The Various Approximations of the Bimetallic Thermostatic Strip

1991 ◽  
Vol 58 (4) ◽  
pp. 1015-1020 ◽  
Author(s):  
Christopher D. Pionke ◽  
Gerald Wempner
Keyword(s):  
Finite Elements ◽  
Normal Stress ◽  
Edge Effects ◽  
Degrees Of Freedom ◽  
Dissimilar Materials ◽  
Interfacial Shear ◽  
Thin Strip ◽  
Reasonable Accuracy ◽  
Interfacial Stresses ◽  
Transverse Normal Stress

A thin strip, formed by bonding two dissimilar materials, constitutes a simple thermostatic element. If edge effects are neglected, then the strip is reduced to a uniform beam, or plate, with two degrees-of-freedom. The flexure occurs only because of the bond and interfacial shear which is also accompanied by transverse normal stress. These latter stresses are very localized at the end and edges. Here, the elementary approximations, and refinements via finite elements, are presented and compared. Deflections are given with reasonable accuracy by the simple approximations, but the severe interfacial stresses are revealed only by the refinements.

New mixed finite elements for the discretization of piezoelectric structures or macro-fiber composites

2018 ◽  
Vol 29 (16) ◽  
pp. 3266-3283 ◽  
Author(s):  
Astrid S Pechstein ◽  
Martin Meindlhumer ◽  
Alexander Humer
Keyword(s):  
Finite Elements ◽  
Normal Stress ◽  
Degrees Of Freedom ◽  
Piezoelectric Materials ◽  
Normal Component ◽  
Mixed Finite Elements ◽  
Fiber Composites ◽  
Tangential Component ◽  
Tangential Displacement ◽  
Thin Elements

We propose a new three-dimensional formulation based on the mixed tangential-displacement normal-normal-stress method for elasticity. In elastic tangential-displacement normal-normal-stress elements, the tangential component of the displacement field and the normal component of the stress vector are degrees of freedom and continuous across inter-element interfaces. Tangential-displacement normal-normal-stress finite elements have been shown to be locking-free with respect to shear locking in thin elements, which makes them suitable for the discretization of laminates or macro-fiber composites. In the current paper, we extend the formulation to piezoelectric materials by adding the electric potential as degree of freedom.

scholarly journals Influence of Normal Stress on Creep in Tension and Compression of Polyethylene and Rigid Polyvinyl Chloride Copolymer

1962 ◽  
Vol 84 (2) ◽  
pp. 237-246 ◽  
Author(s):  
D. G. O’Connor ◽  
W. N. Findley
Keyword(s):  
Normal Stress ◽  
Polyvinyl Chloride ◽  
Material Structure ◽  
Reasonable Accuracy ◽  
Creep Tests ◽  
Compression Creep ◽  
Cent Relative Humidity ◽  
Tension And Compression ◽  
New Apparatus ◽  
Shear Planes

New apparatus suitable for compression creep tests of slender specimens is described. The apparatus is designed to prevent buckling and to introduce a minimum of friction. Results are reported for tension and compression creep of polyethylene and annealed, unplasticized polyvinyl chloride copolymer at 75 deg F and 50 per cent relative humidity. The stress σ, strain ε, time t data from these tests were found to be describable with reasonable accuracy by the equation ε=ε0′sinhσ/σε+m′tnsinhσ/σm where ε0′, m′, n, σε, and σm are material constants. The results for polyethylene show that the creep in tension and compression were virtually the same. However, the creep in tension was similar but larger than in compression for polyvinyl chloride. These observations are interpreted in terms of the material structure and the influence of the normal stress on active shear planes.

Large-Amplitude Oscillations of Unsymmetrically Laminated Anisotropic Rectangular Plates Including Shear, Rotatory Inertia, and Transverse Normal Stress

1985 ◽  
Vol 52 (3) ◽  
pp. 536-542 ◽  
Author(s):  
K. S. Sivakumaran ◽  
C. Y. Chia
Keyword(s):  
Boundary Conditions ◽  
Normal Stress ◽  
Transverse Shear ◽  
Plate Theory ◽  
Orientation Angle ◽  
Nonlinear Frequency ◽  
Rectangular Plates ◽  
Elastic Plates ◽  
Rotatory Inertia ◽  
Transverse Normal Stress

