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1.
A method is proposed for constructing a system of constitutive equations of an incompressible medium with nonlinear dissipative
properties with finite deformations. A scheme of the mechanical behavior of a material is used, in which the points are connected
by horizontally aligned elastic, viscous, plastic, and transmission elements. The properties of each element of the scheme
are described with the use of known equations of the nonlinear elasticity theory, the theory of nonlinear viscous fluids,
and the theory of plastic flow of the material under conditions of finite deformations of the medium. The system of constitutive
equations is closed by equations that express the relation between the deformation rate tensor of the material and the deformation
rate tensor of the plastic element. Transmission elements are used to take into account a significant difference between macroscopic
deformations of the material and deformations of elements of the medium at the structural level.
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 3, pp. 158–170, May–June, 2009. 相似文献
2.
Based on a seven-degree-of-freedom shear deformable beam model, a geometrical nonlinear analysis of thin-walled composite
beams with arbitrary lay-ups under various types of loads is presented. This model accounts for all the structural coupling
coming from both material anisotropy and geometric nonlinearity. The general nonlinear governing equations are derived and
solved by means of an incremental Newton–Raphson method. A displacement-based one-dimensional finite element model that accounts
for the geometric nonlinearity in the von Kármán sense is developed to solve the problem. Numerical results are obtained for
thin-walled composite beam under vertical load to investigate the effects of fiber orientation, geometric nonlinearity, and
shear deformation on the axial–flexural–torsional response. 相似文献
3.
Based on Timoshenko's beam theory and Vlasov's thin-walled member theory, a new model of spatial thin-walled beam element is developed for analyzing geometrical and physical nonlinearity, which incorporates an interior node and independent interpolations of bending angles and warp and takes diversified factors into consideration, such as traverse shear deformation, torsional shear deformation and their coupling, coupling of flexure and torsion, and the second shear stress. The geometrical nonlinear strain is formulated in updated Lagarange (UL) and the corresponding stiffness matrix is derived. The perfectly plastic model is used to account for physical nonlinearity, and the yield rule of von Mises and incremental relationship of Prandtle-Reuss are adopted. Elastoplastic stiffness matrix is obtained by numerical integration based on the finite segment method, and a finite element program is compiled. Numerical examples manifest that the proposed model is accurate and feasible in the analysis of thin-walled structures. 相似文献
4.
Dimos J. Polyzois Ioannis G. Raftoyiannis 《Archive of Applied Mechanics (Ingenieur Archiv)》2009,79(4):347-358
This paper presents a semi-analytical finite element analysis of pole-type structures with circular hollow cross-section.
Based on the principle of stationary potential energy and Novozhilov’s derivation of nonlinear strains, the formulations for
the geometric nonlinear analysis of general shells are derived. The nonlinear shell-type analysis is then manipulated and
simplified gradually into a beam-type analysis with special emphasis given on the relationships of shell-type to beam-type
and nonlinear to linear analyses. Based on the theory of general shells and the finite element method, the approach presented
herein is employed to analyze the ovalization of the cross-section, large displacements, the P-Δ effect as well as the overall
buckling of pole-type structures. Illustrative examples are presented to demonstrate the applicability and the efficiency
of the present technique to the large deformation of fiber-reinforced polymer composite poles accompanied with comparisons
employing commercial finite element codes. 相似文献
5.
E. A. Gotsulyak O. K. Luk’yanchenko E. V. Kostina I. G. Garan 《International Applied Mechanics》2011,47(3):302-312
A finite-element method to analyze the stress–strain state and stability of thin shells with geometric imperfections is proposed.
An arbitrary curvilinear finite element with vector approximation of the displacement function is used. To solve the systems
of nonlinear algebraic equations by iteration methods, linearized stiffness matrices of finite elements and residual and load
vectors are formed. The stress–strain state of a thin-walled shell with real geometric imperfections under surface pressure
and axial compression is analyzed. The effect of geometric imperfections on the critical combination of loads is evaluated 相似文献
6.
