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I?m stuck! How to efficiently debug computational solid mechanics models so you can enjoy the beauty of simulations

EUROPEAN JOURNAL OF MECHANICS A-SOLIDS 2023年 97卷

作者： Comellas, Ester Pelteret, Jean-Paul Bangerth, Wolfgang Univ Politecn Cataluna Dept Phys Rambla St Nebridi 2 Terrassa 08222 Barcelona Spain Colorado State Univ Dept Math Dept Geosci Ft Collins CO 80524 USA

A substantial fraction of the time that computational modellers dedicate to developing their models is actually spent trouble-shooting and debugging their code. However, how this process unfolds is seldom spoken about, maybe because it is hard to articulate as it relies mostly on the mental catalogues we have built with the experience of past failures. To help newcomers to the field of material modelling, here we attempt to fill this gap and provide a perspective on how to identify and fix mistakes in computational solid mechanics *** this aim, we describe the components that make up such a model and then identify possible sources of errors. In practice, finding mistakes is often better done by considering the symptoms of what is going wrong. As a consequence, we provide strategies to narrow down where in the model the problem may be, based on observation and a catalogue of frequent causes of observed errors. In a final section, we also discuss how one-time bug-free models can be kept bug-free in view of the fact that computational models are typically under continual *** hope that this collection of approaches and suggestions serves as a "road map"to find and fix mistakes in computational models, and more importantly, keep the problems solved so that modellers can enjoy the beauty of material modelling and simulation.

关键词： Computational solid mechanics Material modelling Constitutive model Finite element method Debugging numerical implementation numerical algorithm

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numerical simulation of vibration of composite pipelines conveying fluids with account for lumped masses

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INTERNATIONAL JOURNAL OF PRESSURE VESSELS AND PIPING 2020年第0期179卷 104034-000页

作者： Khudayarov, B. A. Komilova, Kh M. Turaev, F. Zh Aliyarov, J. A. Tashkent Inst Irrigat & Agr Mechanizat Engineers Dept Higher Math Str Kariniyazova 39 Tashkent 100000 Uzbekistan

Vibration problems of pipelines made of composite materials with account for lumped masses are considered in the paper. A mathematical model of motion of pipelines conveying fluid flow is developed based on the Winkler base with account for viscosity properties of the material of structures and pipeline bases, axial forces, internal pressure, resistance forces and lumped masses. To describe the strain processes in viscoelastic materials, the Boltzmann-Volterra integral model with weakly singular hereditary kernels is used. Using the Bubnov-Galerkin method, the problem is reduced to the study of a system of ordinary integro-differential equations. A computational algorithm is developed based on the elimination of the features of integro-differential equations with weakly singular kernels, followed by the use of quadrature formulas. The effect of rheological parameters of the pipeline material, lumped masses, internal pressure, Reynolds numbers and base parameters on the vibration of a viscoelastic pipeline conveying fluid flow is analyzed. It is revealed that the viscosity parameters of the material and the pipeline base lead to a significant change in critical flow rate. It was found that an increase in the viscosity parameter, the parameters of lumped masses and internal pressure leads to a decrease in critical flow rate. It is shown that when the lumped masses are moved away from the center along the pipeline length the vibration frequency increases.

关键词： Mathematical model Viscoelasticity Pipeline numerical algorithm Vibration Lumped mass

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Implicit Integration algorithm for Solving Evolution of Microstructural Vectors Based on Eulerian Formulation in Plane Stress Condition

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JOURNAL OF APPLIED MECHANICS-TRANSACTIONS OF THE ASME 2023年第4期90卷 041004-041004页

作者： Lee, Eun-Ho Sungkyunkwan Univ Sch Mech Engn Dept Smart Fab Technol Suwon 16419 Gyeonggi South Korea

