dynamic wheel-rail contact model. The mathematical model is implemented in Matlab using numerical differentiation method. The simulated results compare well with the estimated results based on classical theory related to the dynamic behaviour of rail-wheel contact so the model is validated.     

Optimum design with imperfection sensitivity coefficients for limit point loads

A computational method is presented for finding a sequence of optimum designs of a discrete system which exhibits limit point behaviour. Optimality conditions are derived in terms of the theory of imperfection sensitivity coefficients for the limit point load factor. Only those designs of the structures which exhibit limit point behaviour are considered as feasible designs, and the design change is conceived as generating a kind of imperfection. The efficiency of the proposed algorithm will be appreciated particularly for large structures, because incremental nonlinear analysis to find the limit point load factor needs to be carried out only once for the structure of trivial initial optimum design. The sequence of optimum designs is described by piecewise Taylor series expansions with respect to the specified limit point load factor. It is shown in the examples that the proposed method is efficient and of good accuracy for a large space truss.     

A cost-function approach to the assimilation of asynoptic data

This paper describes a method for reconstructing a synoptic state by fitting dynamics to asynoptic data. The best fit is defined by the minimum of a quadratic cost function and dynamics are enforced through the use of a penalty term. When the coefficient of the penalty term is identified as the inverse of the variance of model error, the method yields the same results as Kalman filtering, and in the limit of infinitely large coefficient, the same as strong-constraint formalisms. The self-adjoint nature of the equations for the best fit motivated the use of a relaxation method for their solution. The method is illustrated within the context of one-dimensional, linear, shallow-water wave dynamics, where computational examples indicate that a synoptic state is properly determined only if the asynoptic data are equivalent to complete initial conditions.