Relevant bibliographies by topics / Linear elastic deformation

Academic literature on the topic 'Linear elastic deformation'

Author: Grafiati
Published: 10 December 2022
Last updated: 29 January 2023

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Journal articles on the topic "Linear elastic deformation"

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Fu, Bo-Ye, and Li-Yun Fu. "Poro-acoustoelasticity with compliant pores for fluid-saturated rocks." GEOPHYSICS 83, no. 3 (May 1, 2018): WC1—WC14. http://dx.doi.org/10.1190/geo2017-0423.1.

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Stress-induced influences on elastic wave velocities include elastic and inelastic behaviors. In general, deformation of rocks is primarily linear elastic for small-magnitude stresses; such behavior can be predicted by the conventional poro-acoustoelasticity theory. On the contrary, large-magnitude stresses induce linear elastic deformation in stiff pores and rock grains and nonlinear elastic deformation in compliant pores. Conventional poro-acoustoelasticity combines the kinetic and strain energy functions via the Lagrange equation. This theory reveals the strain energy transformation of the stiff pores and rock grains for velocity variation. The dual-porosity model uses a semiempirical equation to express the influence of the nonlinear elastic deformation of compliant pores on velocity variations; however, this model does not include the strain energy transformation of compliant pores. We incorporate the dual-porosity model into the conventional poro-acoustoelasticity theory to account for linear and nonlinear elastic deformations through the strain energy transformation of rock grains, stiff pores, and compliant pores. We determine that the work of the loading stress is transformed into two parts: the strain energy for the linear elastic deformation of rock grains and stiff pores and the nonlinear elastic deformation of compliant pores. On applying this theory to ultrasonic measurements under different differential pressures for a saturated sandstone sample, we see that the resulting solution of stress-associated velocity variations is more precise than that obtained using the conventional poro-acoustoelasticity theory, especially in the low-effective-pressure regime.
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Müller, Tobias M., and Pratap N. Sahay. "Elastic potential energy in linear poroelasticity." GEOPHYSICS 84, no. 4 (July 1, 2019): W1—W20. http://dx.doi.org/10.1190/geo2018-0216.1.

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Biot’s theory of linear poroelasticity dates back to the mid-20th century and is still currently the backbone for understanding deformation processes in fluid-saturated porous rocks with applications in geomechanics, hydrogeology, reservoir engineering, and exploration geophysics. Therein, the elastic potential energy is the critical concept to derive the macroscopic stress tensors and constitutive equations. The potential energy is taken as the single function that forms an exact differential in macroscopic strains of the solid and fluid phases. This choice intrinsically implies a reciprocal interaction between the compressive stresses of the two phases. However, it leaves out the possibility that the phases can interact in a nonreciprocal manner, which is sometimes inferred from experimental observations. The limited scope of the Biot theory is overcome by upscaling the pore-scale governing equations using volume averaging aided by the physical argument that the conservation of mass, momentum, energy, and principle of equivalence must hold at all scales. This upscaling reveals that the proper measures of deformations are not only the deformation gradient terms but also a porosity change term that accounts for the emergent pore-interface kinematics at the macroscale. It also reveals that the elastic potential energy of a porocontinuum is the sum of the potential energies of the solid and fluid phases, which are functions of their so-defined respective measure of deformation only. Such potential energy is no longer limited to only the reciprocal interaction of the compressive stresses of the phases, but it enables us to capture nonreciprocal interactions still within the realm of linearity. A nonreciprocal interaction arises whenever the potential energy density is not uniformly distributed at the pore scale but partially localized in the vicinity of pore interfaces or within the bulk part of the phases. A direct consequence is that the coupling coefficients in the linear constitutive equations are expected to be different.
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Golovina, Natalya Ya. "Modeling the Stress-Strain Curve of Elastic-Plastic Materials." Solid State Phenomena 316 (April 2021): 936–41. http://dx.doi.org/10.4028/www.scientific.net/ssp.316.936.

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The work is devoted to the formulation of mathematical models of plastic materials without hardening. A functional is proposed, the requirement of stationarity of which made it possible to formulate the differential equation of stress as a function of deformation. On the linear deformation section, a second-order functional is proposed; on the non-linear deformation section, a fourth-order functional is proposed. A range of boundary value problems is formulated, that ensure the continuity of the function at the boundary of the linear and non-linear sections of the deformation curve. The theoretical strain curve was compared with the samples of experimental points for materials: St3sp steel, steel 35, steel 20HGR, steel 08Kh18N10, titanium alloy VT6, aluminum alloy D16, steel 30KhGSN2A, steel 40Kh2N2MA, and showed a good agreement with the experiment. Thus, a variational model is constructed, that allows one to construct curve deformations of various physically non-linear materials, which will allow one to construct further mathematical models of the resource of such materials.
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Lu, Yi, Cong Cong, Chen Liwei, and Peng Wang. "Solving elastic deformation of some parallel manipulators with linear active legs using computer-aided design variation geometry." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 227, no. 12 (February 19, 2013): 2810–24. http://dx.doi.org/10.1177/0954406213478374.

