Computational Mechanics

This paper presents the general purpose framework Peano for the solution of partial differential equations (PDE) on adaptive Cartesian grids. The strict structuredness and inherent multilevel property of these grids allows for very low memory requirements, efficient (in terms of hardware performance) implementations of parallel multigrid solvers on dynamically adaptive grids, and arbitrary spatial dimensions. This combination of advantages distinguishes Peano from other PDE frameworks. We describe shortly the underlying octree-like grid type and its most important properties. The main part of the paper shows the framework concept of Peano and the implementation of a Navier-Stokes solver as one of the main currently implemented application examples. Various results ranging from hardware and numerical performance to concrete application scenarios close the contribution.

Attention is here focused on the implementation of a coupled BEM–FEM procedure employing the BE method for the modelling of the near-crack region and the FEM for the far-field, where no singularities in the stress field are expected to arise. The symmetric variational version of the BE method is utilized, allowing to obtain a final linear system endowed with a symmetric matrix. With respect to 3D linear elastic fracture mechanics, the code developed is used to evaluate stress intensity factors for some benchmarks and simulate fracture propagation.

A dislocation density-based crystalline plasticity formulation, specialized finite-element techniques, and rational crystallographic orientation relations were used to predict and characterize the failure modes associated with the high strain rate behavior of aluminum layered composites. Two alloy layers, a high strength alloy, aluminum 2195, and an aluminum alloy 2139, with high toughness, were modeled with representative microstructures that included precipitates, dispersed particles, and different grain boundary distributions. Different layer arrangements were investigated for high strain rate applications and the optimal arrangement was with the high toughness 2139 layer on the bottom, which provided extensive shear strain localization, and the high strength 2195 layer on the top for high strength resistance The layer thickness of the bottom high toughness layer also affected the bending behavior of the roll-bonded interface and the potential delamination of the layers. Shear strain localization, dynamic cracking, and delamination are the mutually competing failure mechanisms for the layered metallic composite, and control of these failure modes can be used to optimize behavior for high strain rate applications.

On the basis of continuum mechanics, a rate dependent directional damage model for fibred materials with application to soft biological tissues is presented. The structural model is formulated using the concept of internal variables that provides a very general description of materials involving irreversible effects. Continuum damage mechanics is used to describe the softening behavior of soft tissues under large deformation. To account for the rate dependency and to regularize the localization problems associated with strain-softening, a viscous damage mechanism is presented in this paper in decoupled form for matrix and fibers. The numerical implementation in the context of the finite element method is discussed in detail. In order to show the performance of the constitutive model and its algorithmic counterpart some simple examples are included. Results show that the model is able to capture the typical stress–strain behavior observed in fibrous soft tissues and appear to confirm the soundness of the proposed formulation.

We use the meshless local Bubnov–Galerkin (MLPG6) formulation to analyze free and forced vibrations of a segmented bar. Three different techniques are employed to satisfy the continuity of the axial stress at the interface between two materials: Lagrange multipliers, jump functions, and modified moving least square basis functions with discontinuous derivatives. The essential boundary conditions are satisfied in all cases by the method of Lagrange multipliers. The related mixed semidiscrete formulations are shown to be stable, ...

The turning of hardened steels has been applied in many cases in production. It is an important process because all manufacturers are continu¬ally seeking ways to manufacture their parts with lower cost, higher quality, rapid setups, lower investment, and smaller tooling inventory while eliminating non-value added activities. Currently, the most important problem is concerned with the properties of the surface finish. This paper investigates the effect on surface finish and tool wear in a continuous dry turning of hardened steel when using a ceramic wiper tools. This report describes about the hard turning of AISI 4340 alloy steel by varying various parameters. The hard turning parameters are: Cutting speed, Feed and Depth of cut. The main objectives of this project, study the effect of parameters such as cutting speed, feed, depth of cut on surface roughness, tool wear and cutting force during the hard turning of AISI 4340alloy steel using ceramic wiper tool and the effect of various process parameters on hard tuning and optimize the cutting parameters. The dry turning experiments were performed on hardened AISI 4340 steel material using ceramic wiper tool .AISI 4340 steel having hardness: 48 (48–52) HRC was used.

Keywords— Hard turning, surface roughness, taguchi’s method.

 A differential quadrature element method (DQEM) based on first order shear deformation theory is developed for free vibration analysis of non-uniform beams on elastic foundations. By decomposing the system into a series of sub-domains or elements, any discontinuity in loading, geometry, material properties, and even elastic foundations can be considered conveniently. Using this method, the vibration analysis of general beam-like structures is to be studied. The governing equations of each element, natural compatibility conditions at the interface of two adjacent elements and the external boundary conditions are developed in a systematic manner, using Hamilton's principle. The present DQEM is to be implemented to Timoshenko beams resting on partially supported elastic foundations with various types of boundary conditions under the action of axial loading. The general versality, accuracy, and efficiency of the presented DQEM are demonstrated having solved different examples and compared to the exact or other numerical procedure solutions.

