Endochronic Simulation on the Effect of Curvature Rate at the Preloading Stage on the Subsequent Creep or Relaxation of Thin-Walled Tubes Under Pure Bending

2011 ◽  
Vol 27 (4) ◽  
pp. 511-519 ◽  
Author(s):  
K.-H. Chang ◽  
C.-Y. Hung
Keyword(s):  
Experimental Data ◽  
Virtual Work ◽  
Algebraic Equations ◽  
Principle Of Virtual Work ◽  
Pure Bending ◽  
Endochronic Theory ◽  
First Order ◽  
Nonlinear Algebraic Equations ◽  
Thin Walled ◽  
Theoretical Simulations

ABSTRACTIn this paper, the first-order ordinary differential constitutive equations of endochronic theory were combined with the principle of virtual work for simulating the response of creep (moment is kept constant for a period of time) or relaxation (curvature is kept constant for a period of time) of thin-walled tubes subjected to pure bending with different curvature-rates at the preloading stage. A group of Fourier series was used to describe the circumferential displacements of the tube. Thus, a system of nonlinear algebraic equations was determined. This system of equations can be solved by numerical method. Experimental data tested by Pan and Fan [1] were compared with the theoretical simulations in this study. It is shown that the theoretical formulations effectively simulate the experimental data.

Analytical Modelling of the Dynamics of the Four-Bar Mechanism: A Comparison of Some Methods

2018 ◽  
Author(s):  
J. P. Meijaard ◽  
V. van der Wijk
Keyword(s):  
Virtual Work ◽  
Equations Of Motion ◽  
Differential Algebraic Equations ◽  
Force Balance ◽  
Dynamic Force ◽  
Algebraic Equations ◽  
Principle Of Virtual Work ◽  
Principal Vector ◽  
Reaction Forces ◽  
Principal Points

Some thoughts about different ways of formulating the equations of motion of a four-bar mechanism are communicated. Four analytic methods to derive the equations of motion are compared. In the first method, Lagrange’s equations in the traditional form are used, and in a second method, the principle of virtual work is used, which leads to equivalent equations. In the third method, the loop is opened, principal points and a principal vector linkage are introduced, and the equations are formulated in terms of these principal vectors, which leads, with the introduced reaction forces, to a system of differential-algebraic equations. In the fourth method, equivalent masses are introduced, which leads to a simpler system of principal points and principal vectors. By considering the links as pseudorigid bodies that can have a uniform planar dilatation, a compact form of the equations of motion is obtained. The conditions for dynamic force balance become almost trivial. Also the equations for the resulting reaction moment are considered for all four methods.

scholarly journals A microstructure-based constitutive law for snow

1993 ◽  
Vol 18 ◽  
pp. 287-294 ◽  
Author(s):  
Puneet Mahajan ◽  
Robert L. Brown
Keyword(s):  
Experimental Data ◽  
Mechanical Properties ◽  
Deformation Mechanism ◽  
Virtual Work ◽  
Constitutive Law ◽  
Constitutive Theory ◽  
Deformation Mechanisms ◽  
Principle Of Virtual Work ◽  
Computational Capability ◽  
Load Conditions

A constitutive theory of snow is developed to describe the mechanical properties of snow in terms of the properties of the ice grains and the necks that interconnect them. The principle of virtual work is used to calculate the stresses in the particles and necks. A number of different deformation mechanisms are investigated and, depending upon the deformation mechanism which is dominant for given load conditions, different equations are used to calculate the strains in the grains and necks. These strains around a representative ice grain are then averaged and scaled to obtain the global strains in the snow. The theory is then compared with experimental data to determine if the mechanical properties of snow can be adequately represented. Results show that the constitutive theory does work, but that it is cumbersome to implement, and that for practical use substantial computational capability is needed.

scholarly journals The stress-strain state of the universal chassis of the tractor trailer in T-Flex

2021 ◽  
Vol 264 ◽  
pp. 02008
Author(s):  
Ruslan Khakimzyanov ◽  
Anvar Togaev ◽  
Aziz Rashidov
Keyword(s):  
Experimental Data ◽  
Comparative Analysis ◽  
Software Package ◽  
Strain State ◽  
Virtual Work ◽  
Frame Structure ◽  
Principle Of Virtual Work ◽  
Model Data ◽  
Stress Strain ◽  
Stress Strain State

