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Three-dimensional lower bound finite element limit analysis of an anisotropic undrained strength criterion using second-order cone programming

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COMPUTERS AND GEOTECHNICS 2019年 106卷 327-344页

作者： Ukritchon, Boonchai Keawsawasvong, Suraparb Chulalongkorn Univ Fac Engn Dept Civil Engn Ctr Excellence Geotech & Geoenvironm Engn Bangkok 10330 Thailand

This paper describes a formulation of second-order cone programming for three-dimensional lower bound finite element limit analysis considering a cross-anisotropic undrained strength criterion. A three-dimensional generalized yield criterion accounting for the cross-anisotropic undrained strength of clay is proposed and requires four input shear strengths in triaxial compression and extension, direct simple shear, and pressuremeter tests. The proposed formulation is verified through the predictions of various compressions of anisotropic soil blocks while the importance of undrained strength anisotropy is demonstrated by analyses of undrained bearing capacity of strip, circular and square footings on anisotropic clays.

关键词： Lower bound Limit analysis second-order cone programming Anisotropic strength Finite element limit analysis Stability

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An interval power flow method for radial distribution systems based on hybrid second-order cone and linear programming

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SUSTAINABLE ENERGY GRIDS & NETWORKS 2023年 36卷

作者： Zhang, Xuehan Woo, Hyeon Choi, Sungyun Fuzhou Univ Coll Elect Engn & Automat Fuzhou 350116 Peoples R China Korea Univ Sch Elect Engn Seoul 02841 South Korea

Interval power flow (IPF) analysis is a promising approach to handling the uncertainty of renewable energy sources and loads in power systems. However, most existing studies are based on standard interval arithmetic or affine arithmetic. Little work can be found that employs traditional optimization methods to obtain the interval results, especially based on convexified power flow formulation. Therefore, this paper proposes an IPF method based on a hybrid second-order cone and linear programming for radial distribution systems. First, the optimization process of IPF based on the standard power flow model is introduced. Given the non-convexity of the standard power flow model, an IPF framework based on second-order cone programming (SOCP) for radial distribution systems is proposed. Moreover, considering that the SOCP formulation can only achieve half of the whole IPF process, a revised linear DistFlow formulation is adopted, and the IPF method based on a hybrid second-order cone and linear programming is devised. Finally, the proposed IPF method is compared with the standard power flow equation-based IPF method and the Monte Carlo method. The simulation results on modified IEEE 33-node and 69-node distribution systems demonstrate the effectiveness and prospects of the proposed IPF method. (c) 2023 Elsevier Ltd. All rights reserved.

关键词： Interval power flow Radial distribution system second-order cone programming Revised linearized distFlow formulation Renewable energy sources

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Geotechnical localization analysis based on Cosserat continuum theory and second-order cone programming optimized finite element method

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COMPUTERS AND GEOTECHNICS 2019年 114卷 103118-000页

作者： Wang, Dongyong Chen, Xi Lyu, Yannan Tang, Chong Beijing Jiaotong Univ Minist Educ State Key Lab Urban Underground Engn Beijing 100044 Peoples R China Natl Univ Singapore Dept Civil & Environm Engn E1A07-031 Engn Dr 2 Singapore 117576 Singapore

Based on the Hellinger-Reissner mixed variational principle, a second-order cone programming optimized finite element method for elastic and elastoplastic analyses of Cosserat continuum (named CosFEM-SOCP) is proposed. To examine the correctness and effectiveness of CosFEM-SOCP, three well-known numerical examples are revisited. In the plane-strain elastic problem of stress concentration around a circular hole, the stress concentration factors calculated by CosFEM-SOCP are in good agreement with the existing solutions, and the correctness of CosFEM-SOCP can be verified. In the analysis of load-displacement response of a flexible strip footing resting on the soil ground, it is found that load-displacement response may be affected by the internal characteristic length l(c), and generally a larger l(c) may result in a wider and deeper slip surface as well as more elements being included in the shear bands. From the plane-strain soil strip with the Drucker-Prager (DP) failure criterion subjected to the prescribed incremental displacement, it can also be observed that the pathologically mesh-dependent problem can be partially or even completely removed by employing CosFEM-SOCP, as long as the mesh is fine enough so that the average element size in the mesh discretization is smaller than l(c).

