2 Benchmark Problems 1: Introduction

2011 ◽  
pp. 131-154
Keyword(s):  
Benchmark Problems

An Eight-Node Hexahedral Finite Element with Rotational DOFs for Elastoplastic Applications

2019 ◽  
Vol 11 (1) ◽  
pp. 54-66
Author(s):  
Ayoub Ayadi ◽  
Kamel Meftah ◽  
Lakhdar Sedira ◽  
Hossam Djahara
Keyword(s):  
Mathematical Model ◽  
Finite Element ◽  
Plastic Zone ◽  
Displacement Vector ◽  
Small Strain ◽  
Benchmark Problems ◽  
Plasticity Model ◽  
Vector Approximation ◽  
Calculation Code

Abstract In this paper, the earlier formulation of the eight-node hexahedral SFR8 element is extended in order to analyze material nonlinearities. This element stems from the so-called Space Fiber Rotation (SFR) concept which considers virtual rotations of a nodal fiber within the element that enhances the displacement vector approximation. The resulting mathematical model of the proposed SFR8 element and the classical associative plasticity model are implemented into a Fortran calculation code to account for small strain elastoplastic problems. The performance of this element is assessed by means of a set of nonlinear benchmark problems in which the development of the plastic zone has been investigated. The accuracy of the obtained results is principally evaluated with some reference solutions.

Model Order Reduction of Transmission Line Model

2020 ◽  
Vol 19 ◽  
Keyword(s):  
Transmission Line ◽  
Large Scale ◽  
Original System ◽  
Reduced Order Model ◽  
Benchmark Problems ◽  
Transmission Line Model ◽  
Order Model ◽  
Line Model ◽  
Reduced Order ◽  
Numerical Effort

Transmission Line model are an important role in the electrical power supply. Modeling of such system remains a challenge for simulations are necessary for designing and controlling modern power systems.In order to analyze the numerical approach for a benchmark collection Comprehensive of some needful real-world examples, which can be utilized to evaluate and compare mathematical approaches for model reduction. The approach is based on retaining the dominant modes of the system and truncation comparatively the less significant once.as the reduced order model has been derived from retaining the dominate modes of the large-scale stable system, the reduction preserves the stability. The strong demerit of the many MOR methods is that, the steady state values of the reduced order model does not match with the higher order systems. This drawback has been try to eliminated through the Different MOR method using sssMOR tools. This makes it possible for a new assessment of the error system Offered that the Observability Gramian of the original system has as soon as been thought about, an H∞ and H2 error bound can be calculated with minimal numerical effort for any minimized model attributable to The reduced order model (ROM) of a large-scale dynamical system is essential to effortlessness the study of the system utilizing approximation Algorithms. The response evaluation is considered in terms of response constraints and graphical assessments. the application of Approximation methods is offered for arising ROM of the large-scale LTI systems which consist of benchmark problems. The time response of approximated system, assessed by the proposed method, is also shown which is excellent matching of the response of original system when compared to the response of other existing approaches .

Buckling characteristics of cut-out borne composite stiffened hyperbolic paraboloid shell panel

2021 ◽  
pp. 146442072110058
Author(s):  
Sarmila Sahoo
Keyword(s):  
Finite Element ◽  
Orientation Angle ◽  
Buckling Load ◽  
Benchmark Problems ◽  
Hyperbolic Paraboloid ◽  
Element Analysis ◽  
Load Effect ◽  
Global Buckling ◽  
Fiber Orientation Angle ◽  
Shell Panel

The present study investigates buckling characteristics of cut-out borne stiffened hyperbolic paraboloid shell panel made of laminated composites using finite element analysis to evaluate the governing differential equations of global buckling of the structure. The finite element code is validated by solving benchmark problems from literature. Different parametric variations are studied to find the optimum panel buckling load. Laminations, boundary conditions, depth of stiffener and arrangement of stiffeners are found to influence the panel buckling load. Effect of different parameters like cut-out size, shell width to thickness ratio, degree of orthotropy and fiber orientation angle of the composite layers on buckling load are also studied. Parametric and comparative studies are conducted to analyze the buckling strength of composite hyperbolic paraboloid shell panel with cut-out.

scholarly journals Particle Swarm Optimization Combined with Inertia-Free Velocity and Direction Search

Electronics ◽  
2021 ◽  
Vol 10 (5) ◽  
pp. 597
Author(s):  
Kun Miao ◽  
Qian Feng ◽  
Wei Kuang
Keyword(s):  
Particle Swarm Optimization ◽  
Optimization Algorithm ◽  
Particle Swarm ◽  
Optimal Solution ◽  
Small Region ◽  
Benchmark Problems ◽  
Swarm Optimization ◽  
Local Searches ◽  
Engineering Design Problems ◽  
Direction Search