Sebastian Geiger Thomas Driesner Christoph A. Heinrich Stephan K. Matthäi 《Transport in Porous Media》2006,63(3):399-434
We present a new finite element – finite volume (FEFV) method combined with a realistic equation of state for NaCl–H2O to model fluid convection driven by temperature and salinity gradients. This method can deal with the nonlinear variations
in fluid properties, separation of a saline fluid into a high-density, high-salinity brine phase and low-density, low-salinity
vapor phase well above the critical point of pure H2O, and geometrically complex geological structures. Similar to the well-known implicit pressure explicit saturation formulation,
this approach decouples the governing equations. We formulate a fluid pressure equation that is solved using an implicit finite
element method. We derive the fluid velocities from the updated pressure field and employ them in a higher-order, mass conserving
finite volume formulation to solve hyperbolic parts of the conservation laws. The parabolic parts are solved by finite element
methods. This FEFV method provides for geometric flexibility and numerical efficiency. The equation of state for NaCl–H2O is valid from 0 to 750°C, 0 to 4000 bar, and 0–100 wt.% NaCl. This allows the simulation of thermohaline convection in high-temperature
and high-pressure environments, such as continental or oceanic hydrothermal systems where phase separation is common. 相似文献
7.
S. V. Levyakov 《Journal of Applied Mechanics and Technical Physics》2012,53(2):258-265
A finite element is proposed for analyzing nonlinear deformation and stability of three-dimensional rods at arbitrarily large
elastic displacements. Timoshenko’s model is used for taking transverse shear strains into account. The accuracy and convergence
of numerical solutions are studied by an example of problems of nonlinear bending of curvilinear rods. 相似文献
8.
A. Z. Galishin 《International Applied Mechanics》2008,44(2):158-166
The paper presents a technique to determine the axisymmetric geometrically nonlinear thermoviscoelastoplastic state of thin
shells with damages. The technique is based on the geometrically nonlinear equations that incorporate transverse-shear strains.
The equations of thermoelasticity that describe the deformation of the body’s element along paths of small curvature are used
as equations of state. The equivalent stress in the kinetic equations of damage and creep is determined from a failure criterion
that accounts for the stress mode. As an example, the geometrically nonlinear thermoviscoelastoplastic deformation of a corrugated
shell is analyzed and the time to its failure is determined
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Translated from Prikladnaya Mekhanika, Vol. 44, No. 2, pp. 49–60, February 2008. 相似文献
9.
L. P. Zheleznov V. V. Kabanov D. V. Boiko 《Journal of Applied Mechanics and Technical Physics》2008,49(1):109-113
A study is made of the stability of cylindrical shells of oval cross section loaded by a shear force combined with torsional
and bending moments. The variational method of finite elements in displacements is used. The subcritical stress-strain state
of the shells is considered momental and nonlinear. The effects of the nonlinearity of shell deformation and shell ovalization
on the critical load and buckling mode are determined.
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 1, pp. 134–138, January–February, 2008. 相似文献
10.
Alemdar Bayraktar Ahmet Can Altunişik Barış Sevim Murat Emre Kartal Temel Türker Yasemin Bilici 《Nonlinear dynamics》2009,58(4):655-673
In this paper, it is aimed to compare the near- and far-fault ground motion effects on the nonlinear dynamic response of dams
including dam–reservoir–foundation interaction. Two different types of dams, which are concrete arch and concrete faced rockfill
dams, are selected to investigate the near- and far-fault ground motion effects on the dam responses. The behavior of reservoir
water is taken into account using Lagrangian approach. The Drucker–Prager material model is employed in nonlinear analyses.
Near and far-fault strong ground motion records, which have approximately identical peak ground accelerations, of Loma Prieta
(1989) earthquake are selected for the analyses. Displacements, maximum and minimum principal stresses are determined using
the finite element method. The displacements and principal stresses obtained from the analyses of dams subjected to each fault
effect are compared with each other. It is clearly seen that there is more seismic demand on displacements and stresses when
the dam is subjected to near-fault ground motion. 相似文献
11.
A. A. Markin 《Journal of Applied Mechanics and Technical Physics》1999,40(5):922-929
Using the process theory of A. A. Il’yushin, we consider the problem of determining the thermomechanical parameters of a material
element for specified deformation and temperature-variation processes with allowance for the elastic, plastic, and viscous
properties of superplastic deformation. The relations obtained are applicable for the case of arbitrary stresses and finite
strains. The strain and stress measures are decomposed into elastic, plastic, and viscous components by classifying the processes
into reversible, irreversible equilibrium, and nonequilibrium processes.
Tula State University, Tula 300600. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 5, pp. 164–172,
September–October, 1999. 相似文献
12.
