Elastic deformations of infinite strips

1950 ◽  
Vol 46 (1) ◽  
pp. 164-181 ◽  
Author(s):  
H. G. Hopkins
Keyword(s):  
Boundary Conditions ◽  
Mathematical Problem ◽  
The Other ◽  
Transverse Displacement ◽  
Two Dimensional ◽  
Airy Stress Function ◽  
Elastic Deformations ◽  
Isotropic Plates ◽  
Edge Force ◽  
Harmonic Equation

ABSTRACTIn this paper, Fourier integrals are used to solve some elastic problems of generalized plane stress and small transverse displacements in infinitely long, rectangular, isotropic plates stressed only at their edges. The Airy stress function and the transverse displacement satisfy the two-dimensional bi-harmonic equation, and the basic mathematical problem is to solve this equation subject to different sets of boundary conditions. Little attention has been given hitherto to problems in which some of the boundary conditions depend directly upon displacements. Here the general problem is solved when one long edge is fixed, and stresses or displacements are arbitrarily prescribed at the other, with no stresses and displacements at infinity. The problem of a concentrated edge force is discussed in detail and numerical values of the stresses at the fixed edge are given.

CHIRAL ZEROMODES ON VORTEX-TYPE INTERSECTING FIVE-BRANE IN HETEROTIC STRING

2013 ◽  
Vol 21 ◽  
pp. 191-192
Author(s):  
MASAYA YATA
Keyword(s):  
Dirac Equation ◽  
String Theory ◽  
Boundary Conditions ◽  
Heterotic String ◽  
The Other ◽  
Two Dimensional ◽  
Complete Spectrum ◽  
Heterotic String Theory ◽  
Brane Solution ◽  
Opposite Chirality

We solve the gaugino Dirac equation on a smeared intersecting five-brane solution in E8 × E8 heterotic string theory to search for localized chiral zeromodes on the intersection. The background is chosen to depend on the full two-dimensional overall transverse coordinates to the branes. Under some appropriate boundary conditions, we compute the complete spectrum of zeromodes to find that, among infinite towers of Fourier modes, there exist only three localized normalizable zeromodes, one of which has opposite chirality to the other two.

A Comparative Study of Artificial Boundary Conditions in ABAQUS

2013 ◽  
Vol 671-674 ◽  
pp. 1386-1389
Author(s):  
Yan Wei Wang ◽  
Shan You Li ◽  
Qiang Ma ◽  
Wei Li
Keyword(s):  
Wave Propagation ◽  
Boundary Conditions ◽  
Element Model ◽  
The Other ◽  
Two Dimensional ◽  
Artificial Boundary ◽  
Artificial Boundary Conditions ◽  
Dimensional Finite Element ◽  
Viscous Boundary ◽  
Better Than

Viscous boundary, viscous spring boundary, infinite boundary have been widely used during the last decades to solve the wave propagation in the infinite ground. In this paper we evaluate the performance of the three boundary conditions focusing on their solution precision. The comparison is performed on a two dimensional finite element model built by ABAQUS. The results show that viscous spring boundary outperforms the other boundary conditions, and viscous boundary is better than infinite element.

Study of the Effect of Boundary Conditions on Residual Stresses in Welding Using Element Birth and Element Movement Techniques

2003 ◽  
Vol 125 (4) ◽  
pp. 432-439 ◽  
Author(s):  
Ihab F. Z. Fanous ◽  
Maher Y. A. Younan ◽  
Abdalla S. Wifi
Keyword(s):  
Residual Stresses ◽  
Boundary Conditions ◽  
Three Dimensional ◽  
Welding Process ◽  
Computation Time ◽  
The Other ◽  
Two Dimensional ◽  
The Media ◽  
Three Dimensional Models ◽  
Element Movement