关键词： second-order cone programming Finite element method Cosserat continuum Stress concentration Strain localization Shear band

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Unpowered approach and landing trajectory planning using second-order cone programming

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AEROSPACE SCIENCE AND TECHNOLOGY 2020年 101卷 105841-105841页

作者： Yan, Xiaodong He, Lei Northwestern Polytech Univ Sch Astronaut Xian 710072 Shaanxi Peoples R China Northwestern Polytech Univ Natl Key Lab Aerosp Flight Dynam Xian 710072 Shaanxi Peoples R China

Online trajectory planning is an effective way to improve the adaptability of a mission and the guidance reliability. This paper presents a trajectory planning algorithm developed by applying the convex optimization for the approach and landing phase of unpowered winged vehicles. Considering a four degree-of-freedom (DoF) dynamics system, as well as a number of control constraints, path constraints and terminal constraints, the trajectory planning problem is formulated as a nonconvex optimization problem. By using the exact convexification and successive convexification approaches, the nonconvex optimization problem is converted to a second-order cone programming problem, which can be efficiently solved by the interior point method. The exactness of the convex relaxation for the control variables is proved theoretically, and the numerical simulation results verify the effectiveness of the approach. The numerical simulation results also indicate that the proposed algorithm has high efficiency, and the trajectory generated using the proposed algorithm is remarkably similar to that obtained using the propagation algorithm developed for the Space Shuttle. (C) 2020 Elsevier Masson SAS. All rights reserved.

关键词： Unpowered winged vehicles Approach and landing Trajectory planning second-order cone programming Convex optimization

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A smoothed finite element method using second-order cone programming

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COMPUTERS AND GEOTECHNICS 2020年 123卷 103547-103547页

作者： Meng, Jingjing Zhang, Xue Huang, Jinsong Tang, Hongxiang Mattsson, Hans Laue, Jan Lulea Univ Technol Dept Civil Environm & Nat Resources Engn Lulea Sweden Univ Liverpool Dept Civil Engn & Ind Design Liverpool Merseyside England Dalian Univ Technol State Key Lab Coastal & Offshore Engn Dalian Peoples R China Univ Newcastle Prior Res Ctr Geotech Sci & Engn Discipline Civil Surveying & Environm Engn Callaghan NSW 2308 Australia

In this paper, a new approach abbreviated as SOCP-SFEM is developed for analysing geomechanical problems in elastoplasticity. The SOCP-SFEM combines a strain smoothing technique with the finite element method (FEM) in second-order cone programming (SOCP) and thereby inherits the advantages of both the smoothed finite element method (SFEM) and the SOCP-FEM. Specifically, the low-order mixed element can be used in the SOCP-SFEM without volumetric locking issues and the singularity associated with some typical constitutive models (e.g. the Mohr-Coulomb model and the Drucker-Prager model) is no longer a problem. In addition, the frictional and the cohesive-frictional interfaces can be implemented straightforward in the developed SOCP-SFEM owing to the adopted mixed variational principle and the smoothing technique. Furthermore, the multiple contact constraints, such as a cohesive interface with tension cut-off which is commonly used for analysing the bearing capacity of a pipeline buried in clays, can be simulated with little extra effort. To verify the correctness and robustness of the developed formulation for SOCP-SFEM, a series of benchmarks are considered where the simulation results are in good agreements with the analytical solutions and the reported numerical results.

关键词： Smoothed finite element method Convex programming Strain smoothing technique second-order cone programming Contact problems

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Elastoplastic and limit analysis of 3D steel assemblies using second-order cone programming and dual finite-elements

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ENGINEERING STRUCTURES 2020年 221卷 111041-111041页

作者： El Boustani, Chadi Bleyer, Jeremy Arquier, Mathieu Ferradi, Mohammed-Khalil Sab, Karam Univ Gustave Eiffel Lab Navier CNRS Ecole Ponts ParisTech F-77455 Marne La Vallee France Strains F-75012 Paris France

We investigate the use of a second-order cone programming (SOCP) framework for computing complex 3D steel assemblies in the context of elastoplasticity and limit analysis. Displacement and stress-based variational formulations are considered and appropriate finite-element discretization strategies are chosen, yielding respectively an upper and lower bound estimate of the exact solution. An efficient interior-point algorithm is used to solve the associated optimization problems. The discrete solution convergence is estimated by comparing both static and kinematic solutions, offering a way to perform local mesh adaptation. The proposed framework is illustrated on the design of a moment-transmitting assembly, its performance is assessed by comparison with classical elastoplastic computations using Abaqus and, finally, T-stub resistance and failure mechanisms when assessing the strength of a column base plate are compared with the Eurocodes design rules.