Using the Stochastic Finite Element Method (SFEM) to perform reliability analysis of the free vibration of composite plates with material and fabrication uncertainties has received much attention lately. In this work the stochastic analysis is performed using the First-Order Reliability Method (FORM-method 2) and the Second-Order Reliability Method (SORM). The basic random variables include laminae stiffness properties and material density, as well as the randomness in ply orientation angles. Modeling of the composite behavior utilizes a nine-noded isoparametric Lagrangian element based on the third-order shear deformation theory. Calculating the eigenvectors at the mean values of the variables proves to be a reasonable simplification which significantly increases solution speed. The stochastic finite element code is validated using comparisons with results of Monte Carlo simulation technique with importance sampling. Results show that SORM is an excellent rapid tool in the stochastic analysis of free vibration of composite plates, when compared to the slower Monte Carlo simulation techniques.

Currently, the gantry crane in LAPAN Garut still uses steel material. The steel material is protected using a coating to minimize the impact of corrosion. However, this method is less efficient, considering the corrosion rate in LAPAN Garut is very high because it is located on the coast of Cilauteureun. It also creates problems in terms of maintenance because it has to be done regularly and periodically repainting. In addition, not all equipment is available maintenance funds every year. The objective of this paper is to design and analyze the stress of a gantry crane with a capacity of 9 tons using Aluminum 6061 material. The material used is three units of JIS G 3192 H standard frame (I-shape) with a size of 150 x 150 x 7 mm, four units of JIS G 3466 frame (square profile) with a size of 150 x 150 x 6 mm, and four units of JIS G 3466 frame (square profile) with a size of 125 x 125 x 6 mm. Finite element analysis is performed using Autodesk Inventor Professional 2017 software. The simulation results show that the gantry crane has a mass, von Mises stress, deformation, and safety factors respectively at 165.36 kg; 132.9 MPa; 13.67 mm; and 2.07.

Im Laufe der letzten zehn Jahre sind in Zusammenarbeit zwischen Schwab Verkehrstechnik AG in Schaffhausen und der Züricher Hochschule Winterthur hydraulische Stoss-und Zugvorrichtungen für Güter-und Personenzüge entwickelt worden. Dank den Simulationsmodellen konnte die Zahl der Prototypen sehr klein gehalten werden. In den ersten Jahren ist das systemdynamische Werkzeug STELLA, danach Matlab/Simulink und zuletzt Modelica eingesetzt worden. Trotz Umfang und Erfolg dieses Unternehmens handelt es sich eigentlich um ein " Abfallprodukt " didaktischer Bemühungen, der Entwicklung der Physik der dynamischen Systeme.

The loading of a granular material induces anisotropies of the particle arrangement (fabric) and of the material’s strength, incremental stiffness, and permeability. Thirteen measures of fabric anisotropy are developed, which are arranged in four categories: as preferred orientations of the particle bodies, the particle surfaces, the contact normals, and the void space. Anisotropy of the voids is described through image analysis and with Minkowski tensors. The thirteen measures of anisotropy change during loading, as determined with three-dimensional discrete element simulations of biaxial plane strain compression with constant mean stress. Assemblies with four different particle shapes were simulated. The measures of contact orientation are the most responsive to loading, and they change greatly at small strains, whereas the other measures lag the loading process and continue to change beyond the state of peak stress and even after the deviatoric stress has nearly reached a steady state. The paper implements a methodology for characterizing the incremental stiffness of a granular assembly during biaxial loading, with orthotropic loading increments that preserve the principal axes of the fabric and stiffness tensors. The linear part of the hypoplastic tangential stiffness is monitored with oedometric loading increments. This stiffness increases in the direction of the initial compressive loading but decreases in the direction of extension. Anisotropy of this stiffness is closely correlated with a particular measure of the contact fabric. Permeabilities are measured in three directions with lattice Boltzmann methods at various stages of loading and for assemblies with four particle shapes. Effective permeability is negatively correlated with the directional mean free path and is positively correlated with pore width, indicating that the anisotropy of effective permeability induced by loading is produced by changes in the directional hydraulic radius.