The structure in which the welding process is performed highly affects the residual stresses generated in the welding. This effect is simulated by choosing the appropriate boundary conditions in modeling the welding process. The major parameters of the boundary conditions are the method by which the base metal is being fixed and the amount of heat being applied through the torch. Other parameters may include the coefficients of thermal heat loss from the plate which may simulate the media in which the welding is taking place. In modeling the welding process, two-dimensional forms of approximation were developed in analyzing most of the models of such problem. Three-dimensional models analyzing the welding process were developed in limited applications due to its high computation time and cost. With the development of new finite element tools, namely the element movement technique developed by the authors, full three-dimensional analysis of the welding process is becoming in hand. In the present work, three different boundary conditions shall be modeled comparing their effect on the welding. These boundary conditions shall be applied to two models of the welding process: one using the element birth technique and the other using the element movement technique showing the similarity in their responses verifying the effectiveness of the latter being accomplished in a shorter time.

scholarly journals Properties of RG interfaces for 2D boundary flows

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Anatoly Konechny
Keyword(s):  
Boundary Condition ◽  
Fixed Point ◽  
Variational Method ◽  
Boundary Conditions ◽  
The Other ◽  
Two Dimensional ◽  
Conformal Boundary ◽  
First Approximation ◽  
Local Operators

Abstract We consider RG interfaces for boundary RG flows in two-dimensional QFTs. Such interfaces are particular boundary condition changing operators linking the UV and IR conformal boundary conditions. We refer to them as RG operators. In this paper we study their general properties putting forward a number of conjectures. We conjecture that an RG operator is always a conformal primary such that the OPE of this operator with its conjugate must contain the perturbing UV operator when taken in one order and the leading irrelevant operator (when it exists) along which the flow enters the IR fixed point, when taken in the other order. We support our conjectures by perturbative calculations for flows between nearby fixed points, by a non-perturbative variational method inspired by the variational method proposed by J. Cardy for massive RG flows, and by numerical results obtained using boundary TCSA. The variational method has a merit of its own as it can be used as a first approximation in charting the global structure of the space of boundary RG flows. We also discuss the role of the RG operators in the transport of states and local operators. Some of our considerations can be generalised to two-dimensional bulk flows, clarifying some conceptual issues related to the RG interface put forward by D. Gaiotto for bulk 𝜙1,3 flows.

Polynomial Based Elasticity Solutions of Beams and their Numerical Validation: A Review

2011 ◽  
Vol 311-313 ◽  
pp. 2315-2321
Author(s):  
Sebin Jose ◽  
Sunil Bhat
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Boundary Conditions ◽  
Two Dimensional ◽  
Element Analysis ◽  
Stress Problem ◽  
Elasticity Solutions ◽  
Harmonic Equation ◽  
Complex Cases ◽  
Good Agreement

Solution of two-dimensional stress problem is reduced to integration of bi-harmonic equation[1].A polynomial is chosen as Airy’s stress function.Constants of the polynomial[2] are found by fulfilling the boundary conditions. Stress solutions are obtained from.The paper presents polynomial based stress solutions of beams for complex cases involving offset loads and other combinations with offset loads.The results are compared with those obtained from finite element analysis[3] and conventional methods.The results are in good agreement with each other.

Separated Solution Procedure for Bending of Circular Plates With Circular Holes

1991 ◽  
Vol 44 (11S) ◽  
pp. S27-S35 ◽  
Author(s):  
M. D. Bird ◽  
C. R. Steele
Keyword(s):  
Boundary Conditions ◽  
Processing Time ◽  
Solution Procedure ◽  
Trigonometric Fourier Series ◽  
Two Dimensional ◽  
Circular Plates ◽  
Arbitrary Boundary ◽  
Circular Holes ◽  
Circular Domains ◽  
Harmonic Equation

A separated solution procedure is presented for the two-dimensional bi-harmonic equation on circular domains with circular holes and arbitrary boundary conditions. The solutions use the traditional trigonometric Fourier series on the boundaries with a power series decay into the domain. The interaction of the boundaries is expressed simply and exactly resulting in quick processing time. The only simplification made is the use of a finite number of terms in the boundary conditions.