This paper is concerned with nonlinear free vibrations of generally laminated anisotropic elastic plates. Based on Reissner’s variational principle a nonlinear plate theory is developed. The effects of transverse shear, rotatory inertia, transverse normal stress, and transverse normal contraction or extension are included in this theory. Using the Galerkin procedure and principle of harmonic balance, approximate solutions to governing equations of unsymmetrically laminated rectangular plates including transverse shear, rotatory inertia, and transverse normal stress are formulated for various boundary conditions. Numerical results for the ratio of nonlinear frequency to linear frequency of unsymmetric angle-ply and cross-ply laminates are presented graphically for various values of elastic properties, fiber orientation angle, number of layers, and aspect ratio and for different boundary conditions. Present results are also compared with available data.

Three-Dimensional Solutions for Rotor Blades Using High-Order Geometrical Nonlinear Beam Finite Elements

2019 ◽  
Vol 64 (3) ◽  
pp. 1-10
Author(s):  
Matteo Filippi ◽  
Alfonso Pagani ◽  
Erasmo Carrera
Keyword(s):  
Finite Elements ◽  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Shear Deformation Theory ◽  
High Order ◽  
Rotor Blades ◽  
Constitutive Law ◽  
Displacement Fields ◽  
Cross Sectional ◽  
The Cross

This paper proposes a geometrically nonlinear three-dimensional formalism for the static and dynamic study of rotor blades. The structures are modeled using high-order beam finite elements whose kinematics are input parameters of the analysis. The displacement fields are written using two-dimensional Taylor- and Lagrange-like expansions of the cross-sectional coordinates. As far as the Taylor-like polynomials are concerned, the linear case is similar to the first-order shear deformation theory, whereas the higher-order expansions include additional contributions that describe the warping of the cross section. The Lagrange-type kinematics instead utilizes the displacements of certain physical points as degrees of freedom. The inherent three-dimensional nature of the Carrera unified formulation enables one to include all Green–Lagrange strain components as well as all coupling effects due to the geometrical features and the three-dimensional constitutive law. A number of test cases are considered to compare the current solutions with experimental and theoretical results reported in terms of large deflections/rotations and frequencies related to small amplitude vibrations.

Structural and Continuum Mechanics Approaches for a 3D Shear Deformable ANCF Beam Finite Element: Application to Buckling and Nonlinear Dynamic Examples

2013 ◽  
Vol 9 (1) ◽  
Author(s):  
Karin Nachbagauer ◽  
Johannes Gerstmayr
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Continuum Mechanics ◽  
Degrees Of Freedom ◽  
Mass Matrix ◽  
Finite Element Software ◽  
High Order Convergence ◽  
Dynamics Problems ◽  
Transverse Slope ◽  
Shear Deformable

For the modeling of large deformations in multibody dynamics problems, the absolute nodal coordinate formulation (ANCF) is advantageous since in general, the ANCF leads to a constant mass matrix. The proposed ANCF beam finite elements in this approach use the transverse slope vectors for the parameterization of the orientation of the cross section and do not employ an axial nodal slope vector. The geometric description, the degrees of freedom, and a continuum-mechanics-based and a structural-mechanics-based formulation for the elastic forces of the beam finite elements, as well as their usage in several static problems, have been presented in a previous work. A comparison to results provided in the literature to analytical solution and to the solution found by commercial finite element software shows accuracy and high order convergence in statics. The main subject of the present paper is to show the usability of the beam finite elements in dynamic and buckling applications.

Nondimensional Analysis of Interfacial Stresses of Wavy CNT/Polymer Composites

2008 ◽  
Author(s):  
K. Yazdchi ◽  
M. Salehi
Keyword(s):  
Carbon Nanotube ◽  
Polymer Composites ◽  
Analytical Model ◽  
Stress Transfer ◽  
Interfacial Shear ◽  
Linear Regression Method ◽  
Shear Stresses ◽  
Interfacial Stresses ◽  
Single Walled Carbon Nanotube ◽  
Reinforced Polymer

In this paper, with introducing a new simplified 3-D Representative Volume Element (RVE) for a wavy carbon nanotube (CNT), an analytical model has been developed to study the stress transfer in single-walled carbon nanotube (SWNT) reinforced polymer composites (NRPCs). The model is capable of predicting axial as well as interfacial shear stresses, along a wavy CNT embedded in a matrix. Based on the pullout modeling technique, the effects of waviness, wavelength and matrix modulus on axial and interfacial shear stresses have also been analyzed in details also using the statistical multiple non-linear regression method, the best-fitted functions for the interfacial stresses of CNT/polymer composites are obtained. The results of the present analytical model are in good agreements when compared with the corresponding results for straight NTs.