This paper presents a mathematical formulation and implicit numerical algorithm for solving the integral of a three-dimensional momentum balance based on the inelastic evolution of microstructural vectors for thin plates in Eulerian formulation. A recent theoretical discussion (Lee and Rubin, 2020, Modeling Anisotropic Inelastic Effects in Sheet Metal Forming Using Microstructural Vectors-Part I: Theory, Int. J. Plast., 134, p. 102783. 10.1016/***.2020.102783) showed that Eulerian constitutive equation based on micro structural vectors for thin plates has the advantage of capturing the anisotropic behavior of the material axis with insensitivity to the randomness of the reference configuration. However, all the discussions were theoretically conducted only at a local material point in homogeneous deformation conditions, which do not require consideration of the momentum balance with flexible velocity gradients in a three-dimensional volume. For usability, numerical algorithms are needed to solve evolution of the microstructural vectors in the three-dimensional space. This paper presents the first numerical algorithm to solve the inelastic evolution of microstructural vectors in the Eulerian formulation. A generalized material coordinated system is matched to the microstructural vectors in a three-dimensional space by considering the Eulerian constitutive equations insensitive to the superposed rigid body motions (SRBM). numerical algorithms were then introduced to implicitly solve the nonlinear momentum balance, evolution of the microstructural vectors, and tangent modulus. The formula and numerical algorithms were validated by predicting the tension tests when the principal loading angle varied from the reference axis. The results show that the proposed numerical algorithm can describe the evolution of the microstructure based on the Eulerian formulation.

关键词： eulerian formulation momentum balance microstructural vectors inelastic deformation material axes numerical algorithm computational mechanics mechanical properties of materials plasticity

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Validity and error analysis of calculating matrix exponential function and vector product

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NONLINEAR ENGINEERING - MODELING AND APPLICATION 2024年第1期13卷

作者： Tu, Lihui Hong, Huanjie NingboTech Univ Sch Comp & Data Engn Ningbo 315100 Peoples R China

In this study, an efficient calculation method of matrix exponential function and vector product is proposed to reduce the calculation error. This method is based on the flexible exponential integral scheme;using B-series theory and two-color tree theory, the numerical series expression is obtained, and the exponential integral of the matrix exponential function is solved. By constructing a specific numerical integration scheme and analyzing its convergence under the theoretical framework of analytic semigroups, the convergence analysis of numerical schemes is studied and perfected. The numerical results show that the proposed method of matrix exponential function and vector product has a small error, which shows obvious advantages in reducing the calculation error.

关键词： matrix exponential function vector product efficient calculation numerical algorithm

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Application of fractional derivatives in a Darcy medium natural convection flow of MHD nanofluid

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AIN SHAMS ENGINEERING JOURNAL 2023年第9期14卷

作者： Khan, Mumtaz Rasheed, Amer Anwar, Muhammad Shoaib Shah, Syed Touqeer Hussain Lahore Univ Management Sci Sch Sci & Engn Dept Math Opposite Sect UDHA Lahore 54792 Pakistan Univ Jhang Dept Math Jhang 35200 Pakistan

Nanofluid thermophysical characteristics are critical for predicting heat transfer behavior. This attempt provides a computational assessment of boundary layer flow and heat transfer behavior of fractional Maxwell viscoelastic nanofluid and their hybrids over a permeable vertical surface. The effects of Lorents and buoyancy forces are also considered in the flow region. The flow problem is modeled with novel distributed order time fractional derivatives to achieve control of the flow and heat transfer. Mid-point quadrature approach is used to process the distributed order integrals, whereas nonlinear cou-pled time fractional derivatives are discretized through the finite difference method along withL1- algo- *** results shows that heat transfer rate enhanced 56:51% by enhancing the thermal Grashof number. Further, increase in nanoparticles volume fraction causes enhancement in thermal conductivity. More effects of the flow characteristic on velocity and temperature fields are shown graphically and ana-lyzed in detail. The involvement of novel distributed fractional order derivatives, and nanoparticles enhanced the importance of the simulated results, which can be helpful to effectively control related thermal engineering issues, like temperature management in internal combustion engines, cooling devices, and heat exchangers. (c) 2022 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Ain Shams Uni-versity. This is an open access article under the CC BY-NC-ND license (http://***/licenses/ by-nc-nd/4.0/).