Theories for Elastic Plates Via Orthogonal Polynomials

1981 ◽  
Vol 48 (4) ◽  
pp. 900-904 ◽  
Author(s):  
S. Krenk
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Three Dimensional ◽  
Transversely Isotropic ◽  
Displacement Function ◽  
Shear Stresses ◽  
Transverse Displacement ◽  
Normal Strain ◽  
Two Dimensional ◽  
Elastic Plates

A complementary energy functional is used to derive an infinite system of two-dimensional differential equations and appropriate boundary conditions for stresses and displacements in homogeneous anisotropic elastic plates. Stress boundary conditions are imposed on the faces a priori, and this introduces a weight function in the variations of the transverse normal and shear stresses. As a result the coupling between the two-dimensional differential equations is described in terms of a single difference operator. Special attention is given to a truncated system of equations for bending of transversely isotropic plates. This theory has three boundary conditions, like Reissner’s, but includes the effect of transverse normal strain, essentially through a reinterpretation of the transverse displacement function. Full agreement with general integrals to the homogeneous three-dimensional equations is established to within polynomial approximation.

Three-Dimensional Reconstruction of Two Forms of the Chaperonin GRO EL

1990 ◽  
Vol 48 (1) ◽  
pp. 258-259
Author(s):  
J.L. Carrascosa ◽  
G. Abella ◽  
S. Marco ◽  
M. Muyal ◽  
J.M. Carazo
Keyword(s):  
Three Dimensional ◽  
The Other ◽  
Two Dimensional ◽  
Series Method ◽  
Three Dimensional Reconstruction ◽  
Structural Components ◽  
E Coli ◽  
Dimensional Reconstruction ◽  
Morphogenetic Factors ◽  
Tilt Series

Chaperonins are a class of proteins characterized by their role as morphogenetic factors. They trantsiently interact with the structural components of certain biological aggregates (viruses, enzymes etc), promoting their correct folding, assembly and, eventually transport. The groEL factor from E. coli is a conspicuous member of the chaperonins, as it promotes the assembly and morphogenesis of bacterial oligomers and/viral structures.We have studied groEL-like factors from two different bacteria:E. coli and B.subtilis. These factors share common morphological features , showing two different views: one is 6-fold, while the other shows 7 morphological units. There is also a correlation between the presence of a dominant 6-fold view and the fact of both bacteria been grown at low temperature (32°C), while the 7-fold is the main view at higher temperatures (42°C). As the two-dimensional projections of groEL were difficult to interprete, we studied their three-dimensional reconstruction by the random conical tilt series method from negatively stained particles.

Symbolic computation to estimate two-sided boundary conditions in two-dimensional conduction problems

10.2514/3.920 ◽  
1997 ◽  
Vol 11 ◽  
pp. 472-476
Author(s):  
Henry H. Kerr ◽  
F. C. Frank ◽  
Jae-Woo Lee ◽  
W. H. Mason ◽  
Ching-Yu Yang
Keyword(s):  
Boundary Conditions ◽  
Symbolic Computation ◽  
Two Dimensional

Polymer-Graphene Nanoassemblies and their Applications in Cancer Theranostics

2020 ◽  
Vol 20 (11) ◽  
pp. 1340-1351 ◽  
Author(s):  
Ponnurengam M. Sivakumar ◽  
Matin Islami ◽  
Ali Zarrabi ◽  
Arezoo Khosravi ◽  
Shohreh Peimanfard
Keyword(s):  
Mechanical Stability ◽  
Chemical Properties ◽  
The Other ◽  
Hydrophilic Polymer ◽  
Two Dimensional ◽  
Normal Tissues ◽  
Physical Chemical ◽  
Anti Cancer ◽  
Good Biocompatibility ◽  
Cancer Theranostics

Background and objective: Graphene-based nanomaterials have received increasing attention due to their unique physical-chemical properties including two-dimensional planar structure, large surface area, chemical and mechanical stability, superconductivity and good biocompatibility. On the other hand, graphene-based nanomaterials have been explored as theranostics agents, the combination of therapeutics and diagnostics. In recent years, grafting hydrophilic polymer moieties have been introduced as an efficient approach to improve the properties of graphene-based nanomaterials and obtain new nanoassemblies for cancer therapy. Methods and results: This review would illustrate biodistribution, cellular uptake and toxicity of polymergraphene nanoassemblies and summarize part of successes achieved in cancer treatment using such nanoassemblies. Conclusion: The observations showed successful targeting functionality of the polymer-GO conjugations and demonstrated a reduction of the side effects of anti-cancer drugs for normal tissues.

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