The Application of Harmonic Finite Elements in the Seismic Response Spectrum Analysis of a Skirt Supported Vessel

2010 ◽  
Author(s):  
Bikramjit Singh Antaal ◽  
Yogeshwar Hari ◽  
Dennis K. Williams
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Seismic Response ◽  
Spectrum Analysis ◽  
Degrees Of Freedom ◽  
Response Spectrum ◽  
Response Spectrum Analysis ◽  
Element Analysis ◽  
Structure Interaction ◽  
Input Response

This paper describes the finite element considerations employed in a seismic response spectrum analysis of a skirt supported, liquid containing pressure vessel. Like many axisymmetric cylindrical vessels, the gross seismic response to an input response spectrum can be categorized by a simplified lump mass model that includes both the mass of the vessel proper in combination with the associated mass of multiple fluid levels. This simplified response may be utilized to determine the initial sizing of the supporting configuration, such as a skirt, but lacks the ability to properly address the fluid-structure interaction that creates sloshing loads on the vessel walls. The most obvious method to address the fluid-structure interaction when considering the finite element method is to build a three-dimensional model of the vessel proper, including, but not limited to the shell courses, the top and bottom heads (for a vertical vessel), and the support skirt. The inclusion of the fluid effects may now be incorporated with a “contained fluid” finite element, however, for vessels of any significant volume, the number of finite elements can easily exceed 100,000 and the number of degrees of freedom can sore from as few as 300,000 to as many as 500,000 or more. While these types of finite element analysis problems can be solved with today’s computer hardware and software, it is not desirable in any analysis to have that volume of information that has to be reviewed and approved in a highly regulated nuclear QA environment (if at all possible). With these items in mind, the methodology described in this paper seeks to minimize the number of degrees of freedom associated with a response spectrum analysis of a liquid filled, skirt supported vertical pressure vessel. The input response spectra are almost always provided in Cartesian coordinates, while many, if not most liquid containing pressure vessels are almost always axisymmetric in geometry without having benefit of being subjected to an axisymmetric load (acceleration in this case) due to the specified seismic event. The use of harmonic finite elements for both the vessel structure and the contained fluid medium permit the efficiencies associated with an axisymmetric geometry to be leveraged when the seismic response spectrum is formulated in terms of a Fourier series and combined to regain the effects of the two orthogonal, horizontally applied accelerations as a function of frequency. The end result as discussed and shown in this paper is a finite element model that permits a dense mesh of both the fluid and the structure, while economizing on the number of simultaneous equations required to be solved by the chosen finite element analysis.

scholarly journals Shear Behaviors of the Intersurface between Rice Straw Rope and Dredger Fill Silt: Experimental and Mechanism Studies

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Guizhong Xu ◽  
Ji Chen ◽  
Shenjie Shi ◽  
Angran Tian ◽  
Qiang Tang
Keyword(s):  
Shear Strength ◽  
Normal Stress ◽  
Rice Straw ◽  
Immersion Time ◽  
Interfacial Shear Strength ◽  
Land Reclamation ◽  
Tensile Force ◽  
Interfacial Shear ◽  
Pull Out ◽  
Dredger Fill

The further development of land reclamation, port waterway, and wharf construction brings about proper treatments of dredger fill silt, while huge amounts of rice straw set aside in China argument rational disposal every year. Therefore, rice straw is bundled up as ropes, which represent as drainage body and reinforcement, to make eco-friendly treatment for dredger fill silt. This paper investigates the mechanical properties and validity of rice straw rope as certain treating material of dredger fill silt through a series of pull-out test, mass loss test, and tension test on specimens with different water contents and dry densities. The results reveal that peak value of interfacial shear strength rises with the increase of normal stress at the same immersion time, and in particular, it rises by up to 250.0% when the normal stress is 40 kPa. The tensile force of rice straw rope increases slowly with the rise of tensile displacement, and the failure mode changes from brittle to ductile with the rise of immersion time, which witnesses first rapid back slow degradation trend. The proper interfacial shear strength, tensile force, and reasonable degradation rate of rice straw rope make it ideal in drainage and consolidation of dredger fill silt.

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