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A novel upper bound finite-element for the limit analysis of plates and shells

EUROPEAN JOURNAL OF MECHANICS A-SOLIDS 2021年 90卷 104378-104378页

作者： Bleyer, Jeremy Univ Gustave Eiffel CNRS Lab Navier ENPC Marne La Vallee France

Shear-locking is a classical issue in displacement-based finite-element approaches for thick plates and shells. It is even more important when considering kinematic limit analysis approaches which attempt at producing an upper bound estimate of the structure collapse load. Previous locking-free finite-element discretizations for thick plates either rely on mixed approaches or approximate strain compatibility relations which inevitably loose the upper bound status of the solution or on discontinuous interpolations which are difficult to implement and have a much higher computational cost. In this contribution, we investigate the use of a simple element with a continuous quadratic displacement and a piecewise linear rotation with continuity at the element mid edges only. We show that this element can either produce strict upper-bound estimates taking into account the contribution of rotation jumps or a pseudo-upper bound when neglecting this contribution. Although the upper bound status is lost a priori in this case, numerical evidence indicate that limit loads usually converge from above and have a very good accuracy. Finally, we also use this element for shell problems and discuss in particular the formulation of strength criteria for thick shells. Illustrative applications show that the proposed element is free from any shear locking and produces very accurate limit load estimates for plate as well as shell problems.

关键词： Limit analysis Yield design Thick plates Thick shells Shear-locking conic programming

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A genetic algorithm for the close-enough traveling salesman problem with application to solar panels diagnostic reconnaissance

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COMPUTERS & OPERATIONS RESEARCH 2022年 145卷 1页

作者： Di Placido, Andrea Archetti, Claudia Cerrone, Carmine Univ Molise Dept Biosci & Terr Molise Italy ESSEC Business Sch Dept Informat Syst Decis Sci & Stat Cergy France Univ Genoa Dept Econ & Business Studies Genoa Italy

This paper addresses a variant of the classical Traveling Salesman Problem known as Close-Enough Traveling Salesman Problem . In this problem, there is a set of nodes (customers, targets), each of them associated with a region, denoted as neighborhood, that contains it. The goal is to determine the shortest tour that visits all the nodes, where a node is visited when the tour traverses or reaches the region associated with the node. We propose a genetic algorithm (GA), which uses several strategies to optimize the tour, such as 2opt, second-order cone programming, and a bisection algorithm. The proposed approach is tested on 62 benchmark instances. The results show that GA produces better or similar solutions compared to the ones produced by state-of-the-art algorithms in a reasonable computing time. Besides, GA found 32 new best solutions out of 62 instances. Furthermore, we propose different metrics to classify problem instances with the goal of detecting which problem characteristics have a larger impact on the difficulty of solving the problem. We also revised the already proposed metric, called Overlap Ratio, and correct its calculation done in previous contributions. Finally, we present a case study related to the diagnostic reconnaissance of solar panels. The case study is related to a research project developed at the University of Molise in collaboration with private IT companies. We show that the problem under study is properly modeled as a Close-Enough Traveling Salesman Problem and apply the GA to solve it, focusing on the benefits obtained by applying this solution approach.

关键词： Close-enough TSP Genetic algorithm conic programming Solar panel diagnosis

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Automating the Formulation and Resolution of Convex Variational Problems: Applications from Image Processing to Computational Mechanics

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ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE 2020年第3期46卷 27-27页

作者： Bleyer, Jeremy Univ Gustave Eiffel CNRS ENPC Lab Navier 6-8 Av Blaise Pascal F-77455 Champs Sur Marne France

Convex variational problems arise in many fields ranging from image processing to fluid and solid mechanics communities. Interesting applications usually involve non-smooth terms, which require well-designed optimization algorithms for their resolution. The present manuscript presents the Python package called fenics_optim built on top of the FEniCS finite element software, which enables one to automate the formulation and resolution of various convex variational problems. Formulating such a problem relies on FEniCS domain-specific language and the representation of convex functions, in particular, non-smooth ones, in the conic programming framework. The discrete formulation of the corresponding optimization problems hinges on the finite element discretization capabilities offered by FEniCS, while their numerical resolution is carried out by the interior-point solver Mosek. Through various illustrative examples, we show that convex optimization problems can be formulated using only a few lines of code, discretized in a very simple manner, and solved extremely efficiently.