关键词： Distributed order fractional derivative Nanofluid Natural Convection Darcy medium numerical algorithm

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Fractional mathematical modeling of the Stuxnet virus along with an optimal control problem

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AIN SHAMS ENGINEERING JOURNAL 2023年第7期14卷

作者： Kumar, Pushpendra Govindaraj, V. Erturk, Vedat Suat Nisar, Kottakkaran Sooppy Inc, Mustafa Natl Inst Technol Puducherry Dept Math Karaikal 609609 India Fac Arts & Sci Ondokuz Mayis Univ Dept Math TR-55200 Samsun Turkiye Prince Sattam bin Abdulaziz Univ Coll Arts & Sci Dept Math Wadi Aldawaser 11991 Saudi Arabia Firat Univ Sci Fac Dept Math TR-23119 Elazig Turkiye China Med Univ China Med Univ Hosp Dept Med Res Taichung Taiwan

In this digital, internet-based world, it is not new to face cyber attacks from time to time. A number of heavy viruses have been made by hackers, and they have successfully given big losses to our systems. In the family of these viruses, the Stuxnet virus is a well-known name. Stuxnet is a very dangerous virus that probably targets the control systems of our industry. The main source of this virus can be an infected USB drive or flash drive. In this research paper, we study a mathematical model to define the dynamical structure or the effects of the Stuxnet virus on our computer systems. To study the given dynamics, we use a modified version of the Caputo-type fractional derivative, which can be used as an old Caputo derivative by fixing some slight changes, which is an advantage of this study. We demonstrate that the given fractional Caputo-type dynamical model has a unique solution using fixed point theory. We derive the solution of the proposed non-linear non-classical model with the application of a recent version of the Predictor-Corrector scheme. We analyze various graphs at different values of the arrival rate of new computers, damage rate, virus transmission rate, and natural removal rate. In the graphical interpretations, we verify the values of fractional orders and simulate 2-D and 3-D graphics to understand the dynamics clearly. The major novelty of this study is that we formulate the optimal control problem and its important consequences both theoretically and mathematically, which can be further extended graphically. The main contribution of this research work is to provide some novel results on the Stuxnet virus dynamics and explore the uses of fractional derivatives in computer science. The given methodology is effective, fully novel, and very easy to understand. (c) 2022 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Ain Shams University.

关键词： Fractional mathematical modelling Stuxnet virus Computer networks Industrial systems numerical algorithm Modified version of Caputo fractional derivative

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Shallow water modeling of wave-structure interaction over irregular bottom?

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OCEAN ENGINEERING 2023年 267卷

作者： Gusev, Oleg Igorevich Khakimzyanov, Gayaz Salimovich Skiba, Vasiliy Savelievich Chubarov, Leonid Borisovich Fed Res Ctr Informat & Computat Technol Acad MA Lavrentiev Ave 6 Novosibirsk 630090 Novosibirsk Russia Novosibirsk State Univ 1 Pirogova str Novosibirsk 630090 Novosibirsk Russia

This paper describes the results from a numerical simulation of long surface waves interaction with fixed and partially immersed structure located over irregular bottom. The topic is connected with risk of critical wave impact on structures placed in the coastal waters of seas and oceans. The wave-structure interaction is simulated within the framework of a hierarchy of mathematical models, including the model of potential flows of an ideal fluid, a fully nonlinear dispersive and dispersionless shallow water models. The numerical algorithm for the dispersive model is described in detail. The obtained results show that rectangular cutout in the structure bottom reduces the amplitude of the reflected wave and increases that of the transmitted one;the basin bottom irregularity plays the most important role when located directly under the body. The protrusion behind the body may slightly decrease the wave force, and it significantly increases the force at other locations. Generally, the results obtained by the dispersive model correspond well with those of potential model, while the dispersionless model often significantly overestimates the wave force and amplitude of the reflected wave.