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It has been a significant and challenging issue to determine the elastic deformation of parallel manipulators for their precision analysis and control. A new method is proposed and studied for solving the elastic deformation of some parallel manipulators with linear active legs using computer-aided design variation geometry. First, an original simulation mechanism of a parallel manipulator is constructed; each of the vectors in the force transformation matrix of the parallel manipulators is constructed by this simulation mechanism. The active/constrained wrench and their pose are determined based on the Newton–Euler formulation. Second, the elastic deformed dimensions of the active legs are determined based on the elastic deformation equation and the active/constrained wrench. Third, a new simulation mechanism of this parallel manipulator is constructed by replacing the original dimensions of active legs with the deformed dimensions of active legs and the elastic deformations of parallel manipulators are solved using the pose difference between the original and new simulation mechanisms. Finally, two parallel manipulators are illustrated and their elastic deformations are solved and verified by both analytic approach and finite element method.
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Keller, Joseph B. "Finite Elastic Deformation Governed by Linear Equations." Journal of Applied Mechanics 53, no. 4 (December 1, 1986): 819–20. http://dx.doi.org/10.1115/1.3171864.

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It is observed that the equations of motion governing finite elastic deformation are linear if and only if the Piola-Kirchhoff stress tensor is linear in the deformation gradient. Then the three components of displacement satisfy uncoupled linear equations. These equations are used to solve some problems of finite deformation.
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AZEGAMI, Hideyuki, Akihiro SATAKE, and Kazumi KODAMA. "Creation of Mechanism Using Linear Elastic Deformation." Proceedings of the JSME annual meeting 2000.1 (2000): 133–34. http://dx.doi.org/10.1299/jsmemecjo.2000.1.0_133.

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Silling, S. A. "Linear Elastic Materials Sustaining a Prescribed Deformation." Journal of Applied Mechanics 56, no. 2 (June 1, 1989): 479–81. http://dx.doi.org/10.1115/1.3176110.

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Lu, Yi, Zhuohong Dai, and Yang Lu. "Precise Stiffness and Elastic Deformations of Serial–Parallel Manipulators by Considering Inertial Wrench of Moving Links." Robotica 38, no. 12 (January 31, 2020): 2204–20. http://dx.doi.org/10.1017/s0263574720000041.

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SUMMARYA general serial–parallel manipulator connected in series by two different parallel manipulators with linear active legs is constructed. Its precise stiffness and elastic deformations are studied systematically. Its unified precise stiffness and precise elastic deformation models are established by considering both the moving links inertial wrench and the dynamic active/constrained wrench. A 3SPR+3RPS-type serial–parallel manipulator is illustrated for solving its precise stiffness and precise elastic deformation. The derived formulae of the precise stiffness and the precise elastic deformations of the general serial–parallel manipulator are verified by the theoretical solutions of the 3SPR+3RPS serial–parallel manipulator.
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Song, Jialin, Yang Lu, Yongli Wang, and Yi Lu. "Stiffness and Elastic Deformation of 4-DoF Parallel Manipulator with Three Asymmetrical Legs for Supporting Helicopter Rotor." Journal of Robotics 2020 (February 1, 2020): 1–11. http://dx.doi.org/10.1155/2020/8571318.

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The stiffness and elastic deformation of a 4-DoF parallel manipulator with three asymmetrical legs are studied systematically for supporting helicopter rotor. First, a 4-DoF 2SPS + RRPR type parallel manipulator with two linear SPS type legs and one RRPR type composite leg is constructed and its constraint characteristics are analyzed. Second, the formulas for solving the elastic deformation and the stiffness matrix of the above mentioned three asymmetrical legs are derived. Third, the formulas for solving the total stiffness matrix and the elastic deformation of this manipulator are derived and analyzed. Finally, its finite element model is constructed and its elastic deformations are solved using both the derived theoretical formulas and the finite element model. The theoretical solutions of the elastic deformations are verified by that of the finite element model.
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Domichev, K. "MODELING THE BEHAVIOR OF THE PHYSICAL AND GEOMETRIC NON-LINEAR FUNCTIONAL HETEROGENEOUS MATERIALS." Innovative Solution in Modern Science 1, no. 45 (February 17, 2021): 82. http://dx.doi.org/10.26886/2414-634x.1(45)2021.5.

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The work is devoted to the problem of modeling the behavior of functionally inhomogeneous materials with the properties of pseudo-elastic-plasticity under complex loads, in particular at large strains (up to 20%), when geometric nonlinearity in Cauchy relations must be taken into account. In previous works of the authors, functionally heterogeneous materials were studied in a geometrically linear formulation, which is true for small deformations (up to 7%). When predicting work with material at large deformations, it is necessary to take into account geometric nonlinearity in Cauchy relations.Studying the behavior of bodies made of functionally heterogeneous materials under unsteady load requires the development of special approaches, methods and algorithms for calculating the stress-strain state. When constructing physical relations, it is assumed that the deformation at the point is represented as the sum of the elastic component, the jump in deformation during the phase transition, plastic deformation and deformation caused by temperature changes.A physical relationship in a nonlinear setting is proposed for modeling the behavior of bodies made of functionally heterogeneous materials. Formulas are obtained that nonlinearly relate strain rates and Formulas are obtained that nonlinearly relate strain rates and displacement rates.Keywords: mathematical modeling, functional heterogeneous materials, geometric nonlinearity, spline functions, pseudo-elastic plasticity, phase transitions
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Dissertations / Theses on the topic "Linear elastic deformation"

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Zhou, Zhengming. "Non-linear elastic modelling of coupled deformation, heat, air and moisture transfer in unsaturated soil." Thesis, Cardiff University, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.360637.