关键词： second-order cone programming Interior point method Elastoplasticity Limit analysis Equilibrium finite elements Steel assembly

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Adversarial Model Predictive Control via second-order cone programming 58

Adversarial Model Predictive Control via Second-Order Cone P...

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58th IEEE Conference on Decision and Control (CDC)

作者： Guthrie, James Mallada, Enrique Johns Hopkins Univ Baltimore MD 21218 USA

ISBN: (纸本)9781728113982

We study the problem of designing attacks to safety-critical systems in which the adversary seeks to maximize the overall system cost within a model predictive control framework. Although in general this problem is NP-hard, we characterize a family of problems that can be solved in polynomial time via a second-order cone programming relaxation. In particular, we show that positive systems fall under this family. We provide examples demonstrating the design of optimal attacks on an autonomous vehicle and a microgrid.

关键词： second-order cone programming

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Synthesis of Frequency-invariant Beam Patterns under Accurate Sidelobe Control by second-order cone programming

Synthesis of Frequency-invariant Beam Patterns under Accurat...

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Photonics and Electromagnetics Research Symposium - Fall (PIERS - Fall)

作者： Chen, Liyang Wang, Yuqiang Liu, Yanhui Guo, Y. Jay Inst Electromagnet & Acoust Xiamen 361005 Peoples R China Fujian Prov Key Lab Electromagnet Wave Sci & Dete Xiamen 361005 Peoples R China Southwest China Res Inst Elect Equipment Chengdu 610036 Peoples R China Univ Technol Sydney UTS Global Big Data Technol Ctr Sydney NSW 2007 Australia

ISBN: (纸本)9781728153049

It is shown in this work that the FI pattern synthesis can be treated as an optimization problem for minimizing the mainlobe frequency variation. To control both the mainlobe and sidelobe regions, we introduce several constraints imposed on the broadband pattern, called the look-direction constraint, the spatial response variation constraint and the sidelobe constraint, respectively. The whole optimization process needs to perform the SOCP solver. A synthesis of FI pattern with low sidelobe level (SLL) is given to validate the accuracy and effectiveness of the proposed method.

关键词： second-order cone programming

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A Variant of the Simplex Method for second-order cone programming 18th

A Variant of the Simplex Method for Second-Order Cone Progra...

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18th International Conference on Mathematical Optimization Theory and Operations Research (MOTOR)

作者： Zhadan, Vitaly RAS FRC Comp Sci & Control Dorodnicyn Comp Ctr 40 Vavilova St Moscow 119333 Russia State Res Univ Moscow Inst Phys & Technol 9 Inst Skiy Per Dolgoprudnyi 141701 Moscow Region Russia

ISBN: (纸本)9783030226299;9783030226282

The linear second-order cone programming problem is considered. For its solution a variant of the primal simplex-type method is proposed. This variant is a generalization on the cone programming of the standard simplex method for linear programming. At each iteration the dual variable and dual slack are defined, and the move from the given extreme point to another one is realized. Finite and infinite convergence of the method to the solution of the problem having a special form is discussed.

关键词： second-order cone programming Simplex-type method Finite and infinite convergence

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Multi-objective siting and sizing of distributed generation based on the mixed integer second-order cone programming 8

Multi-objective siting and sizing of distributed generation ...

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8th Renewable Power Generation Conference, RPG 2019

作者： Hong, Shaoyun Huang, Guilin Ren, Hequan Hu, Yuqing Xing, Haijun Construction Branch of State Grid Jiangxi Electric Power Co. Ltd Nanchang Jiangxi Province China Daming Electric Power Design Institute State Grid Shaoxing Power Supply Company Shaoxing Zhejiang Province China School of Electrical Engineering Shanghai University of Electric Power Shanghai China

ISBN: (纸本)9781839531255

The multi-objective model of distribution generation (DG) siting and sizing is proposed. The objectives consist of 1) minimizing the investment and operation and maintenance cost;2) minimizing the total active power loss of the system. The proposed model is transferred to second-order cone programming (SOCP) model based on backward forward sweep-based power flow and constraint relaxation. The CVX platform and GUROBI solver are used for the solution. The Normal Boundary Intersection (NBI) method is used for the multi-objective model in order to obtain the well distributed Pareto front solution, the result is compared with the solution from Non-dominated Sorting Genetic Algorithm (NSGA-II). The proposed model and methodology are verified with IEEE 33 example. © 2019 Institution of Engineering and Technology. All rights reserved.

关键词： second-order cone programming

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