This paper deals with the applications of stochastic spectral methods for structural topology optimization in the presence of uncertainties. A non-intrusive polynomial chaos expansion is integrated into a topology optimization algorithm to calculate low-order statistical moments of the mechanical–mathematical model response. This procedure, known as robust topology optimization, can optimize the mean of the compliance while simultaneously minimizing its standard deviation. In order to address possible variabilities in the loads applied to the mechanical system of interest, magnitude and direction of the external forces are assumed to be uncertain. In this probabilistic framework, forces are described as a random field or a set of random variables. Representation of the random objects and propagation of load uncertainties through the model are efficiently done through Karhunen–Loève and polynomial chaos expansions. We take advantage of using polygonal elements, which have been shown to be effective in suppressing checkerboard patterns and reducing mesh dependency in the solution of topology optimization problems. Accuracy and applicability of the proposed methodology are demonstrated by means of several topology optimization examples. The obtained results, which are in excellent agreement with reference solutions computed via Monte Carlo method, show that load uncertainties play an important role in optimal design of structural systems, so that they must be taken into account to ensure a reliable optimization process.

A force-based fiber beam-column element is proposed for the capacity assessment of frame structures under high shear. The proposed element is suitable for the performance assessment of large scale steel structures, which are not flexure-dominated. The element formulation follows the assumptions of the Timoshenko beam theory, while its kinematics are obtained through the natural-mode method. The element state-determination phase, instead of uniaxial material laws, typically associated with fiber elements, is based on a three-dimensional law taking into consideration the interaction between axial, bending, shear and torsion. Numerical examples are presented confirming the accuracy and the computational efficiency of the proposed formulation under monotonic, cyclic and dynamic/seismic loading. Compared to experimental results and the results of detailed finite element models, excellent agreement is achieved.

One of the successful approaches to model the time-dependent behaviour of elastomers is proposed by Bergström and Boyce (JMPS 46:931–954, 1998). The model is micromechanically inspired from the relaxation of a single entangled chain in a polymer gel matrix. Although the theory of inelasticity based on multiplicative decomposition of the deformation gradient is well established, the complexity of the nonlinear evolution law as well as the nonlinear equilibrium and non-equilibrium material response necessitates a precise description of the algorithmic setting. This contribution presents for the first time a novel numerical implementation of the Bergström–Boyce model in the context of finite element analysis and elaborates theoretical aspects of the model. The thermodynamical consistency of the evolution law is proven and a parameter study with respect to the material parameters has been carried out. The agreement of the model with the recent experimental data is investigated.

Activated neuronal groups typically engage in rhythmic synchronization in the gamma-frequency range (30–100 Hz). Experimental and modeling studies demonstrate that each gamma cycle is framed by synchronized spiking of inhibitory interneurons. Here, we review evidence suggesting that the resulting rhythmic network inhibition interacts with excitatory input to pyramidal cells such that the more excited cells fire earlier in the gamma cycle. Thus, the amplitude of excitatory drive is recoded into phase values of discharges relative to the gamma cycle. This recoding enables transmission and read out of amplitude information within a single gamma cycle without requiring rate integration. Furthermore, variation of phase relations can be exploited to facilitate or inhibit exchange of information between oscillating cell assemblies. The gamma cycle could thus serve as a fundamental computational mechanism for the implementation of a temporal coding scheme that enables fast processing and flexible routing of activity, supporting fast selection and binding of distributed responses. This review is part of the INMED/TINS special issue Physiogenic and pathogenic oscillations: the beauty and the beast, based on presentations at the annual INMED/TINS symposium (http://inmednet.com).

Preface

This book collects most of the lecture notes I have developed and I have been using in a course on Continuum Mechanics for the Master of Science Course on Computational Mechanics and the Master Course on Numerical Methods in Engineering taught at the Barcelona School of Civil Engineering, Technical University of Catalonia, UPC BarcelonaTech, in Barcelona, Spain.
When the Master of Science Course on Computational Mechanics began, the Director of the Master asked me to take charge and to develop a course on Continuum Mechanics. The course should have around 40-45 class hours and  would be scheduled to be taught in the first semester of the first year of the Master. I embarked on this path by designing and developing what has been my flagship and signature course on Continuum Mechanics.

This book has been designed as an updated and expanded version of my Continuum Mechanics lecture notes and has been structured in 10 chapters. As an introduction, Chapters 1 and 2 are devoted to Tensor Algebra and Tensor Analysis. Part I of the book includes the next 3 chapters. Chapter 3 is devoted to Nonlinear Kinematics, Chapter 4 deals with Stresses, and Chapter 5 addresses the Fundamental Conservation/Balance Laws. Part II includes the next 4 chapters. Chapter 6 is devoted to Finite Deformation Hyperelasticity, Chapter 7 to Finite Deformation Plasticity, Chapter 8 to Finite Deformation Coupled Thermoplasticity, and Chapter 9 to Finite Deformation Contact Mechanics. The last chapter, Chapter 10, deals with Variational Methods in Solid Mechanics, including coupled thermoplasticity and contact problems.