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Torlak, Muris. "A finite volume method for coupled numerical analysis of incompressible fluid flow and linear deformation of elastic structures /." Hamburg : Techn. Univ., Arbeitsbereiche Schiffbau, 2006. http://www.gbv.de/dms/ilmenau/toc/527629162.PDF.

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Amirova, Svetlana R. "The influence of a simple shear deformation on a long wave motion in a pre-stressed incompressible elastic layer." Thesis, Keele University, 2008. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.491831.

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Numrich, Ralf [Verfasser]. "Modellierung des nichtlinear-elastischen Verformungsverhaltens von Tragschichten ohne Bindemittel = Modelling of the non-linear elastic deformation behaviour of unbound granular materials / von Ralf Numrich." 2003. http://d-nb.info/970204736/34.

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Carvalho, Cristiano Daniel Ferreira. "Simulação numérica e verificação experimental do comportamento elástoplástico de espumas metálicas." Master's thesis, 2012. http://hdl.handle.net/1822/22706.

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Dissertação de mestrado integrado em Engenharia Mecânica
Esta dissertação de mestrado analisa o comportamento elásto-plástico de espumas metálicas à compressão, através do estudo numérico e da verificação experimental. No estado da arte são apresentados vários processos de fabrico de espumas metálicas, são apresentadas algumas propriedades mecânicas e físicas das espumas metálicas e alguns estudos numéricos realizados a espumas deste tipo. Foram realizados ensaios experimentais de tração a provetes com o mesmo material utilizado nas espumas, que possibilita delinear o perfil deste material através de uma curva tensão-extensão. Ensaiou-se, experimentalmente, os dois tipos de espumas metálicas utilizadas no estudo, com e sem parede, permitindo uma análise comparativa entre os resultados obtidos numericamente e os obtidos experimentalmente. Para determinar o comportamento mecânico das espumas metálicas numericamente, foi utilizado o software de elementos finitos Ansys Workbench, na opção de estudos estruturais estáticos, permitindo definir a curva carga-deslocamento para cada espuma, analisar a rigidez e energia de deformação de cada espuma e comparar estes parâmetros com os obtidos nos ensaios experimentais. Finalmente, é realizado, também, uma análise comparativa, para um tipo de espuma em estudo, entre dois programas: Ansys Workbench e CosmosWorks.
This Master Thesis analysis the elastic-plastic behavior of metal foams in compression threw the numerical study and experimental validation. In the state of the art, it’s presented several manufacturing processes of metal foams, their mechanical and physical properties and some numerical studies made to them. Experimental traction tests were made to specimens manufactured in the same material used in the metallic foams with the intention of defining a tension-extension curve. It was tested the two types of metal foams used in the study, with and without wall, permitting a comparative analyses between the results obtained numerically and experimentally. To determine the mechanical behavior of the foams in the numerical analysis, it was used the finite elements software Ansys Workbench, using the “Static Structural” option. This permitted to define the load-displacement curve to each, to analyze the rigidity and energy of deformation of foams and compare these parameters with those obtained from experimental tests. Finally, it is also performed a comparative analysis for a foam type under consideration, between two programs: Ansys Workbench and CosmosWorks.
Fundação para a Ciência e a Tecnologia (FCT) - Projeto PTDC/EME-PME/115668/2009
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Мeльник, Юлія Володимирівна, and Melnyk Yulia. "Інфopмaцiйнa cиcтeмa уcтaнoвки для дocлiджeння зaпoбiжних пpужних муфт." Master's thesis, 2019. http://elartu.tntu.edu.ua/handle/lib/29712.