关键词： Convex optimization conic programming finite element method FEniCS

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Limit state analysis of thin plates and slabs by a numerical pseudo-lower yield design approach

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THIN-WALLED STRUCTURES 2022年 172卷 108852-108852页

作者： Le, Canh, V Ho, Vu Q. Ho, Phuc L. H. Nguyen, Phuong H. Int Univ Dept Civil Engn Ho Chi Minh City Vietnam Vietnam Natl Univ Ho Chi Minh City Vietnam

The prediction of failure load, collapse mechanism and moment distribution at limit state plays a crucial role in structural design. For plates and slabs, numerical lower bound solutions and associated limit moment distribution are rarely reported due to the difficulties in constructing moment-based plate elements used in the static formulation. In this paper, a novel numerical limit state analysis procedure, which uses pseudo-static theorem and conic programming, is developed. The total moment fields are decomposed into parts involving a fictitious elastic moment and a self-equilibrated residual moment. Equilibrium equations for the self-equilibrated residual moment field are satisfied in a weak sense by means of the displacement -based elements. Numerical solutions are obtained rapidly with the use of second-order cone programming. Various plates and slabs with arbitrary geometries and boundary conditions are examined, providing accurately estimated collapse load factors and the moment distribution at limit state.

关键词： Limit analysis Collapse load Limit state moments conic programming

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Joint location and cost planning in maximum capture facility location under random utilities

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COMPUTERS & OPERATIONS RESEARCH 2023年第1期159卷

作者： Duong, Ngan Ha Dam, Tien Thanh Ta, Thuy Anh Mai, Tien Phenikaa Univ Dept Comp Sci ORLab Hanoi Vietnam Singapore Management Univ Sch Comp & Informat Syst Singapore Singapore

We study a joint facility location and cost planning problem in a competitive market under random utility maximization (RUM) models. The objective is to locate new facilities and make decisions on the costs (or budgets) to spend on the new facilities, aiming to maximize an expected captured customer demand, assuming that customers choose a facility among all available facilities according to a RUM model. We examine two RUM frameworks in the discrete choice literature, namely, the additive and multiplicative RUM. While the former has been widely used in facility location problems, we are the first to explore the latter in the context. We numerically show that the two RUM frameworks can well approximate each other in the context of the cost optimization problem. In addition, we show that, under the additive RUM framework, the resultant cost optimization problem becomes highly non-convex and may have several local optima. In contrast, the use of the multiplicative RUM brings several advantages to the competitive facility location problem. For instance, the cost optimization problem under the multiplicative RUM can be solved efficiently by a general convex optimization solver, or can be reformulated as a conic quadratic program and handled by a conic solver available in some off-the-shelf solvers such as CPLEX or GUROBI. Furthermore, we consider a joint location and cost optimization problem under the multiplicative RUM and propose three approaches to solve the problem, namely, an equivalent conic reformulation, a multi-cut outer-approximation algorithm, and a local search heuristic. We provide numerical experiments based on synthetic instances of various sizes to evaluate the performances of the proposed algorithms in solving the cost optimization and the joint location and cost optimization problems.

关键词： Competitive facility location Maximum capture Joint location and cost optimization Multiplicative random utility maximization Convex optimization conic programming Outer-approximation Local search heuristic

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Collapse analysis of soils by adaptive pseudo-static limit analysis

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COMPUTERS AND GEOTECHNICS 2021年 139卷 104423-104423页

作者： Le, Canh, V Ho, Phuc L. H. Ly, Huy T. Nguyen, Thanh T. Nguyen, Phuong H. Int Univ Dept Civil Engn Ho Chi Minh City Vietnam Vietnam Natl Univ Ho Chi Minh City Vietnam

The prediction of failure load factor and stress distribution at limit state plays an important role in geo-technical engineering design. This paper develops a pseudo-lower bound numerical procedure for adaptive limit analysis of geo-mechanics problems governed by the Mohr-Coulomb failure criterion. Equilibrium equations for the residual stress are enforced in a weak manner, allowing the use of displacement-based elements within the static limit analysis framework. The method does not require the construction of stress-based elements, but the stress fields at limit state can still be obtained. Non-linear failure criterion is cast in the form of a standard conic constraint, enabling the use of the highly efficient second-order cone based solvers. A refinement indicator based on Mohr-Coulomb yield function values is proposed, and adaptive mesh refinement is performed to speed up the computational progress. The proposed method is applied to various soil engineering problems, providing accurate bearing capacity together with stress distribution at limit state.

关键词： Limit analysis Pseudo-lower bound conic programming Adaptive mesh

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Prepositioning network design for humanitarian relief purposes under correlated demand uncertainty

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COMPUTERS & INDUSTRIAL ENGINEERING 2023年第1期182卷 109365页

作者： Zhang, Xun Chen, Du Shanghai Jiao Tong Univ Antai Coll Econ & Management Shanghai 200030 Peoples R China

Prepositioning relief network is an effective strategy to mitigate the impact of natural disasters and public health emergencies, such as the COVID-19 pandemic. However, designing a proper network is challenging due to limited information and, more importantly, the correlated demand uncertainty that exists among affected areas. We consider a network design problem for humanitarian relief purposes, where demand correlations exist and demand information is limited, i.e., only the mean demand and covariance matrix are known. Note that the covariance matrix can explicitly capture the correlated demand among areas. We formulate this problem as a mixed-integer two-stage distributionally robust location-inventory model, which is generally NP-hard and computationally intractable. The model is further reformulated as a mixed-integer conic problem based on copositive cones, and it is tractable with positive semidefinite relaxation. To accelerate the problem-solving process, we design an interpretable branching-and-pricing heuristic with a warm start. Both semi-case study and simulation results demonstrate that explicitly modelling demand correlation can decrease unmet demand.

