A nonlinear programming approach, along with finite element implementation, has been developed to perform plastic limit analysis for materials under non-associated plastic flow, so the plastic stability condition of n...
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A nonlinear programming approach, along with finite element implementation, has been developed to perform plastic limit analysis for materials under non-associated plastic flow, so the plastic stability condition of non-standard materials can be directly calculated. In the framework of Radenkovic's theorems, a decoupled material model with non-associated plastic flow was introduced into kinematic limit analysis so that the classic limit theorems were extended for non-standard plastic flow materials, such as cohesive-frictional materials. A non-associated plastic dissipation power is derived, and a purely kinematic formulation is obtained for limit analysis. Based on the mathematical programming theory and the finite element method, the numerical implementation of kinematic limit analysis is formulated as a nonlinear programming problem subject only to one equality constraint. An extended direct iterative algorithm is proposed to solve the resulting programming problem. The developed method has a wide applicability for limit analysis. The effectiveness and efficiency of the proposed method are validated through numerical examples and the influence of non-associated plastic flow on stability conditions of structures is numerically investigated.
This article proposes a hybrid optimization algorithm based on a modified BFGS and particle swarm optimization to solve medium scale nonlinear programs. The hybrid algorithm integrates the modified BFGS into particle ...
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This article proposes a hybrid optimization algorithm based on a modified BFGS and particle swarm optimization to solve medium scale nonlinear programs. The hybrid algorithm integrates the modified BFGS into particle swarm optimization to solve augmented Lagrangian penalty function. In doing so, the algorithm launches into a global search over the solution space while keeping a detailed exploration into the neighborhoods. To shed light on the merit of the algorithm, we provide a test bed consisting of 30 test problems to compare our algorithm against two of its variations along with two state-of-the-art nonlinear optimization algorithms. The numerical experiments illustrate that the proposed algorithm makes an effective use of hybrid framework when dealing with nonlinear equality constraints although its convergence cannot be guaranteed. (C) 2012 Elsevier Ltd. All rights reserved.
We present a class of trust region algorithms that do not use any penalty function or a filter for nonlinear equality constrained optimization. In each iteration, the infeasibility is controlled by a progressively dec...
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We present a class of trust region algorithms that do not use any penalty function or a filter for nonlinear equality constrained optimization. In each iteration, the infeasibility is controlled by a progressively decreasing upper limit and trial steps are computed by a Byrd-Omojokun-type trust region strategy. Measures of optimality and infeasibility are computed, whose relationship serves as a criterion on which the algorithm decides which one to focus on improving. As a result, the algorithm keeps a balance between the improvements on optimality and feasibility even if no restoration phase which is required by filter methods is used. The framework of the algorithm ensures the global convergence without assuming regularity or boundedness on the iterative sequence. By using a second order correction strategy, Marato's effect is avoided and fast local convergence is shown. The preliminary numerical results are reported. (C) 2012 Elsevier Ltd. All rights reserved.
We propose a new class of incremental primal-dual techniques for solving nonlinear programming problems with special structure. Specifically, the objective functions of the problems are sums of independent nonconvex c...
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We propose a new class of incremental primal-dual techniques for solving nonlinear programming problems with special structure. Specifically, the objective functions of the problems are sums of independent nonconvex continuously differentiable terms minimized subject to a set of nonlinear constraints for each term. The technique performs successive primal-dual increments for each decomposition term of the objective function. The primal-dual increments are calculated by performing one Newton step towards the solution of the Karush-Kuhn-Tucker optimality conditions of each subproblem associated with each objective function term. We show that the resulting incremental algorithm is q-linearly convergent under mild assumptions for the original problem.
This paper presents a numerical upper bound limit analysis using radial point interpolation method (RPIM) and a direct iterative method with nonlinear programming. By expressing the internal plastic dissipation power ...
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This paper presents a numerical upper bound limit analysis using radial point interpolation method (RPIM) and a direct iterative method with nonlinear programming. By expressing the internal plastic dissipation power with a kinematically admissible velocity field obtained through RPIM interpolation, the upper bound problem is formulated mathematically as a nonlinear programming subjected to single equality constraint which is solved by a direct iterative method. To evaluate the integration of internal power dissipation rate without any background integral cell, a new meshless integration technique based on Cartesian Transformation Method (CTM) is employed to transform the domain integration first as boundary integration and then one-dimensional integration. The effectiveness and accuracy of the proposed approach are demonstrated by two classical limit analysis problems. Further discussion is devoted to optimal selection of relevant parameters for the computation. (C) 2013 Published by Elsevier Ltd.
This is Part II of a two-part paper. Part I presented a universal Birkhoff theory for fast and accurate trajectory optimization. The theory rested on two main hypotheses. In this paper, it is shown that if the computa...