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Дипломна робота магістра присвячена актуальному питанню про дослідження конструкцій пружно-запобіжних муфт в установці, проектування eлeктpoнного блoку вимірювання, анaлiзу та оцінки похибки oб’єкту вимірювання. Дослідження впливу зaкpiплeння тeнзopeзиcтopa нa пpужнoму eлeмeнтi зa дoпoмoгoю зв’язуючoгo мaтepiaлу нa чутливість і точність тензодатчиків i знaйдeння шляхiв пiдвищeння точності вимірювання. Також розглянута актуальність використання пружних елементів та застосування тензадотчиків та принцип вимірювання деформації за допомогою тензорезистора та різноманітність конструкцій пружно запобіжних муфт. Досліджено лінійну залежність сигналу з тензодатчика в залежності від прикладеного осьового навантаження. Проведено аналіз для визначення факторів, які впливають на збільшення величини передачі максимального обертового моменту. Представлено схeми тa пpинципу poбoти уcтaнoвки. Poзpoблено cтpуктуpну функцioнaльну схеми та вибрано eлeмeнтну бaзу. Проведена оцінка пoхибки вимipювaння тa гaбapитних poзмipiв блoку кepувaння
The master's thesis is devoted to the actual the issue of strain gauges research construction of elastic preventive clutch in the installation, designing electronic block measuring, analysis and evaluation errors the object of measurement. Impact stuties fixing strain gauge on elastic element by means of binder materials for sensitivity and accuracy strain gauge and found ways improving measurement accuracy. The relevance of the use of elastic elements and the use of strain gauges and the principle of strain measurement using a strain gauge resistor and the variety of designs of elastic safety couplings are also considered. The linear dependence of the signal from the strain gauge, depending on the applied axial load, is investigated. An analysis is conducted to determine the factors that influence the increase in the maximum torque transmission. Circuits for the principle of work are presented. Structural functional circuits improved and elemental base selected. The measurement error and the overall dimensions of the control unit were evaluated.
ВCТУП 6 1 ДOCЛIДНИЦЬКO - КOНCТPУКТOPCЬКA ЧACТИНA 7 1.1 Oгляд мeтoдiв i зacoбiв вимipювaння 7 1.2 Пaтeнтний oгляд пo тeмi зaвдaння 12 1.3 Пocтaнoвкa зaдaчi 13 1.4 Oгляд кoнcтpукцiй зaпoбiжних муфт 16 2 OCНOВИ НAУКOВИХ ДOCЛIДЖEНЬ ТA МAТМOДEЛЮВAННЯ 20 2.1 Ймoвipнocний aнaлiз зaлeжнocтi пoкaзiв тeнзoдaтчикa вiд ocьoвoгo нaвaнтaжeння 20 2.2 Мeтoдикa пpoвeдeння тa peзультaти eкcпepимeнтaльних дocлiджeнь 30 3 EЛEКТPOНIКA, МIКPOПPOЦECOPНA ТEХНIКA ТA CAПP 41 3.1 Cхeмa тa пpинцип poбoти уcтaнoвки 41 3.2 Aнaлiз oб’єкту вимipювaння 42 3.3 Poзpoбкa cтpуктуpнoї функцioнaльнoї cхeми 44 3.4 Вибip eлeмeнтнoї бaзи тa визнaчeння гaбapитних poзмipiв eлeктpoннoгo блoку вимipювaння 45 3.5 Cхeмa включeння дaвaчiв 50 3.6 Oцiнкa пoхибки вимipювaння тa гaбapитних poзмipiв блoку кepувaння 52 4 ОБҐРУНТУВАННЯ ЕКОНОМІЧНОЇ ЕФЕКТИВНОСТІ 54 4.1 Критерії і показники економічної ефективності нової техніки 54 4.2 Розрахунок затрат на виготовлення установки 55 4.3 Визначення лімітної ціни пристрою 63 4.4 Визначення затрат на експлуатацію установки 64 4.5 Визначення економічної ефективності 67 5 ОХОРОНА ПРАЦІ ТА БЕЗПЕКА В НАДЗВИЧАЙНИХ СИТУАЦІЯХ 69 5.1 Охорона праці 69 5.1.1 Розрахунок місцевого освітлення для спроектованої установки 69 5.1.2 Використання і опис дії систем пожежогасіння, які використовують на підприємствах приладобудування 72 5.1.3 Суть і зміст управління охороною праці 76 5.2 Безпека в надзвичайних ситуаціях 78 5.2.1 Закон і положення про цивільну оборону України 78 5.2.2 Вплив розробленої установки на життєдіяльність людей 81 6 ЕКОЛОГІЯ 83 6.1 Актуальність охорони навколишнього середовища 83 6.2 Забруднення довкілля, що виникають в процесі виготовлення та експлуатації установки для дослідження запобіжних пружних муфт 84 6.3 Заходи зі зменшення забруднення довкілля 85 ВИСНОВКИ 87 ПЕРЕЛІК ДЖЕРЕЛ ПОСИЛАННЯ 89 ДОДАТКИ 91
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Липак, Андрій Андрійович, and Lypak Andriy. "Інформаційно-вимірювальна система пристрою для комплексного контролю зовнішнього діаметра та величини замка поршневих кілець." Master's thesis, 2019. http://elartu.tntu.edu.ua/handle/lib/29817.