The particle swarm optimization algorithm (PSO) is a widely used swarm-based natural inspired optimization algorithm. However, it suffers search stagnation from being trapped into a sub-optimal solution in an optimization problem. This paper proposes a novel hybrid algorithm (SDPSO) to improve its performance on local searches. The algorithm merges two strategies, the static exploitation (SE, a velocity updating strategy considering inertia-free velocity), and the direction search (DS) of Rosenbrock method, into the original PSO. With this hybrid, on the one hand, extensive exploration is still maintained by PSO; on the other hand, the SE is responsible for locating a small region, and then the DS further intensifies the search. The SDPSO algorithm was implemented and tested on unconstrained benchmark problems (CEC2014) and some constrained engineering design problems. The performance of SDPSO is compared with that of other optimization algorithms, and the results show that SDPSO has a competitive performance.

scholarly journals A numerical study of fish adaption behaviors in complex environments with a deep reinforcement learning and immersed boundary–lattice Boltzmann method

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Yi Zhu ◽  
Fang-Bao Tian ◽  
John Young ◽  
James C. Liao ◽  
Joseph C. S. Lai
Keyword(s):  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Prey Capture ◽  
Numerical Study ◽  
Benchmark Problems ◽  
Immersed Boundary ◽  
Complex Environments ◽  
Fish Model ◽  
Point To Point ◽  
Boltzmann Method

AbstractFish adaption behaviors in complex environments are of great importance in improving the performance of underwater vehicles. This work presents a numerical study of the adaption behaviors of self-propelled fish in complex environments by developing a numerical framework of deep learning and immersed boundary–lattice Boltzmann method (IB–LBM). In this framework, the fish swimming in a viscous incompressible flow is simulated with an IB–LBM which is validated by conducting two benchmark problems including a uniform flow over a stationary cylinder and a self-propelled anguilliform swimming in a quiescent flow. Furthermore, a deep recurrent Q-network (DRQN) is incorporated with the IB–LBM to train the fish model to adapt its motion to optimally achieve a specific task, such as prey capture, rheotaxis and Kármán gaiting. Compared to existing learning models for fish, this work incorporates the fish position, velocity and acceleration into the state space in the DRQN; and it considers the amplitude and frequency action spaces as well as the historical effects. This framework makes use of the high computational efficiency of the IB–LBM which is of crucial importance for the effective coupling with learning algorithms. Applications of the proposed numerical framework in point-to-point swimming in quiescent flow and position holding both in a uniform stream and a Kármán vortex street demonstrate the strategies used to adapt to different situations.

scholarly journals Trust-Region Based Penalty Barrier Algorithm for Constrained Nonlinear Programming Problems: An Application of Design of Minimum Cost Canal Sections

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1551
Author(s):  
Bothina El-Sobky ◽  
Yousria Abo-Elnaga ◽  
Abd Allah A. Mousa ◽  
Mohamed A. El-Shorbagy
Keyword(s):  
Nonlinear Programming ◽  
Global Convergence ◽  
Programming Problem ◽  
Trust Region ◽  
Convergence Theory ◽  
Benchmark Problems ◽  
Nonlinear Programming Problem ◽  
Barrier Method ◽  
Starting Point ◽  
Constrained Nonlinear Programming

In this paper, a penalty method is used together with a barrier method to transform a constrained nonlinear programming problem into an unconstrained nonlinear programming problem. In the proposed approach, Newton’s method is applied to the barrier Karush–Kuhn–Tucker conditions. To ensure global convergence from any starting point, a trust-region globalization strategy is used. A global convergence theory of the penalty–barrier trust-region (PBTR) algorithm is studied under four standard assumptions. The PBTR has new features; it is simpler, has rapid convergerce, and is easy to implement. Numerical simulation was performed on some benchmark problems. The proposed algorithm was implemented to find the optimal design of a canal section for minimum water loss for a triangle cross-section application. The results are promising when compared with well-known algorithms.

scholarly journals Variable-order fracture mechanics and its application to dynamic fracture

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Sansit Patnaik ◽  
Fabio Semperlotti
Keyword(s):  
Dynamic Fracture ◽  
Crack Surface ◽  
A Priori ◽  
Computational Cost ◽  
Dynamic Crack Propagation ◽  
Benchmark Problems ◽  
Variable Order ◽  
Dynamic Crack ◽  
Brittle Solids ◽  
Complex Crack

AbstractThis study presents the formulation, the numerical solution, and the validation of a theoretical framework based on the concept of variable-order mechanics and capable of modeling dynamic fracture in brittle and quasi-brittle solids. More specifically, the reformulation of the elastodynamic problem via variable and fractional-order operators enables a unique and extremely powerful approach to model nucleation and propagation of cracks in solids under dynamic loading. The resulting dynamic fracture formulation is fully evolutionary, hence enabling the analysis of complex crack patterns without requiring any a priori assumption on the damage location and the growth path, and without using any algorithm to numerically track the evolving crack surface. The evolutionary nature of the variable-order formalism also prevents the need for additional partial differential equations to predict the evolution of the damage field, hence suggesting a conspicuous reduction in complexity and computational cost. Remarkably, the variable-order formulation is naturally capable of capturing extremely detailed features characteristic of dynamic crack propagation such as crack surface roughening as well as single and multiple branching. The accuracy and robustness of the proposed variable-order formulation are validated by comparing the results of direct numerical simulations with experimental data of typical benchmark problems available in the literature.

