A Circular Elastic Cylinder Under Extension

2011 ◽  
Vol 27 (3) ◽  
pp. 399-407 ◽  
Author(s):  
W.-D. Tseng ◽  
J.-Q. Tarn
Keyword(s):  
Transversely Isotropic ◽  
Elastic Cylinder ◽  
Axisymmetric Deformation ◽  
Axial Stiffness ◽  
Stress Distributions ◽  
End Effect ◽  
Rigorous Solution ◽  
Concentrated Load ◽  
End Conditions ◽  
Space Formalism

ABSTRACTAnalysis of deformation and stress field in a circular elastic cylinder under the extension is presented, with emphasis on the end effect. The problem is formulated on the basis of the state space formalism for axisymmetric deformation of transversely isotropic materials. A rigorous solution that satisfies the prescribed end conditions is determined by using symplectic eigenfunction expansion, thereby, the applicability of the Saint-Venant solution is examined. The results show that the end effect is significant but confined to a local region near the base of the cylinder where the end plane is perfectly bonded or subjected to a concentrated load. As the axial stiffness increases, the end effect on the stress state increases at the loaded end but decreases at the bonded end. The displacement and stress distributions across the section are uniform throughout the length of the cylinder except near the ends.

Laminated Tubes under Extension, Internal and External Pressure

2014 ◽  
Vol 30 (5) ◽  
pp. 455-466 ◽  
Author(s):  
W.-D. Tseng ◽  
J.-Q. Tarn ◽  
J.-H. Chang
Keyword(s):  
Transversely Isotropic ◽  
External Pressure ◽  
Axisymmetric Deformation ◽  
Elastic Tube ◽  
The State ◽  
Isotropic Layer ◽  
Stress Distributions ◽  
End Effect ◽  
Lateral Boundary Conditions ◽  
Symplectic Orthogonality

AbstractAn exact analysis of deformation and stress field in a laminated elastic tube under extension and uniform pressuring is presented. The problem of finite laminated tube is considered with emphasis on the end effect. The problem is formulated on the basis of the state space formalism for axisymmetric deformation of transversely isotropic layer. The transfer matrix transmits the state vector in radial direction from inner surface to outer surface and takes into account the interfacial continuity and lateral boundary conditions in a rigorous manner. Upon delineating the symplectic orthogonality relations of the eigenvectors and by using eigenfunction expansion, an exact solution which satisfies the end conditions is determined. The results show that the end effect is significant but confined to a local region near the base where the displacement and stress distributions are remarkably different from those according to the simplified solutions that only satisfy lateral BC.

A Cantilever Subjected to Axial Force, Bending Moment, and Shear Force

2014 ◽  
Vol 30 (5) ◽  
pp. 549-559 ◽  
Author(s):  
W.-D. Tseng ◽  
J.-Q. Tarn ◽  
C.-C. Chang
Keyword(s):  
State Space ◽  
Axial Force ◽  
Eigenfunction Expansion ◽  
Shear Force ◽  
Bending Moment ◽  
Stress Fields ◽  
Orthotropic Body ◽  
Rigorous Solution ◽  
End Conditions ◽  
Space Formalism

AbstractWe present an exact analysis of the displacement and stress fields in an elastic 2-D cantilever subjected to axial force, shear force and moment, in which the end conditions are exactly satisfied. The problem is formulated on the basis of the state space formalism for 2-D deformation of an orthotropic body. Upon delineating the Hamiltonian characteristics of the formulation and by using eigenfunction expansion, a rigorous solution which satisfies the end conditions is determined. The results show that the end condition alters the stress significantly only near the end, and elementary solutions in the form of polynomials can give sufficiently accurate results except near the ends. Such a system would give rise to localized stresses and displacements in the immediate neighborhood of the ends, and the effect may be expected to diminish with distance on account of geometrical divergence.