Yuanwen Gao 《Acta Mechanica Sinica》2009,25(1):139-147
In this paper, the magnetic-elastic-plastic deformation behavior is studied for a ferromagnetic plate with simple supports. The perturbation formula of magnetic force is first derived based on the perturbation technique, and is then applied to the analysis of deformation characteristics with emphasis laid on the analyses of modes, symmetry of deformation and influences of incident angle of applied magnetic field on the plate deformation. The theoretical analyses offer explanations why the configuration offer- romagnetic rectangular plate with simple supports under an oblique magnetic field is in-wavy type along the x-direction, and why the largest deformation of the ferromagnetic plate occurs at the incident angle of 45°for the magnetic field. A numerical code based on the finite element method is developed to simulate quantitatively behaviors of the nonlinearly coupled multi-field problem. Some characteristic curves are plotted to illustrate the magneto--elastic-plastic deflections, and to reveal how the deflections can be influenced by the incident angle of applied magnetic field. The deformation characteristics obtained from the numerical simulations are found in good agreement with the theoretical analyses. 相似文献
13.
Barış Sevim Alemdar Bayraktar Ahmet Can Altunişik Sezer Atamtürktür Fatma Birinci 《Nonlinear dynamics》2011,63(4):755-770
Historic masonry arch bridges are vital components of transportation systems in many countries worldwide, ensuring the ready
access of goods and services to millions of people. The structural failure of these historic structures would severely and
adversely impact the economies of these nations due to the massive disruptions of transportation systems accompanying such
failures. To successfully maintain these aging masonry structures, performance assessment must incorporate the unique mechanical
characteristics of masonry. Therefore, the preferred analysis technique must go beyond a linear approach. This study assesses
the earthquake performance of a restored historical masonry arch bridge through nonlinear finite element analysis incorporating
the Drucker–Prager damage criterion. The case study structure is the Mikron Arch Bridge, a nineteenth century Ottoman Era
structure built over the Firtina River near Rize, Turkey, and restored in 1998. The Mikron Arch Bridge was first subjected
to ambient vibration testing, during which accelerometers were placed at several points on the bridge span to record the bridge
vibratory response. The investigators then used Enhanced Frequency Domain Decomposition and Stochastic Subspace Identification
techniques to extract the experimental natural frequencies, mode shapes, and damping ratios from these measurements. Experimental
results were compared with those obtained by the linear finite element analysis of the bridge. Good agreement between mode
shapes was observed during this comparison, though natural frequencies disagree by 8–10%. The boundary conditions of the linear
finite element model of Mikron Arch Bridge are adjusted such that the analytical predictions agree with the ambient vibration
test results. By introducing the Drucker–Prager damage criterion, the calibrated linear FE model was next extended into a
nonlinear model. Nonlinear analysis of seismic behavior of Mikron arch bridge was performed considering the acceleration record
of Erzincan earthquake in 1992 that occurred near the Mikron Bridge region. The displacement and stress results were observed
to be allowable level of the stone material. Moreover, linear FE model calibrations elicited a significant influence on the
nonlinear FE model simulations. 相似文献
14.
Summary This paper presents the solution of geometrically nonlinear problems in solid mechanics by the Domain-Boundary Element Method.
Because of the Total-Lagrange approach, the arising domain and boundary integrals are evaluated in the undeformed configuration.
Therefore, the system matrices remain unchanged during the solution procedure, and their time-consuming computation needs
to be performed only once. While the integral equations for axisymmetric finite deformation problems will be derived in detail,
the basic ideas of the formulation in two and three dimensions can be found in [1]. The present formulation includes torsional
problems with finite deformations, where additional terms arise due to the curvilinear coordinate system. A Newton–Raphson
scheme is used to solve the nonlinear set of equations. This involves the solution of a large system of linear equations,
which has been a very time-consuming task in former implementations, [1, 2]. In this work, an iterative solver, i.e. the generalized
minimum residual method, is used within the Newton–Raphson algorithm, which leads to a significant reduction of the computation
time. Finally, numerical examples will be given for axisymmetric and two/three-dimensional problems.
Received 29 August 2000; accepted for publication 10 October 2000 相似文献
15.
Giuseppe Alì Vidar Furuholt Roberto Natalini Isabella Torcicollo 《Transport in Porous Media》2007,69(2):175-188
We present a numerical investigation of a degenerate nonlinear parabolic–elliptic system, which describes the chemical aggression
of limestones under the attack of SO2, in high permeability regime. This system has been introduced in the first part of this paper. We present a finite element
scheme for our model and its numerical stability is given under suitable CFL conditions. Numerical tests are discussed as
well as some examples of the numerical behavior of the solutions. 相似文献
16.