Application of Combined Feedforward and Feedback Controller With Shaped Input to Benchmark Problem

2010 ◽  
Vol 132 (2) ◽  
Author(s):  
Young Joo Shin ◽  
Peter H. Meckl
Keyword(s):  
Feedback Control ◽  
Control Strategy ◽  
Control Strategies ◽  
Control Design ◽  
Single Frequency ◽  
Benchmark Problems ◽  
Control Force ◽  
Benchmark Problem ◽  
Advantages And Disadvantages ◽  
Robust Control Design

Benchmark problems have been used to evaluate the performance of a variety of robust control design methodologies by many control engineers over the past 2 decades. A benchmark is a simple but meaningful problem to highlight the advantages and disadvantages of different control strategies. This paper verifies the performance of a new control strategy, which is called combined feedforward and feedback control with shaped input (CFFS), through a benchmark problem applied to a two-mass-spring system. CFFS, which consists of feedback and feedforward controllers and shaped input, can achieve high performance with a simple controller design. This control strategy has several unique characteristics. First, the shaped input is designed to extract energy from the flexible modes, which means that a simpler feedback control design based on a rigid-body model can be used. In addition, only a single frequency must be attenuated to reduce residual vibration of both masses. Second, only the dynamics between control force and the first mass need to be considered in designing both feedback and feedforward controllers. The proposed control strategy is applied to a benchmark problem and its performance is compared with that obtained using two alternative control strategies.

TABU PROGRAMMING: A NEW PROBLEM SOLVER THROUGH ADAPTIVE MEMORY PROGRAMMING OVER TREE DATA STRUCTURES

2011 ◽  
Vol 10 (02) ◽  
pp. 373-406 ◽  
Author(s):  
ABDEL-RAHMAN HEDAR ◽  
EMAD MABROUK ◽  
MASAO FUKUSHIMA
Keyword(s):  
Search Algorithm ◽  
Benchmark Problems ◽  
Problem Solver ◽  
Learning Tools ◽  
Mutation Operators ◽  
Tree Data ◽  
Tree Data Structure ◽  
Comprehensive Framework ◽  
Rate Of Success ◽  
Crossover And Mutation

Since the first appearance of the Genetic Programming (GP) algorithm, extensive theoretical and application studies on it have been conducted. Nowadays, the GP algorithm is considered one of the most important tools in Artificial Intelligence (AI). Nevertheless, several questions have been raised about the complexity of the GP algorithm and the disruption effect of the crossover and mutation operators. In this paper, the Tabu Programming (TP) algorithm is proposed to employ the search strategy of the classical Tabu Search algorithm with the tree data structure. Moreover, the TP algorithm exploits a set of local search procedures over a tree space in order to mitigate the drawbacks of the crossover and mutation operators. Extensive numerical experiments are performed to study the performance of the proposed algorithm for a set of benchmark problems. The results of those experiments show that the TP algorithm compares favorably to recent versions of the GP algorithm in terms of computational efforts and the rate of success. Finally, we present a comprehensive framework called Meta-Heuristics Programming (MHP) as general machine learning tools.

scholarly journals A Modified Harmony Search Algorithm for Solving the Dynamic Vehicle Routing Problem with Time Windows

2017 ◽  
Vol 2017 ◽  
pp. 1-13 ◽  
Author(s):  
Shifeng Chen ◽  
Rong Chen ◽  
Jian Gao
Keyword(s):  
Vehicle Routing ◽  
Vehicle Routing Problem ◽  
Search Algorithm ◽  
Time Windows ◽  
Harmony Search ◽  
Population Diversity ◽  
Benchmark Problems ◽  
Dynamic Vehicle Routing ◽  
Dynamic Vehicle Routing Problem ◽  
Routing Problem

The Vehicle Routing Problem (VRP) is a classical combinatorial optimization problem. It is usually modelled in a static fashion; however, in practice, new requests by customers arrive after the initial workday plan is in progress. In this case, routes must be replanned dynamically. This paper investigates the Dynamic Vehicle Routing Problem with Time Windows (DVRPTW) in which customers’ requests either can be known at the beginning of working day or occur dynamically over time. We propose a hybrid heuristic algorithm that combines the harmony search (HS) algorithm and the Variable Neighbourhood Descent (VND) algorithm. It uses the HS to provide global exploration capabilities and uses the VND for its local search capability. In order to prevent premature convergence of the solution, we evaluate the population diversity by using entropy. Computational results on the Lackner benchmark problems show that the proposed algorithm is competitive with the best existing algorithms from the literature.

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