Torsional oscillation of rigid disk in infinite transversely isotropic elastic cylinder

2006 ◽  
Vol 27 (7) ◽  
pp. 911-917 ◽  
Author(s):  
Sakti Pada Barik ◽  
Mridula Kanoria ◽  
P. K. Chaudhuri
Keyword(s):  
Torsional Oscillation ◽  
Transversely Isotropic ◽  
Elastic Cylinder ◽  
Rigid Disk

Anisotropic Porochemoelectroelastic Solution for an Inclined Wellbore Drilled in Shale

2013 ◽  
Vol 80 (2) ◽  
Author(s):  
Minh H. Tran ◽  
Younane N. Abousleiman
Keyword(s):  
Porous Media ◽  
Fluid Pressure ◽  
Transversely Isotropic ◽  
Biological Tissues ◽  
Analytical Models ◽  
Combined Effects ◽  
Saturated Porous Media ◽  
Stress Distributions ◽  
Shale Formations ◽  
Electrically Charged

The porochemoelectroelastic analytical models have been used to describe the response of chemically active and electrically charged saturated porous media such as clay soils, shales, and biological tissues. However, existing studies have ignored the anisotropic nature commonly observed on these porous media. In this work, the anisotropic porochemoelectroelastic theory is presented. Then, the solution for an inclined wellbore drilled in transversely isotropic shale formations subjected to anisotropic far-field stresses with time-dependent down-hole fluid pressure and fluid activity is derived. Numerical examples illustrating the combined effects of porochemoelectroelastic behavior and anisotropy on wellbore responses are also included. The analysis shows that ignoring either the porochemoelectroelastic effects or the formation anisotropy leads to inaccurate prediction of the near-wellbore pore pressure and effective stress distributions. Finally, wellbore responses during a leak-off test conducted soon after drilling are analyzed to demonstrate the versatility of the solution in simulating complex down-hole conditions.

scholarly journals ANALISIS PENGARUH BENTUK DAN LOKASI BUKAAN PADA BALOK TINGGI MENGGUNAKAN METODE ELEMEN HINGGA

2020 ◽  
Vol 3 (4) ◽  
pp. 1209
Author(s):  
Anthony Fariman ◽  
Leo S. Tedianto
Keyword(s):  
Finite Element ◽  
Three Dimensional ◽  
Wall Structure ◽  
Deep Beam ◽  
Stress Distributions ◽  
Stress Concentrations ◽  
Offshore Structure ◽  
Deep Beams ◽  
Concentrated Load ◽  
Cable Networks

ABSTRAKBalok tinggi beton bertulang merupakan salah satu struktur khusus yang dapat memikul beban cukup besar dan umumnya digunakan sebagai transfer girder, struktur lepas pantai, struktur dinding, dan pondasi. Kehadiran bukaan pada balok tinggi dapat memfasilitasi jalur saluran AC, saluran pipa, jaringan kabel dan lain-lain. Dengan adanya bukaan pada balok tinggi dapat memberikan beberapa efek samping yaitu terjadinya diskontinuitas geometri, tegangan terdistribusi non-linier pada balok tinggi, berkurangnya kekuatan dari balok, dan timbulnya konsentrasi tegangan di sekitar bukaan. Penelitian ini bertujuan untuk menganalisis efek dari kehadiran bukaan pada balok tinggi di atas dua perletakan (sendi-rol) dan dibebani beban terpusat di tengah bentang balok lalu memvariasikan bentuk bukaan (persegi, persegi panjang, dan lingkaran) dan lokasi bukaan. Tegangan lentur pada balok tinggi dan konsentrasi tegangan yang terjadi di sekitar bukaan merupakan hal yang akan dibahas dalam penelitian. Analisis akan dibantu dengan Midas FEA yang merupakan program berbasis elemen hingga dan  pemodelan dilakukan dengan elemen solid tiga dimensi. Hasil dari analisis ini menunjukkan bahwa kehadiran bukaan pada balok tinggi menyebabkan kenaikan tegangan secara signifikan. Lokasi dari bukaan yang mendekati daerah tengah bentang balok juga sangat mempengaruhi besarnya tegangan yang terjadi.ABSTRACTReinforced concrete deep beam is one of the special structures that can carry quite a big load and generally used as a transfer girder, offshore structure, wall structure, and foundation. The appearance of openings in deep beams can facilitate AC pipelines, plumbing pipes, cable networks, etc. The existence of openings in deep beams can provide a few side effects such as geometric discontinuity, non-linear stress distributions over the deep beams, reduced strength of the deep beams, and stresses concentration will emerged around the openings. The purpose of this research is to analyze the effects from the existence of openings in deep beams on two supports (hinge and roller) and loaded by concentrated load in mid-span then variate the shape of openings (square, rectangle, and circle) and location of the openings. Flexural stresses in deep beams and the stress concentrations that occur around the openings are discussed in this research. The analysis will be assisted by Midas FEA which is a finite element based program and modelling will be executed in three dimensional solid elements. The result of this analysis showed that the existence of the openings in deep beams can cause stresses to increase significantly high. The location of the openings close to the mid-span of the deep beams also affect the amount of the stresses that occurs.