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This is Part II of a two-part paper. Part I presented a universal Birkhoff theory for fast and accurate trajectory optimization. The theory rested on two main hypotheses. In this paper, it is shown that if the computational grid is selected from any one of the Legendre and Chebyshev families of node points, be it Lobatto, Radau, or Gauss, then the resulting collection of trajectory optimization methods satisfies the hypotheses required for the universal Birkhoff theory to hold. All of these grid points can be generated at an O(1) computational speed. Furthermore, all Birkhoff-generated solutions can be tested for optimality by a joint application of Pontryagin's- and covector-mapping principles, where the latter was developed in Part I. More importantly, the optimality checks can be performed without resorting to an indirect method or even explicitly producing the totality of necessary conditions that result from an application of Pontryagin's principle. Numerical problems are solved to illustrate all these ideas in addition to demonstrating near-exponential rates of convergence. The examples are chosen to particularly highlight three practically useful features of Birkhoff methods: 1) bang-bang optimal controls can be produced without suffering any Gibbs phenomenon, 2) discontinuous and even Dirac delta covector trajectories can be well approximated, and 3) extremal solutions over dense grids can be computed in a stable and efficient manner.
In this work, preliminary results of human motion synthesis are presented. Specifically, a single stride motion (consisting of two steps) of a human lower-body model is obtained. The optimal control problem was reform...
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ISBN:
(纸本)9798350309799
In this work, preliminary results of human motion synthesis are presented. Specifically, a single stride motion (consisting of two steps) of a human lower-body model is obtained. The optimal control problem was reformulated as a nonlinear programming problem using the differential inclusion method. The main goal of this study is to compare the performance of trigonometric and polynomial (B-spline) discretization methods. The obtained results indicate that the trigonometric spline method performs similarly to the B-spline method and results in a smooth motion.
Time delay is a ubiquitous phenomenon in chemical engineering. In the development of a practical rigorous model for process system, the influence of time delay cannot be ignored. A simultaneous approach for estimating...
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Time delay is a ubiquitous phenomenon in chemical engineering. In the development of a practical rigorous model for process system, the influence of time delay cannot be ignored. A simultaneous approach for estimating time delays and model parameters is proposed in this work. The critical issue is how to address the approximation for state variable with time delay, which depends on the quotient and remainder obtained by dividing time delay by length of finite element. The strategies for handling the unknown quotient and remainder are designed. Finally, two case studies are considered. The effectiveness of the proposed approach is verified. Moreover, the proposed approach exhibits better performance compared with the gradient-based sequential approach.
This paper pertains to the finite-element lower bound limit analysis (FELA-LB) of vertical strip anchors embedded in cohesionless and cohesive soils and subjected to static and earthquake forces (using pseudostatic an...
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This paper pertains to the finite-element lower bound limit analysis (FELA-LB) of vertical strip anchors embedded in cohesionless and cohesive soils and subjected to static and earthquake forces (using pseudostatic analysis) to estimate the optimal horizontal pullout capacity using nonlinear programming (NLP) technique for isolating the optimal solution. In the developed procedure, a mesh of finite-number triangular elements and assuming a linear stress field that satisfies all the equations of internal equilibrium at all points within the soil medium, elemental interface equilibrium, boundary conditions and no-yield conditions at all the nodal points, has been adopted. In contrast to the use of linear programming (LP), as used in the early phase of the development of FELA of stability problems, in the adopted optimization scheme (NLP), the nonlinear no-yield conditions are incorporated directly, eliminating the necessity of successive linearization of the no-yield constraints. The convergence of the solutions (by varying the number of elements in the soil mesh) and extensibility of the selected stress field (by extending the mesh of elements) has been checked and ensured. The correctness of the estimated lower bound has been checked by comparing the obtained solutions with those reported in the literature. Parametric studies showing the effect of the embedment depth of the vertical anchor, soil properties, and earthquake acceleration on the horizontal pullout capacity of the vertical anchor have also been presented in the paper. Anchor plates are used in the design and construction of foundation for retaining walls, sheet piles, bulkheads, transmission towers, bridge abutments, and buried pipelines to withstand the horizontal, vertical, or inclined loads. The present study adds to the existing state of art for the design and installation of anchor systems subjected to static and seismic conditions and may improve the performance of such foundation systems.
This article thoroughly investigates the design and optimization of an off-grid hybrid renewable energy system for a remote town in the province of Ankara, whose traditional power infrastructure is lacking. The goal i...
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This article thoroughly investigates the design and optimization of an off-grid hybrid renewable energy system for a remote town in the province of Ankara, whose traditional power infrastructure is lacking. The goal is to provide an efficient and cost-effective energy system that can supply the village's power needs indefinitely. The optimization process entails selecting the best mix of renewable energy sources and sizing components to obtain the best economic and technical performance. To handle the complexity of the optimization problem, the Nelder-Mead simplex search method is used, taking into account the stochastic nature of renewable energy generation and the nonlinear features of RES-based power plants. The simulation results show that the suggested hybrid system outperforms traditional diesel power generators in terms of economic viability and environmental sustainability. The system assures consistent power supply by using reserve energy devices such as batteries, thereby minimizing the intermittent nature of renewable sources. With a competitive energy cost of 0.63/kWh, the optimized hybrid system ensures a dependable and continuous power supply, fulfilling the village's electrical requirement for an amazing 16 years.
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