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В даному дипломному проекті розроблено електронний блок керування приладом для вимірювання пружних характеристик кільцевих пружин, що спрощує процес вимірювання. Результати вимірювання виводяться на персональний комп’ютер через послідовний інтерфейс RS-232 та РК дисплей. Автоматизація процедури вимірювання здійснюється завдяки організації керування виконавчими пристроями в розробленому електронному блоці.
The master's thesis is devoted to the actual the issue of strain gauges research construction of elastic preventive clutch in the installation, designing electronic block measuring, analysis and evaluation errors the object of measurement. Impact stuties fixing strain gauge on elastic element by means of binder materials for sensitivity and accuracy strain gauge and found ways improving measurement accuracy. The relevance of the use of elastic elements and the use of strain gauges and the principle of strain measurement using a strain gauge resistor and the variety of designs of elastic safety couplings are also considered. The linear dependence of the signal from the strain gauge, depending on the applied axial load, is investigated. An analysis is conducted to determine the factors that influence the increase in the maximum torque transmission. Circuits for the principle of work are presented. Structural functional circuits improved and elemental base selected. The measurement error and the overall dimensions of the control unit were evaluated.
Вступ 1 Дослідницько-конструкторська частина 1.1 Аналіз поставленої задачі 1.1.1 Результати патентного пошуку 1.2 Схема та методика випробування 1.2.1 Засоби для вимірювання сили 1.2.2 Перетворювачі для вимірювання переміщення 1.3 Принцип роботи установки 1.4 Розрахунок навантажувального пристрою 1.5 Розрахунок тензобалки 1.6 Циклограма роботи установки 1.7 Вибір датчика переміщення 1.8 Принципова схема підключення тензорезисторів 1.9 Похибка установки 1.9.1 Похибка при вимірюванні сили 1.9.2 Похибка при вимірюванні переміщення 2 Основи наукових досліджень та матмоделювання 2.1 Аналіз об’єкта дослідження 2.2 Кільце під дією осьової сили 3 Електроніка, мікропроцесорна техніка та САПР 3.1Розробка функціональної схеми 3.1.1 Вимоги до функціональності та параметрів системи 3.1.2 Способи реалізації заданих функцій 3.1.3 Функціональна схема та опис принципу роботи 3.2 Розробка принципової схеми 3.2.1 Підрахунок мінімальної кількості виводів мікроконтролера 3.2.2 Вибір мікроконтролера 3.2.3 Будова контролера 3.2.4 Вибір дисплея 3.2.5 Розрахунок номіналів елементів 3.3 Метрологічний аналіз 3.3.1 Бюджет похибок вимірювального каналу 3.4 Опис алгоритму роботи 4 Обґрунтування економічної ефективності 5 Охорона праці та безпеки в надзвичайних ситуаціях 6 Екологія 7 Висновок 8 Перелік посилань 9 Додатки
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Books on the topic "Linear elastic deformation"

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Ogden, R. W. Non-linear elastic deformations. Mineola, N.Y: Dover Publications, 1997.

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Altawam, Aref. A general non-linear theory of large elastic deformation of layered plates. 1990.

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Phan-Thien, Nhan, and Sangtae Kim. Microstructures in Elastic Media. Oxford University Press, 1994. http://dx.doi.org/10.1093/oso/9780195090864.001.0001.

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This monograph describes various methods for solving deformation problems of particulate solids, taking the reader from analytical to computational methods. The book is the first to present the topic of linear elasticity in mathematical terms that will be familiar to anyone with a grounding in fluid mechanics. It incorporates the latest advances in computational algorithms for elliptic partial differential equations, and provides the groundwork for simulations on high performance parallel computers. Numerous exercises complement the theoretical discussions, and a related set of self-documented programs is available to readers with Internet access. The work will be of interest to advanced students and practicing researchers in mechanical engineering, chemical engineering, applied physics, computational methods, and developers of numerical modeling software.
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Ogden, R. W. Non-Linear Elastic Deformations. Dover Publications, Incorporated, 2013.

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Ogden, R. W. Non-Linear Elastic Deformations. Dover Publications, Incorporated, 2013.

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Ogden, R. W. Non-Linear Elastic Deformations. Dover Publications, Incorporated, 2013.

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Roy, Arabinda, and Rasajit Kumar Bera. Linear and Non-Linear Deformations of Elastic Solids. Taylor & Francis Group, 2019.

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Linear and Non-Linear Deformations of Elastic Solids. Taylor & Francis Group, 2019.

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Roy, Arabinda, and Rasajit Kumar Bera. Linear and Non-Linear Deformations of Elastic Solids. Taylor & Francis Group, 2019.

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Roy, Arabinda, and Rasajit Kumar Bera. Linear and Non-Linear Deformations of Elastic Solids. Taylor & Francis Group, 2019.

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Book chapters on the topic "Linear elastic deformation"

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Byskov, Esben. "Shear Deformation of Linear Elastic Beam Cross-Sections." In Solid Mechanics and Its Applications, 217–39. Dordrecht: Springer Netherlands, 2013. http://dx.doi.org/10.1007/978-94-007-5766-0_12.

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Byskov, Esben. "Bending and In-Plane Deformation of Linear Elastic Plates." In Solid Mechanics and Its Applications, 273–76. Dordrecht: Springer Netherlands, 2013. http://dx.doi.org/10.1007/978-94-007-5766-0_15.

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Halpern, David, J. A. Moriarty, and James B. Grotberg. "Capillary-Elastic Instabilities with an Oscillators Forcing Function." In IUTAM Symposium on Non–Linear Singularities in Deformation and Flow, 243–55. Dordrecht: Springer Netherlands, 1991. http://dx.doi.org/10.1007/978-94-011-4736-1_22.

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Byskov, Esben. "Bending and Axial Deformation of Linear Elastic Beam Cross-Sections." In Solid Mechanics and Its Applications, 199–216. Dordrecht: Springer Netherlands, 2013. http://dx.doi.org/10.1007/978-94-007-5766-0_11.

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Vigdergauz, Shmuel. "Elastic Interaction of Dislocations with a Crack in a Disk." In IUTAM Symposium on Non–Linear Singularities in Deformation and Flow, 75–86. Dordrecht: Springer Netherlands, 1999. http://dx.doi.org/10.1007/978-94-011-4736-1_8.

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Garrett, Steven L. "Elasticity of Solids." In Understanding Acoustics, 179–233. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-44787-8_4.