Forced Flexural Vibrations in a Thin Nonlocal Rectangular Plate with Kirchhoff’s Thin Plate Theory

2020 ◽  
Vol 20 (09) ◽  
pp. 2050107
Author(s):  
Iqbal Kaur ◽  
Parveen Lata ◽  
Kulvinder Singh
Keyword(s):  
Rectangular Plate ◽  
Thin Plate ◽  
Plate Theory ◽  
Nonlocal Parameter ◽  
Generalized Thermoelasticity ◽  
Transversely Isotropic ◽  
Small Scale ◽  
Concentrated Load ◽  
Thin Rectangular Plate ◽  
Flexural Vibrations

This study deals with a novel model of forced flexural vibrations in a transversely isotropic thermoelastic thin rectangular plate (TRP) due to time harmonic concentrated load. The mathematical model is prepared for the thin plate in a closed form with the application of Kirchhoff’s love plate theory for nonlocal generalized thermoelasticity with Green–Naghdi (GN)-III theory of thermoelasticity. The nonlocal thin plate has a nonlocal parameter to depict small-scale effect. The double finite Fourier transform technique has been used to find the expressions for lateral deflection, thermal moment and temperature distribution for simply supported (SS) thin rectangular plate in the transformed domain. The effect of classical thermoelasticity (CTE) theory of thermoelasticity and nonlocal parameters has been shown on the computed quantities. Few particular cases have also been deduced.

Buckling of Bars of Variable Rigidity with Varying Axial Load

1963 ◽  
Vol 67 (635) ◽  
pp. 734-736
Author(s):  
K. T. Sundara Raja Iyengar ◽  
S. Anantharamu
Keyword(s):  
Numerical Methods ◽  
Approximate Method ◽  
Convenient Method ◽  
Axial Load ◽  
Difficult Problem ◽  
Variable Rigidity ◽  
Rigorous Solution ◽  
Approximate Methods ◽  
Buckling Loads ◽  
End Conditions

The Evaluation of buckling loads of columns presents a difficult problem whose rigorous solution may be very difficult particularly when the variation of moment of inertia or the axial load does not follow a simple law. Hence approximate methods such as the variational and numerical methods will have to be employed. An approximate method is suggested in this note which offers a convenient method for the calculation of buckling loads of bars with any type of end conditions.

Experimental and Numerical Investigations of a Split-Ring Test for Springback

2006 ◽  
Vol 129 (2) ◽  
pp. 352-359 ◽  
Author(s):  
Z. Cedric Xia ◽  
Craig E. Miller ◽  
Feng Ren
Keyword(s):  
Experimental Data ◽  
Thickness Distribution ◽  
Transversely Isotropic ◽  
Ring Test ◽  
Stress Distributions ◽  
Opening Displacement ◽  
Split Ring ◽  
Punch Force ◽  
Hardening Models ◽  
Cylindrical Cup

This paper presents an in-depth experimental and numerical investigation of a split-ring test, which provides a simple yet effective benchmark for correlating forming and springback predictive capabilities with experimental measurements. The experimental procedure consists of deep drawing a circular 6111-T4 aluminum alloy into a cylindrical cup of 55mm depth, crosscutting nine rings each of 5mm wide from the cup, splitting the rings, and measuring their opening displacement, i.e., the springback amount. Experimental data obtained included punch force trajectories, drawn cup profile, thickness distribution after forming, and the ring openings after splitting. A numerical model is built to analyze the process, and both transversely isotropic and fully orthotropic yield criteria are investigated. Simulation results are validated against experimental data. A detailed numerical analysis is also conducted for stress distributions in each ring after each step and their relationship to the total springback amount. Stress and strain signatures suggested that the test is well suited for validating material models, such as anisotropic yield surface models and hardening models.

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