关键词： Long surface wave Partially immersed structure Irregular bottom Shallow water Nonlinear dispersion numerical algorithm

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An iterative numerical algorithm for modeling a class of Wiener nonlinear systems

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APPLIED MATHEMATICS LETTERS 2013年第4期26卷 487-493页

作者： Xiong, Weili Ma, Junxia Ding, Ruifeng Jiangnan Univ Minist Educ Key Lab Adv Proc Control Light Ind Wuxi 214122 Peoples R China Jiangnan Univ Sch Internet Things Engn Wuxi 214122 Peoples R China

This letter presents an iterative estimation algorithm for modeling a class of output nonlinear systems. The basic idea is to derive an estimation model and to solve an optimization problem using the gradient search. The proposed iterative numerical algorithm can estimate the parameters of a class of Wiener nonlinear systems from input-output measurement data. The proposed algorithm has faster convergence rates compared with the stochastic gradient algorithm. The numerical simulation results indicate that the proposed algorithm works well. (C) 2012 Elsevier Ltd. All rights reserved.

关键词： System modeling numerical algorithm Gradient search Parameter estimation Wiener nonlinear system

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numerical calculation of the intercept factor for parabolic trough solar collector with secondary mirror

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ENERGY 2021年 233卷 121175-121175页

作者： Wu, Shaobing Tang, Runsheng Wang, Changmei Yunnan Normal Univ Educ Minist Key Lab Adv Technol & Preparat Renewable Energy M Kunming 650500 Yunnan Peoples R China Yunnan Police Coll Inst Informat Secur Kunming 650223 Yunnan Peoples R China

The intercept factor is the most complex parameter involved in determining the optical efficiency of a parabolic trough solar collector. A numerical algorithm method was proposed to calculate the intercept factors of a parabolic trough solar collector using the Gauss error function and a Python program. The results indicate that the intercept factors can be calculated quickly and conveniently using the proposed method. We also introduced a numerical solution to calculate the intercept factor of the parabolic trough solar collector, which can provide accurate interception factors for different types of secondary reflection concentrators. The new analytical method was validated and benchmarked against a Gauss error function and Python program, demonstrating that the deviations were below 0.0015% for most cases studied. The primary goals of this study were to determine an appropriate numerical method to solve the intercept factors and errors for different secondary mirror types and to incorporate the selected intercept factor calculation into a secondary mirror design for a parabolic trough solar collector under various conditions. (c) 2021 Elsevier Ltd. All rights reserved.

关键词： Parabolic trough collector Intercept factor Secondary mirror numerical algorithm

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numerical implementation, comparison and validation of a pressure dependent model for polymer composites

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INTERNATIONAL JOURNAL OF MECHANICAL SCIENCES 2021年 212卷 106818-106818页

作者： Xu, Kailong Chen, Wei Liu, Lulu Zhao, Zhenhua Luo, Gang Nanjing Univ Aeronaut & Astronaut Coll Energy & Power Engn Jiangsu Prov Key Lab Aerosp Power Syst Nanjing 210016 Peoples R China Nanjing Univ Aeronaut & Astronaut State Key Lab Mech & Control Mech Struct Nanjing 210016 Peoples R China

A pressure-dependent elastoplastic damage constitutive model for polymer composites is established, in which the Implicit and Explicit numerical algorithm has been implemented in ABAQUS/Standard in terms of elastoplastic phase with the aid of UMAT. The off-axis tension/compression tests for T800H/3633,T800S/3900-2B carbon/epoxy laminated composites, and quasi-isotropic compression tests for T800H/3633 laminated composites, have been simulated, in order to validate the efficiencies and accuracies of two algorithms. Additionally, the open-hole compression simulation is employed to analyze the progressive failure of T800H/3633 laminated composites. Compared with the Implicit and Explicit algorithm based the elasto-plastic model, the Explicit algorithm is recommended based on the computational efficiency on the premise of ensuring the numerical convergence, which may be extended to the large-scale engineering applications either statics or dynamics. Furthermore, the open-hole compression simulation of T800H/3633 composites shows the developed elastoplastic damage model can predict well the stiffness and strength properties of the specimen. The failure mode and deformation of the open-hole specimen of T800H/3633 composites are also briefly discussed.

关键词： Polymer composites numerical algorithm Elasto-plastic damage UMAT Pressure-dependent

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