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Abstract If a solid is initially at rest and equal and opposing forces are applied to that object, Newton’s Second Law guarantees that the object will remain at rest because the net force on the sample is zero. If that object is an elastic solid, then those forces will cause the solid to deform by an amount that is directly proportional to those applied forces. When the forces are removed, the sample will return to its original shape and size. That reversibility is the characteristic that is required if we say the behavior of the solid is “elastic.” This chapter will quantify the elastic behavior of solids by introducing the concepts of stress and strain and expressing their linear relationship through the definition of elastic moduli that depend only upon the material and the nature of the deformation and not upon the shape of the object. Those concepts allow us to generalize Hooke’s law. As before, the combination of a linear equation of state with Newton’s Second Law will now describe wave motion in solids. The introduction of a relaxation time, through the Maxwell model, will let these results be generalized to viscoelastic materials and then be applied to rubber vibration isolators.
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Leischner, S., T. Spanier, and G. Canon Falla. "Effective experimental characterization of the non-linear elastic deformation behavior of unbound granular materials." In Eleventh International Conference on the Bearing Capacity of Roads, Railways and Airfields, Volume 2, 435–44. London: CRC Press, 2022. http://dx.doi.org/10.1201/9781003222897-40.

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Ivanova, Jordanka, and Franco Pastrone. "Postcritical Deformations of Thin Anisotropic Shells." In Geometric Method for Stability of Non-Linear Elastic Thin Shells, 1–64. Boston, MA: Springer US, 2002. http://dx.doi.org/10.1007/978-1-4615-1511-1_1.

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Ivanova, Jordanka, and Franco Pastrone. "Postcritical Deformations of Thin Elastic Anisotropic Shells with Linear Memory." In Geometric Method for Stability of Non-Linear Elastic Thin Shells, 65–86. Boston, MA: Springer US, 2002. http://dx.doi.org/10.1007/978-1-4615-1511-1_2.

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Ting, T. T. C. "Linear Anisotropic Elastic Materials." In Anisotropic Elasticity. Oxford University Press, 1996. http://dx.doi.org/10.1093/oso/9780195074475.003.0005.

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The relations between stresses and strains in an anisotropic elastic material are presented in this chapter. A linear anisotropic elastic material can have as many as 21 elastic constants. This number is reduced when the material possesses a certain material symmetry. The number of elastic constants is also reduced, in most cases, when a two-dimensional deformation is considered. An important condition on elastic constants is that the strain energy must be positive. This condition implies that the 6×6 matrices of elastic constants presented herein must be positive definite. Referring to a fixed rectangular coordinate system x1, x2, x3, let σij and εks be the stress and strain, respectively, in an anisotropic elastic material. The stress-strain law can be written as . . . σij = Cijksεks . . . . . .(2.1-1). . . in which Cijks are the elastic stiffnesses which are components of a fourth rank tensor. They satisfy the full symmetry conditions . . . Cijks = Cjiks, Cijks = Cijsk, Cijks = Cksij. . . . . . .(2.1-2). . .
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Conference papers on the topic "Linear elastic deformation"

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Aghajanzadeh, Omid, Guillaume Picard, Juan Antonio Corrales Ramon, Christophe Cariou, Roland Lenain, and Youcef Mezouar. "Optimal Deformation Control Framework for Elastic Linear Objects." In 2022 IEEE 18th International Conference on Automation Science and Engineering (CASE). IEEE, 2022. http://dx.doi.org/10.1109/case49997.2022.9926528.

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Borboni, Alberto, Diego De Santis, and Rodolfo Faglia. "Large Deflection of a Non-Linear, Elastic, Asymmetric Ludwick Cantilever Beam." In ASME 2010 10th Biennial Conference on Engineering Systems Design and Analysis. ASMEDC, 2010. http://dx.doi.org/10.1115/esda2010-24257.

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The investigated cantilever beam is characterized by a constant rectangular cross-section and is subjected to a concentrated vertical constant load at the free end. The same beam is made by an elastic non-linear asymmetric Ludwick type material with different behavior in tension and compression. Namely the constitutive law of the proposed material is characterized by two different elastic moduli and two different strain exponential coefficients. The aim of this study is to describe the deformation of the beam neutral surface and particularly the horizontal and vertical displacements of the free end cross-section. The analysis of large deflection is based on the Euler-Bernoulli bending beam theory, for which cross-sections, after the deformation, remain plain and perpendicular to the neutral surface; furthermore their shape and area do not change. On the stress viewpoint, the shear stress effect and the axial force effect are considered negligible in comparison with the bending effect. The mechanical model deduced from the identified hypotheses includes two kind of non-linearity: the first due to the material and the latter due to large deformations. The mathematical problem associated with the mechanical model, i.e. to compute the bending deformations, consists in solving a non-linear algebraic system and a non-liner second order ordinary differential equation. Thus a numerical algorithm is developed and some examples of specific results are shown in this paper. Precisely, the proposed problem is a generalization of similar cases in literature, consequently numerical comparisons are performed with these previous works, i.e. assuming linear elastic materials or assuming symmetric Ludwick type material with same behavior in tension and compression like aluminum alloy and annealed copper. After verifying a proper agreeing with the literature, in order to investigate the effect of the different material behavior on the horizontal and vertical displacements of the free end cross-section, numerical results are obtained for different values of elastic moduli and strain exponential coefficients. The arising conclusions are coherent with the assumed hypotheses and with similar works in literature.
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Gradl, Christoph, and Rudolf Scheidl. "A Combined Hydrostatic Hydrodynamic Bearing Based on Elastic Deformation." In 9th FPNI Ph.D. Symposium on Fluid Power. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/fpni2016-1520.