This article discusses the calculation of the strength of the frame structure of the universal chassis of the tractor trailer in the T-Flex software package and the comparative analysis of the results with experimental data and model data based on the principle of virtual work (possible movements).

scholarly journals THE MATHEMATICAL MODELLING OF THE NONLINEAR HEAT TRANSPORT IN THIN PLATE

1999 ◽  
Vol 4 (1) ◽  
pp. 44-50
Author(s):  
A. Buikis
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Mathematical Modelling ◽  
Heat Transport ◽  
Initial Value Problem ◽  
Nonlinear Ordinary Differential Equations ◽  
Algebraic Equations ◽  
Initial Value ◽  
First Order ◽  
Nonlinear Algebraic Equations

The approximations of the nonlinear heat transport problem are based on the finite volume (FM) and averaging (AM) methods [1,2]. This procedures allows reduce the nonlinear 2‐D problem for partial differential equation (PDE) to a initial‐value problem for a system of 2 nonlinear ordinary differential equations(ODE) of first order in the time t or to a initial‐value problem for one nonlinear ODE of first order with two nonlinear algebraic equations.

scholarly journals A microstructure-based constitutive law for snow

1993 ◽  
Vol 18 ◽  
pp. 287-294 ◽  
Author(s):  
Puneet Mahajan ◽  
Robert L. Brown
Keyword(s):  
Experimental Data ◽  
Mechanical Properties ◽  
Deformation Mechanism ◽  
Virtual Work ◽  
Constitutive Law ◽  
Constitutive Theory ◽  
Deformation Mechanisms ◽  
Principle Of Virtual Work ◽  
Computational Capability ◽  
Load Conditions

A constitutive theory of snow is developed to describe the mechanical properties of snow in terms of the properties of the ice grains and the necks that interconnect them. The principle of virtual work is used to calculate the stresses in the particles and necks. A number of different deformation mechanisms are investigated and, depending upon the deformation mechanism which is dominant for given load conditions, different equations are used to calculate the strains in the grains and necks. These strains around a representative ice grain are then averaged and scaled to obtain the global strains in the snow. The theory is then compared with experimental data to determine if the mechanical properties of snow can be adequately represented. Results show that the constitutive theory does work, but that it is cumbersome to implement, and that for practical use substantial computational capability is needed.

Simulation of Nonlinear Multiport Systems Using Bond Graphs

1973 ◽  
Vol 95 (1) ◽  
pp. 49-54 ◽  
Author(s):  
H. R. Martens
Keyword(s):  
Original System ◽  
Differential Algebraic Equations ◽  
Newton Iteration ◽  
System Of Equations ◽  
Algebraic Equations ◽  
Bond Graphs ◽  
First Order ◽  
Nonlinear Algebraic Equations ◽  
Previous Solution ◽  
Speed And Accuracy

An approach for the computer simulation of nonlinear multiport systems is presented. Bond graph techniques are utilized in the development. The objective of the formulation is to derive a system of mixed first-order differential/algebraic equations, whose solution is facilitated by approximating the derivatives by a linear combination of the present and several previous solution points. Thus the original system of equations is converted to a system of implicit nonlinear algebraic equations which are solved by a Newton iteration procedure. The formulation procedure lends itself to mechanization similar to ENPORT. Computational results from an illustrative example show the method to be excellent in speed and accuracy relative to other simulation approaches.

scholarly journals Plastic Buckling of Initially Imperfect Stiffened Cylinders in Axial Compression

1983 ◽  
Vol 50 (1) ◽  
pp. 88-94
Author(s):  
G. A. Duffett ◽  
B. D. Reddy
Keyword(s):  
Deformation Theory ◽  
Virtual Work ◽  
Compressive Load ◽  
Initial Imperfection ◽  
Complete Information ◽  
Equilibrium Path ◽  
Algebraic Equations ◽  
Buckling Mode ◽  
Nonlinear Algebraic Equations ◽  
Path Bifurcation

