Nonlinear Creep Buckling of Some Simple Structures

1967 ◽  
Vol 34 (3) ◽  
pp. 651-658 ◽  
Author(s):  
N. C. Huang
Keyword(s):  
Cross Section ◽  
Analytical Solutions ◽  
Material Properties ◽  
Numerical Solutions ◽  
Direct Compression ◽  
Nonlinear Creep ◽  
Lateral Buckling ◽  
Nonlinear Viscoelastic ◽  
Buckling Behavior ◽  
Creep Buckling

In this paper, the creep buckling behavior of shallow Mises trusses and two-hinged sinusoidal low arches with sandwich cross section is studied. The material properties are assumed to be nonlinear viscoelastic and obeying the power creep law. The purpose of this study is to find the critical times, critical deflections, and postbuckling deflections of these structures. For Mises trusses, snap-through may be induced by direct compression or lateral buckling of the members. Analytical solutions are obtained. In the arch problem, both symmetrical and antisymmetrical bucklings are considered. Collocation method is used in the analysis, and numerical solutions are obtained.

Nonlinear Viscoelasticity for Short Time Ranges

1966 ◽  
Vol 33 (2) ◽  
pp. 313-321 ◽  
Author(s):  
N. C. Huang ◽  
E. H. Lee
Keyword(s):  
Constitutive Equation ◽  
Numerical Solutions ◽  
Kernel Functions ◽  
Nonlinear Creep ◽  
Experimental Procedure ◽  
Nonlinear Viscoelastic ◽  
Tension Tests ◽  
Incompressible Materials ◽  
Inverse Interpolation ◽  
Short Time

Approximate constitutive equations for nonlinear viscoelastic incompressible materials under small finite deformation and for short time ranges are derived. The error bound of such a constitutive equation is investigated. Nonlinear creep is analyzed on the basis of the proposed equation, and also the problem of a pressurized viscoelastic hollow cylinder bonded to an elastic casing. Numerical solutions, evaluated by assuming particular forms of kernel functions in the constitutive equation, are obtained by means of an inverse interpolation technique, and the effects of nonlinearity of material properties are discussed. An experimental procedure is also proposed for measuring kernel functions from uniaxial tension tests for real materials.

scholarly journals Effect of Lay Angle of Anti-Buckling Tape on Lateral Buckling Behavior of Tensile Armors

2015 ◽  
Author(s):  
Chongyao Zhou ◽  
Svein Sævik ◽  
Naiquan Ye ◽  
Guomin Ji
Keyword(s):  
Cross Section ◽  
Deep Water ◽  
Lateral Stability ◽  
Flexible Pipe ◽  
Lateral Buckling ◽  
Cyclic Bending ◽  
Buckling Behavior ◽  
Vessel Motion ◽  
Empty Condition ◽  
Torsion Deformation

During deep water flexible pipe installation, the pipe is normally free hanging in empty condition from the installation vessel to the seabed. This will introduce large hydrostatic forces to the pipe causing true wall compression. In addition, the pipe will be exposed to cyclic bending caused by waves and vessel motion. The combination of true wall axial compression and cyclic bending may lead to tensile armor instability in both lateral and radial directions. If the anti-buckling tape is assumed to be strong enough, the inner tensile armor will lose its lateral stability first due to the gap that may occur between the inner tensile armor and the pipe core, hence restricting the available friction restraint forces. These may further be reduced by cyclic motions that act to create slip between the layers, hence introducing lateral buckling of the tensile armor, with associated severe global torsion deformation of the pipe, ultimately causing the pipe to lose its integrity. The anti-buckling tape is designed to prevent the radial buckling behavior, however, its effect on lateral buckling has not yet been documented in available literature. In the present paper, the effect of the winding direction of the anti-buckling tape on the twist of the cross section is studied, including comparisons with available test data from literature.

Uniform Horizontal Groundwater Flow against Dispersion in a Shallow Aquifer: Two Analytical Models

1992 ◽  
Vol 23 (1) ◽  
pp. 1-12
Author(s):  
Ram Raj Vinda ◽  
Raja Ram Yadava ◽  
Naveen Kumar
Keyword(s):  
Point Source ◽  
Groundwater Flow ◽  
Cross Section ◽  
Analytical Solutions ◽  
Concentration Distribution ◽  
Analytical Models ◽  
Shallow Aquifer ◽  
Horizontal Cross Section ◽  
Flow Components ◽  
Reactive Pollutant

Analytical solutions converging rapidly at large and small values of times have been obtained for two mathematical models which describe the concentration distribution of a non reactive pollutant from a point source against the flow in a horizontal cross-section of a finite saturated shallow aquifer possessing uniform horizontal groundwater flow. Zero concentration or the conditions in which the flux across the extreme boundaries are proportional to the respective flow components are applied. The effects of flow and dispersion on concentration distribution are also discussed.