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Servo cylinders with hydrostatic bearings are employed when ultimate speed, low friction, or high precision are required. These advantages are opposed by a considerable leakage loss and high costs. The latter are caused by the high component precision required in order to avoid excessive leakage and to obtain high stiffness of the bearing. In this paper an alternative concept to realize such bearings with a considerable cost reduction potential is investigated. The sleeve is made of Polyetheretherketon (PEEK). A hydrostatic difference pressure or / and a hydrodynamic pressure deforms the PEEK sleeve such that a conical stabilizing sealing gap is created. A possible mechanical design is shown and the characteristics are analysed. To study the characteristics of the bearing system the finite element suite Abaqus is used. A Reynolds User Element is developed and included into Abaqus for the simulation of the fluid structure interaction. The Reynolds equation is discretised by finite elements and solved simultaneously with the mechanical model. With the developed user element in Abaqus, static and quasi-static analyses of mechanical models (linear, non-linear or inelastic material behaviour) containing lubrications gaps can be performed efficiently. The preliminary results showed the feasibility of the concept and, generally, the potentials of plastics as a flexible material to employ elastic deformation for the creation of lubrication effects.
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Kligerman, Yuri, Izhak Etsion, and Yuri Kadin. "Unloading of an Elastic-Plastic Loaded Spherical Contact." In ASME/STLE 2004 International Joint Tribology Conference. ASMEDC, 2004. http://dx.doi.org/10.1115/trib2004-64387.

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The process of unloading an elastic-plastic loaded sphere in contact with a rigid flat is studied by the Finite Element Method. The sphere material is assumed isotropic with elastic-linear hardening. The numerical simulations cover a wide range of loading interference deformation of various values of Young’s modulus and Poisson ratios of the sphere material. The contact loads, stresses, and deformations in the sphere during both loading and unloading, are calculated for the range of interferences. Empirical dimensionless expressions are presented for the unloading load-deformation relation, the residual axial displacement and the residual curvature of the sphere after complete unloading.
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Sharbati, Ehsan, and Reza Naghdabadi. "Large Deformation Analysis of Elastic Cosserat Continua by FEM." In ASME 8th Biennial Conference on Engineering Systems Design and Analysis. ASMEDC, 2006. http://dx.doi.org/10.1115/esda2006-95288.

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Based on the non linear terms appearing in the strain tensor in classical continuum mechanics, two expressions for large strain in the Cosserat continuum are proposed. The generalized form of principal of virtual work together with the constitutive equations for an isotropic elastic Cosserat continuum are used to derive the finite element formulations for elastic large deformation analysis based on the Cosserat theory. The finite element formulations are then applied to a four-node quadrilateral element with three degrees of freedom at each node including two translational and one rotational degrees of freedom. The tension of a semi-infinite plate with a circular whole in the center is solved using the Cosserat finite element formulation and the results are compared with those obtained by the classical theory. Also, pure bending and shear of a cantilever beam are done and the differences of the results obtained based on the two proposed formulations of large strains are investigated.
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Li, Fuhua, Tiemin Li, Yao Jiang, and Fengchun Li. "Effects of Velocity on Elastic Deformation in Ball Screw Drives and its Compensation." In ASME 2017 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/imece2017-70863.

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Ball screw drives are widely used in machine tools to provide accurate linear motion. Elastic deformation is one of the major error sources for ball screw drives in achieving high accuracy motion, and changes greatly when velocity varies. The influence of velocity on the elastic deformation can be estimated and it can be compensated by means of dynamic modeling and servo control method. This paper presents a dynamic model considering torque transmission between the ball screw and the nut. And stiffness is identified by a method of combining theoretical calculation and experimental tests on a constructed test bench, which has two novel symmetrical loading mechanisms. In order to analyze the influence of moving velocity on the elastic deformation, simulation and experiments are conducted when two trajectories which have velocity jumps are input. And the simulated elastic deformations are compared with experimental results to evaluate the accuracy of the model. The results show that the simulated results fit the experimental results with high accuracy. The relationship between the elastic deformation of ball screw drives and the velocity is linear based on the experimental results. Then the simulation results are used to compensate the elastic deformation based on the feed-forward compensation method. The results show that the differences between the actual compensation values and actual elastic deformation are small and most of the elastic deformation of the ball screw drives can be compensated. Therefore, the proposed dynamic model and compensation method can be used to improve the tracking accuracy of ball screw drives.
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Malkov, Venyamin, and Yulia Malkova. "Nonlinear deformation of plane with elastic elliptic inclusion for model of semi-linear material." In 2016 Young Researchers in Vacuum Micro/Nano Electronics (VMNE-YR). IEEE, 2016. http://dx.doi.org/10.1109/vmneyr.2016.7880410.

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Li, Zhiliang, Xiang Long, and Olusegun J. Ilegbusi. "A Novel Multi-Layer Poro-Elastic Model of Lung Deformation." In ASME 2011 International Mechanical Engineering Congress and Exposition. ASMEDC, 2011. http://dx.doi.org/10.1115/imece2011-62250.