The common feature of Part I is that all the contents are always valid, regardless of the material, be it solid or fluid. At the end of Part I we should be able to set up in local spatial/material form, the fundamental governing equations and inequalities for a Continuum Mechanics problem. The fundamental governing equations and inequalities arise from the fundamental conservation/balance principles and from the constraints imposed by the second law of thermodynamics, and are valid for any material. At the end of Part I, we should be able to check how many governing equations we have, and how many unknowns are involved in those governing equations and inequalities. We will realize that we have more unknowns than equations. So, to have a well posed problem, we would need to add a number of equations, so that the final number of equations is equal to the number of unknowns. The equations we should add would depend on the material and for some particular material models will be considered in Part II of the book.

Part II of the book is devoted to presenting some nonlinear constitutive models for Nonlinear Solid Mechanics, including Finite Deformation Hyperelasticity, Finite Deformation Plasticity, Finite Deformation Coupled Thermoplasticity, and Finite Deformation Contact Mechanics. Constitutive equations are derived within a thermodynamically consistent framework. Finite deformation elastoplasticity models are based on the multiplicative decomposition of the deformation gradient and the notion of an intermediate configuration. Different formulations based on the intermediate configuration, the current or spatial configuration, and the material configuration, are considered. The last chapter is devoted to Variational Methods in Solid Mechanics, a fundamental topic in Computational Mechanics.

The book may be used as a text book for a Master’s course on Nonlinear Continuum Mechanics for graduate students in Civil, Mechanical or Aerospace Engineering, Applied Mathematics or Applied Physics, with interest in Continuum Mechanics and Computational Mechanics.

I am grateful to my colleagues and friends Jean-Philippe Ponthot at University of Liege, and Mariana Seabra at University of Porto for their careful reading of the manuscript.

I hope you enjoy reading the book as much as I have enjoyed writing it.

Carlos Agelet de Saracibar
Barcelona, Spain, 22 March 2022

ABSTRACT

This study focuses on the deformation behaviour of organic materials under a drop case. A Golden Delicious
apple was chosen as the sample organic material. A three-dimensional (3D) scanner, high speed
camera and finite element method (FEM) simulations were utilised to investigate drop case deformation
events of the organic material. In total, 22 steps after impact were set up in the simulation by comparing
high speed camera screen steps. Maximum equivalent stress of 0.416 MPa and maximum contact force
(resultant normal force from rigid plane at impact) of 250.980 N were obtained from simulation results.
Visual investigations and simulation results relating to deformations observed under the drop case,
agreed well. This study contributes to further our understanding of fruit and vegetable damage/deformation
by using computer aided engineering applications.


Keywords:

Drop test, Finite element method, Organic materials, Golden Delicious apple

A center stand is a device on a bicycle or motorcycle that allows the bike to be kept upright without leaning against another object or the aid of a person. A center stand is usually a made of metal that comes down from the frame and makes contact with the ground. It is generally located in the middle of the bike or towards the rear. Some touring bicycles have two: one at the rear, and a second in the front. A new standing device which replaces center stand using external power which reduces human effort is being proposed. An existing center stand is modified by using electrical and mechanical components at optimum cost. The different mechanical parameters of stand are analyzed using Computational software and the best model is selected for fabrication.

Studying heat transfer through computational methods is increasing in importance, and this volume is right in step with the times. It presents the fundamentals for computational work and offers a wide range of methods useful with basic processes and applied problems of heat transfer ...

Course is intended for Undergraduate Mechanical Engineering students involving on Understanding Kinematics of Mechanisms, simple mechanism study,  Velocity and acceleration analysis of mechanisms, Problem solving on Belt drives, Rope drives, Using Graphical analysis of generating Cam Profiles, Study of all types of gear drives and problem solving on spur gears, study on control and regulation of Governors.

In this paper, a twenty storey multi-storey rigid frame was subjected to a uniformly distributed wind pressure load of 5.05 KN/m 2. The deflection behaviour of the rigid frame was investigated using manual method, and computer based method (finite element analysis). From the results of the two methods employed, it is observed that the value obtained from manual method gave a lower value for the top deflection of the building. The maximum deflection from finite element was 60.441mm, while the result from manual calculation was 55.524mm. This shows that the result from finite element analysis to manual method was about 8.135% greater than that of the manual method. However, this offers a great insight for the speedy check of computer based processes and results.