关键词： Humanitarian relief network design Moments-based distributionally robust optimization conic programming

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An adaptive pseudo-lower bound limit analysis for fracture structures

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THEORETICAL AND APPLIED FRACTURE MECHANICS 2024年 129卷

作者： Do, Hien, V Ho, Phuc L. H. Le, Canh V. Nguyen-Xuan, H. Ho Chi Minh City Univ Technol & Educ Fac Mech Engn Ho Chi Minh City Vietnam Int Univ Sch Civil Engn & Management Ho Chi Minh City Vietnam Univ Core Res Ctr Disaster free & Safe Ocean City Univ Core Res Ctr Disaster Free & Safe Ocean City Busan 49315 South Korea HUTECH Univ CIRTech Inst Ho Chi Minh City Vietnam

In this study, we present a new approach to determine the limit loads of fracture structures by using the pseudo-lower bound method with adaptive quadtree meshes. A significant advantage of the pseudo-lower bound method is that calculations done with the stress field immediately solve the volumetric locking problem. Additionally, by defining quadtree meshes in the context of polygonal elements, it is possible to handle the technique of adaptive quadtree meshes, which poses a significant challenge in traditional finite elements due to the presence of hanging nodes during the refinement procedure. The von Mises yield criterion is employed, and structures containing cracks are assumed to have plane stress or plane strain conditions. The static form of the limit analysis is changed into second-order cone programming (SOCP), and the Mosek tool is then used to solve it. Numerical validation is used to illustrate the reliability and effectiveness of the proposed approach.

关键词： Limit analysis Plasticity Collapse loads conic programming Quadtree mesh refinement Fracture

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Efficient operational planning of active distribution network by embedding uncertainties and network reconfiguration

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ELECTRIC POWER SYSTEMS RESEARCH 2023年 216卷

作者： Rasheed, Shaziya Abhyankar, Abhijit R. Indian Inst Technol Delhi Dept Elect Engn New Delhi 110016 India

Growing interest in renewable energy sources (RES) is raising concern over their uncertain behavior. Installing storage devices (SDs) could be a viable solution to handle uncertainty. Integrating RES and SDs poses more challenges to the operations of the distribution utility (DU), which demands an efficient modeling technique and framework considering the uncertainties. Therefore, this paper proposes an improved and end -to-end DU framework for efficient operational planning of the active distribution system by incorporating network reconfiguration (NRC). The proposed algorithm consists of two mathematical models, which are solved sequentially to handle the binary status of the line switches and the charging/discharging status of SDs simultaneously. The objective of both models is to minimize the cost of power purchased by DU, which is further segregated into different components. A mixed integer second-order conic programming (SOCP) is used to formulate the problem and uncertainties are handled by unsymmetrical 2-point estimation method. The numerical study validates the effectiveness of the proposed algorithm by considering the different seasons and types of days. Simulation results show substantial monetary and energy savings evaluated annually, along with improved voltage levels that encourage the utilities to adopt and practice the proposed algorithm.

关键词： Active distribution system conic programming Distribution utility 2-point estimation method Network reconfiguration

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Coordinating drones with mothership vehicles: The mothership and drone routing problem with graphs

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COMPUTERS & OPERATIONS RESEARCH 2021年 136卷 105445-105445页

作者： Amorosi, Lavinia Puerto, Justo Valverde, Carlos Sapienza Univ Rome Dept Stat I-00185 Rome Italy Univ Seville Dept Stat & Operat Res Seville 41012 Spain

This paper addresses the optimization of routing problems with drones. It analyzes the coordination of one mothership with one drone to obtain optimal routes that have to visit some target objects modeled as general graphs. The goal is to minimize the overall weighted distance traveled by both vehicles while satisfying the requirements in terms of percentages of visits to targets. We discuss different approaches depending on the assumption made on the route followed by the mothership: i) the mothership can move on a continuous framework (the Euclidean plane), ii) on a connected piecewise linear polygonal chain or iii) on a general graph. In all cases, we develop exact formulations resorting to mixed integer second order cone programs that are compared on a testbed of instances to assess their performance. The high complexity of the exact methods makes it difficult to find optimal solutions in short computing time. For that reason, besides the exact formulations we also provide a tailored matheuristic algorithm that allows one to obtain high quality solutions in reasonable time. Computational experiments show the usefulness of our methods in different scenarios.

关键词： Arc routing problems Networks Drones conic programming

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