The behavior in the plastic range of axially compressed stringer-stiffened cylinders is investigated. The shell under consideration is assumed to have an initial imperfection in the form of sinusoidal deviation both axially and circumferentially. The constitutive relation employed here is J2 deformation theory of plasticity. This relation, as well as kinematic assumptions regarding the behavior of the panels and stiffeners that constitute the stiffened shell, is used in the principle of virtual work to obtain a set of nonlinear algebraic equations whose solution provides complete information about the prebuckling equilibrium path. Bifurcation from the primary path is examined by making use of a functional whose first variation is zero when two solutions to the problem are possible. This leads to an eigenvalue problem, the eigenvalue being the critical compressive load and the eigenfunction being the corresponding buckling mode. Results are presented for shells of different geometries and material properties, and a comparison of results is made with results obtained by others. The imperfect shells analyzed all exhibit stable behavior, with sufficiently large imperfections having a beneficial effect. Results for bifurcation from these paths are also discussed.

Basic Equations of Dynamic Elastic Stability for Thin-Walled Structural Members Subjected to Follower Loads and Their Application to Non-Conservative Torque Problems

1985 ◽  
Vol 9 (2) ◽  
pp. 75-83 ◽  
Author(s):  
Tadayoshi Aida
Keyword(s):  
Virtual Work ◽  
Elastic Stability ◽  
Structural Members ◽  
Principle Of Virtual Work ◽  
Torsional Moment ◽  
Channel Section ◽  
Numerical Examples ◽  
Thin Walled ◽  
Basic Equations ◽  
The Stability

The basic equations and the boundary conditions, in which the effect of an initial torsional moment Mz0 is included, and needed for the analysis of the dynamic elastic stability of thin-walled structural members subjected to follower loads are derived by introducing the concept of initial stress and using the principle of virtual work. The stability problems of columns with a channel section subjected to a non-conservative torque are investigated in terms of numerical examples.

The Comparison of the Cantilever Truss Node Displacement Calculation Methods

2014 ◽  
Vol 638-640 ◽  
pp. 279-282
Author(s):  
Sha Sha Wu ◽  
Dong Sheng Gu ◽  
Xiao Jie Gu ◽  
Tai Quan Zhou
Keyword(s):  
Experimental Data ◽  
Virtual Work ◽  
Structural Mechanics ◽  
Truss Structure ◽  
Principle Of Virtual Work ◽  
Calculation Methods ◽  
Show Difference ◽  
Rigid Joints ◽  
Node Displacement

In this paper, some popular software, such as structural mechanics solver, ANSYS and SAP2000 are used to calculate the deformation of truss structure under statics loading. This deformation can also be handy calculated by the principle of virtual work of structural mechanics. By comparing the calculated results with the experimental data, we can test the accuracy of these methods, especially when the joints in a truss structure are modeled as hinge joints or rigid joints. The calculated results show difference of the different modeling is very slight. The accuracy of hand computation is also satisfied compared with the results of software.

Nonlinear Model of Thin-Walled Composite Beams with Moderate Deflections

2010 ◽  
Vol 29-32 ◽  
pp. 22-27 ◽  
Author(s):  
Yong Sheng Ren ◽  
Xiang Hong Du
Keyword(s):  
Nonlinear Model ◽  
Composite Beams ◽  
Beam Deflection ◽  
Geometrically Nonlinear ◽  
Algebraic Equations ◽  
Analysis Model ◽  
Geometrically Nonlinear Analysis ◽  
Box Beam ◽  
Nonlinear Algebraic Equations ◽  
Thin Walled

A geometrically nonlinear model for thin-walled, single-cell composite beams is developed by using variational formulation and the variational-asympotical method. The structural modeling is split into two parts: a two-dimensional analysis over the cross section, and a geometrically nonlinear analysis of a beam along the beam span. The nonlinear model is based on the assumption of moderate beam deflection, accounting for the pitch angle and extends the linear analysis model for anisotropic thin-walled beams. By employing the Galerkin’s method, an nonlinear algebraic equations is derived and then solved by means of an incremental Newton-Raphson method. Numerical results are obtained for one cantilevered box beam: Circumferentially Uniform Stiffness(CUS), under external load to investigate the effect of geometric nonlinearity and the effects of the fiber orientation, laminate stacking sequence, are also addressed.

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