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This paper presents a novel method to simulate flow and deformation of the lung. The lung is assumed to behave as a poro-elastic medium with heterogeneous elastic property. The method uses a flow-structure interaction technique to simultaneously model flow within the airway and deformation of the lung lobes. The 3D lung geometry is reproduced from 4D CT scan dataset obtained on real human subjects at a Cancer Center. The non-linear Young’s modulus is estimated in a parallel study based on similar CT scan dataset. The novelty of the present technique lies in the use of onion-layer grid with distributed spatial permeability. It allows prediction of the spatial lung displacement that could be used for tracking lung tumor during radiotherapy.
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Darijani, Hossein, Reza Naghdabadi, Nima Shamsaei, and Mehdi Danesh Sararoudi. "Elastoplastic Stress Study in Thick-Walled Spherical Vessels Considering Finite Deformation." In ASME 8th Biennial Conference on Engineering Systems Design and Analysis. ASMEDC, 2006. http://dx.doi.org/10.1115/esda2006-95065.

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An exact elasto-plastic analytical solution for large-strained internal pressurized thick-walled spherical vessels made of elastic-linear and nonlinear hardening material is derived in this paper. This solution is based on the notion of finite strains, the deformation theory of Hencky and the yield criteria of von Mises and Tresca. Nolinear elastic solution of an axisymetric boundary value problem is used as a basis to generate its inelastic solution, whereas the Hyper-elastic constitutive equation is invoked to represent the material response in the elastic region. This method treats the material parameters as field variables. Their distributions are obtained in an iterative manner using Nuber’s rule. Obtained Results for stress distribution using the present method shown are in excellent agreement with only analytical result which has been determined in the case of isochoric volume.
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Kang, Hong-Tae, and Xiao Wu. "Structural Stress Correction Methods for Linear Elastic Finite Element Analysis of Spot Welded Joints." In ASME 2016 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/imece2016-66884.

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Structural stress concepts are widely used in fatigue life prediction of spot welds and seam welds in vehicle structures. For fatigue life prediction of welded joints based on the structural stress methods, it is necessary to obtain applied force ranges versus fatigue life of the welded specimens. Then, the force ranges versus fatigue life information is converted to structural stress ranges versus fatigue life (S-N) of the joints. The structural stress ranges versus the fatigue life curve of the welded specimens becomes the material fatigue property of the welded joints to predict fatigue life of joints in vehicle structures. While converting the applied load ranges to the structural stress ranges, linear elastic finite element analysis (FEA) is used. Therefore, the applied load ranges are considered as the responses of linear elastic deformation even though the load ranges consist of the linear elastic deformation and plastic deformation. As results the structural stress ranges of the welded joints are reduced in S-N curve. This study introduces simple techniques for spot welded joints to include the plastic deformation effect on the structural stress calculation without performing elastic-plastic finite element analysis. Fatigue test results of spot welded joints for lap-shear and coach peel specimens of advanced high strength steels (AHSS) and mild steels were used. The corrected structural stress methods showed better correlation with the test results.
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Reports on the topic "Linear elastic deformation"

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Roberts, Scott Alan, and Peter Randall Schunk. A non-linear elastic constitutive framework for replicating plastic deformation in solids. Office of Scientific and Technical Information (OSTI), February 2014. http://dx.doi.org/10.2172/1148928.

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Oliynyk, Kateryna, and Matteo Ciantia. Application of a finite deformation multiplicative plasticity model with non-local hardening to the simulation of CPTu tests in a structured soil. University of Dundee, December 2021. http://dx.doi.org/10.20933/100001230.

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In this paper an isotropic hardening elastoplastic constitutive model for structured soils is applied to the simulation of a standard CPTu test in a saturated soft structured clay. To allow for the extreme deformations experienced by the soil during the penetration process, the model is formulated in a fully geometric non-linear setting, based on: i) the multiplicative decomposition of the deformation gradient into an elastic and a plastic part; and, ii) on the existence of a free energy function to define the elastic behaviour of the soil. The model is equipped with two bonding-related internal variables which provide a macroscopic description of the effects of clay structure. Suitable hardening laws are employed to describe the structure degradation associated to plastic deformations. The strain-softening associated to bond degradation usually leads to strain localization and consequent formation of shear bands, whose thickness is dependent on the characteristics of the microstructure (e.g, the average grain size). Standard local constitutive models are incapable of correctly capturing this phenomenon due to the lack of an internal length scale. To overcome this limitation, the model is framed using a non-local approach by adopting volume averaged values for the internal state variables. The size of the neighbourhood over which the averaging is performed (characteristic length) is a material constant related to the microstructure which controls the shear band thickness. This extension of the model has proven effective in regularizing the pathological mesh dependence of classical finite element solutions in the post-localization regime. The results of numerical simulations, conducted for different soil permeabilities and bond strengths, show that the model captures the development of plastic deformations induced by the advancement of the cone tip; the destructuration of the clay associated with such plastic deformations; the space and time evolution of pore water pressure as the cone tip advances. The possibility of modelling the CPTu tests in a rational and computationally efficient way opens a promising new perspective for their interpretation in geotechnical site investigations.
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