Thermal Post-Buckling Analysis of Functionally Graded Composite Plates with Nonlinear Aerodynamic Forces

2010 ◽  
Vol 123-125 ◽  
pp. 280-283
Author(s):  
Chang Yull Lee ◽  
Ji Hwan Kim
Keyword(s):  
Material Properties ◽  
Numerical Solutions ◽  
Virtual Work ◽  
Shear Deformation Theory ◽  
Composite Plates ◽  
Buckling Analysis ◽  
Functionally Graded ◽  
Governing Equations ◽  
Functionally Graded Composite ◽  
Post Buckling

The post-buckling of the functionally graded composite plate under thermal environment with aerodynamic loading is studied. The structural model has three layers with ceramic, FGM and metal, respectively. The outer layers of the sandwich plate are different homogeneous and isotropic material properties for ceramic and metal. Whereas the core is FGM layer, material properties vary continuously from one interface to the other in the thickness direction according to a simple power law distribution in terms of the volume fractions. Governing equations are derived by using the principle of virtual work and numerical solutions are solved through a finite element method. The first-order shear deformation theory and von-Karman strain-displacement relations are based to derive governing equations of the plate. Aerodynamic effects are dealt by adopting nonlinear third-order piston theory for structural and aerodynamic nonlinearity. The Newton-Raphson iterative method applied for solving the nonlinear equations of the thermal post-buckling analysis

Transient Two-Dimensional Heat Conduction Problem With Partial Heating Near Corners

2016 ◽  
Author(s):  
Robert L. McMasters ◽  
Filippo de Monte ◽  
James V. Beck ◽  
Donald E. Amos
Keyword(s):  
Heat Conduction ◽  
Numerical Integration ◽  
Analytical Solutions ◽  
Numerical Solutions ◽  
Thermal Protection ◽  
Heat Conduction Problem ◽  
Separation Of Variables ◽  
Two Dimensional ◽  
Rectangular Region ◽  
Long Distance

This paper provides a solution for two-dimensional heating over a rectangular region on a homogeneous plate. It has application to verification of numerical conduction codes as well as direct application for heating and cooling of electronic equipment. Additionally, it can be applied as a direct solution for the inverse heat conduction problem, most notably used in thermal protection systems for re-entry vehicles. The solutions used in this work are generated using Green’s functions. Two approaches are used which provide solutions for either semi-infinite plates or finite plates with isothermal conditions which are located a long distance from the heating. The methods are both efficient numerically and have extreme accuracy, which can be used to provide additional solution verification. The solutions have components that are shown to have physical significance. The extremely precise nature of analytical solutions allows them to be used as prime standards for their respective transient conduction cases. This extreme precision also allows an accurate calculation of heat flux by finite differences between two points of very close proximity which would not be possible with numerical solutions. This is particularly useful near heated surfaces and near corners. Similarly, sensitivity coefficients for parameter estimation problems can be calculated with extreme precision using this same technique. Another contribution of these solutions is the insight that they can bring. Important dimensionless groups are identified and their influence can be more readily seen than with numerical results. For linear problems, basic heating elements on plates, for example, can be solved to aid in understanding more complex cases. Furthermore these basic solutions can be superimposed both in time and space to obtain solutions for numerous other problems. This paper provides an analytical two-dimensional, transient solution for heating over a rectangular region on a homogeneous square plate. Several methods are available for the solution of such problems. One of the most common is the separation of variables (SOV) method. In the standard implementation of the SOV method, convergence can be slow and accuracy lacking. Another method of generating a solution to this problem makes use of time-partitioning which can produce accurate results. However, numerical integration may be required in these cases, which, in some ways, negates the advantages offered by the analytical solutions. The method given herein requires no numerical integration; it also exhibits exponential series convergence and can provide excellent accuracy. The procedure involves the derivation of previously-unknown simpler forms for the summations, in some cases by virtue of the use of algebraic components. Also, a mathematical identity given in this paper can be used for a variety of related problems.

Three-Dimensional Vibration Analysis of Twisted Cylinder With Sectorial Cross Section

2013 ◽  
Vol 80 (2) ◽  
Author(s):  
D. Zhou ◽  
S. H. Lo
Keyword(s):  
Cross Section ◽  
Chebyshev Polynomial ◽  
Numerical Solutions ◽  
Twist Angle ◽  
Ritz Method ◽  
Three Dimensional ◽  
Cylindrical Domain ◽  
Linear Elasticity Theory ◽  
Boundary Functions ◽  
Polynomial Series

The three-dimensional (3D) free vibration of twisted cylinders with sectorial cross section or a radial crack through the height of the cylinder is studied by means of the Chebyshev–Ritz method. The analysis is based on the three-dimensional small strain linear elasticity theory. A simple coordinate transformation is applied to map the twisted cylindrical domain into a normal cylindrical domain. The product of a triplicate Chebyshev polynomial series along with properly defined boundary functions is selected as the admissible functions. An eigenvalue matrix equation can be conveniently derived through a minimization process by the Rayleigh–Ritz method. The boundary functions are devised in such a way that the geometric boundary conditions of the cylinder are automatically satisfied. The excellent property of Chebyshev polynomial series ensures robustness and rapid convergence of the numerical computations. The present study provides a full vibration spectrum for thick twisted cylinders with sectorial cross section, which could not be determined by 1D or 2D models. Highly accurate results presented for the first time are systematically produced, which can serve as a benchmark to calibrate other numerical solutions for twisted cylinders with sectorial cross section. The effects of height-to-radius ratio and twist angle on frequency parameters of cylinders with different subtended angles in the sectorial cross section are discussed in detail.

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