Fastener holes used in the mechanical joints are vulnerable to failure due to development of stress concentration at their
edges. Inducing compressive residual stresses by different techniques has been the most common method to reinforce the holes
to date. In this work, a new reinforcement technique called internal torsion, which can be classified as a localized severe
plastic deformation process, is proposed as an alternative to the cold expansion pre-stressing. A special specimen is designed
to represent the behavior of a typical fastener hole during the internal torsion process. The deformation of the specimen
in the vicinity of its hole surface is studied by introducing a parametric kinematically admissible velocity field (PKAVF)
within the deformation affected zone (DAZ). Calibration of the parameters in relation to the deformation of the material during
the process is done by an elastic-plastic finite element solution that was performed in ABAQUS for a specimen made of interstitial
free (IF) steel. Numerical analysis of the deformation is carried out to understand the process and to estimate the optimum
process parameters. Subsequently, the calibrated model is used in an upper-bound solution of the problem to estimate the torque–twist
response of the specimen during internal torsion. Finally, the results of upper-bound solution are compared with those of
finite element analysis. There is a good agreement between the upper-bound solution and finite element results, which verifies
validity of the calibrated velocity field model and the upper-bound solution based on the model for the internal torsion problem. 相似文献
17.
针对大型周边桁架式索网天线由拉索拉压模量不同引起的本构非线性和结构大变形引起的几何非线性问题,给出了基于参变量变分原理的几何非线性有限元方法. 首先针对含预应力索单元拉压模量不同分段描述的本构关系,通过引入参变量,导出了基于参变量及其互补方程的统一描述形式,避免了传统算法需要根据当前变形对索单元张紧/松弛状态的预测,提高了算法收敛性. 然后利用拉格朗日应变描述索网天线结构大变形问题,结合几何非线性有限元法,建立了基于参变量的非线性平衡方程和线性互补方程;并给出了牛顿-拉斐逊迭代法与莱姆算法相结合的求解算法. 数值算例验证了本文提出的算法比传统算法具有更稳定的收敛性和更高的求解精度,特别适合于大型索网天线结构的高精度变形分析和预测. 相似文献
18.
The studies of the deformation of physically nonlinear homogeneous and composite materials are systematized. Algorithms to
determine the effective elastic properties and stress–strain state of particulate, laminated, fibrous, and laminated fibrous
composite materials with physically nonlinear components are outlined, and their deformation patterns are studied. Composites
are considered as two-component materials of random structure. Their effective properties are determined using the conditional
averaging method. The nonlinear equations that allow for the physical nonlinearity of the components are solved by an iterative
method. The relationship between macrostresses and macrostrains is established. Macrostress–macrostrain curves of homogeneous
and composite materials are analyzed
Translated from Prikladnaya Mekhanika, Vol. 44, No. 12, pp. 7–38, December 2008. 相似文献
19.
A finite volume element method is developed for analyzing unsteady scalar reaction-diffusion problems in two dimensions. The method combines the concepts that are employed in the finite volume and the finite element method together. The finite volume method is used to discretize the unsteady reaction-diffusion equation, while the finite element method is applied to estimate the gradient quantities at cell faces. Robustness and efficiency of the combined method have been evaluated on uniform rectangular grids by using available numerical solutions of the two-dimensional reaction-diffusion problems. The numerical solutions demonstrate that the combined method is stable and can provide accurate solution without spurious oscillation along the high-gradient boundary layers. 相似文献
20.
T. Yokoyama 《Archive of Applied Mechanics (Ingenieur Archiv)》2001,71(6-7):359-370
Summary A finite element technique is presented for the analysis of one-dimensional torsional plastic waves in a thin-walled tube.
Three different nonlinear consitutive relations deduced from elementary mechanical models are used to describe the shear stress–strain
characteristics of the tube material at high rates of strain. The resulting incremental equations of torsional motion for
the tube are solved by applying a direct numerical integration technique in conjunction with the constitutive relations. The
finite element solutions for torsional plastic waves in a long copper tube subjected to an imposed angular velocity at one
end are given, and a comparison with available experimental results to assess the accuracy of the constitutive relations considered
is conducted. It is demonstrated that the strain-rate dependent solutions show a better agreement with the experimental results
than the strain-rate independent solutions. The limitations of the constitutive equations are discussed, and some modifications
are suggested.
Received 9 February 1999; accepted for publication 28 March 2000 相似文献