An Inverse Method for the Reduction of Stress Concentration in the Two-dimensional Elastic Problem

1988 ◽  
pp. 445-452
Author(s):  
H. Kawabe ◽  
H. Mano ◽  
M. Bessho
Keyword(s):  
Stress Concentration ◽  
Inverse Method ◽  
Elastic Problem ◽  
Two Dimensional

Determination of Stress Concentration Around an Oblique Hole by a Finite-Element Technique

1983 ◽  
Vol 105 (2) ◽  
pp. 206-212 ◽  
Author(s):  
Hua-Ping Li ◽  
F. Ellyin
Keyword(s):  
Finite Element ◽  
Stress Concentration ◽  
Maximum Stress ◽  
Plate Thickness ◽  
Two Dimensional ◽  
Element Analysis ◽  
The Finite Element Analysis ◽  
Parametric Studies ◽  
Element Technique

A plate weakened by an oblique penetration of a circular cylindrical hole has been investigated. The stress concentration around the hole is determined by a finite-element method. The results are compared with experimental data and other analytical works. Parametric studies of effects of angle of inclination, plate thickness, and width are performed. The maximum stress concentration factor (SCF) obtained from the finite-element analysis is higher than experimental results, and this deviation increases with the increase of angle of skewness. The major reason for this difference is attributed to the shear-action between layers parallel to the plate surface which cannot be directly included in the two-dimensional elements. An empirical formula is derived which accounts for the shear-action and renders the finite-element predictions in line with experimentally observed data.

The Flow and Fracture of a Brittle Material

1950 ◽  
Vol 17 (3) ◽  
pp. 233-248
Author(s):  
L. F. Coffin
Keyword(s):  
Cast Iron ◽  
Stress Concentration ◽  
Stress Concentration Factor ◽  
Concentration Factor ◽  
Gray Cast Iron ◽  
Gray Cast ◽  
Residual Tensile Stress ◽  
Two Dimensional ◽  
Combined Stress ◽  
Plastic Stress

Abstract The mechanism of flow and fracture of a gray cast iron can be understood if one considers the microstructure to consist of a ductile structure with a random dispersion of cracks due to the graphite flakes following the concept of Fisher. A notch effective stress can be calculated for a critically situated crack by a knowledge of the external stresses, a plastic stress-concentration factor of 3, and a residual tensile stress at the sharp edge of the crack, based upon either the “maximum-shear” theory or the “distortion-energy” theory. This allows the formulation of generalized plastic stress-strain relationships and renders gray cast iron applicable to the many known solutions for plastic flow of ductile metals. Fracture in the region of tension-tension and tension-compression can be evaluated by a similar analysis, using the same stress-concentration factor and the same residual stress. A combined stress-testing program is described wherein thin-walled cast-iron tubes are subjected to two-dimensional states of combined stress covering the complete two-dimensional field.

A free-streamline solution for stratified flow into a line sink

1965 ◽  
Vol 21 (3) ◽  
pp. 535-543 ◽  
Author(s):  
Timothy W. Kao
Keyword(s):  
Froude Number ◽  
Inverse Method ◽  
Separated Flows ◽  
Two Dimensional ◽  
Mathematical Solution ◽  
Velocity Discontinuity ◽  
Natural Processes ◽  
A Value ◽  
Line Sink ◽  
Two Dimensional Flow

An analysis is made of the two-dimensional flow under gravity of an inviscid non-diffusive stratified fluid into a line sink, involving a velocity discontinuity in the flow field. The fluid above the discontinuity is stagnant and hence is not drawn into the sink. At sufficiently low values of the modified Froude number, this is the only physically possible mode of flow, and is the cause of flow separation in many industrial and natural processes. A proper mathematical solution for flows with a stagnant zone has so far been lacking. This paper presents such a solution, after posing the problem as one involving a free-streamline, which is the line of velocity discontinuity. The solution to be given here is obtained by an inverse method. It is also found herein that the modified Froude number has a value of 0·345 for all separated flows of the kind in question.

scholarly journals Membrane analogy for multi-material bars under torsion

2019 ◽  
Vol 475 (2225) ◽  
pp. 20190124 ◽  
Author(s):  
Laura Galuppi ◽  
Gianni Royer-Carfagni
Keyword(s):  
Finite Element ◽  
Cross Section ◽  
Cross Sections ◽  
Three Dimensional ◽  
Element Model ◽  
Elastic Problem ◽  
Two Dimensional ◽  
Torsion Problem ◽  
Linear Elastic ◽  
Physical Apparatus

Prandtl's membrane analogy for the torsion problem of prismatic homogeneous bars is extended to multi-material cross sections. The linear elastic problem is governed by the same equations describing the deformation of an inflated membrane, differently tensioned in regions that correspond to the domains hosting different materials in the bar cross section, in a way proportional to the inverse of the material shear modulus. Multi-connected cross sections correspond to materials with vanishing stiffness inside the holes, implying infinite tension in the corresponding portions of the membrane. To define the interface constrains that allow to apply such a state of prestress to the membrane, a physical apparatus is proposed, which can be numerically modelled with a two-dimensional mesh implementable in commercial finite-element model codes. This approach presents noteworthy advantages with respect to the three-dimensional modelling of the twisted bar.

scholarly journals Geometric charges and nonlinear elasticity of two-dimensional elastic metamaterials

2020 ◽  
Vol 117 (19) ◽  
pp. 10195-10202
Author(s):  
Yohai Bar-Sinai ◽  
Gabriele Librandi ◽  
Katia Bertoldi ◽  
Michael Moshe
Keyword(s):  
Elastic Problem ◽  
Porous Solids ◽  
Two Dimensional ◽  
Mechanical Instability ◽  
Mechanical Metamaterials ◽  
Recent Developments ◽  
Elastic Metamaterials ◽  
Geometrical Effects ◽  
Nonlinear Geometric ◽  
Geometric Formulation

Problems of flexible mechanical metamaterials, and highly deformable porous solids in general, are rich and complex due to their nonlinear mechanics and the presence of nontrivial geometrical effects. While numeric approaches are successful, analytic tools and conceptual frameworks are largely lacking. Using an analogy with electrostatics, and building on recent developments in a nonlinear geometric formulation of elasticity, we develop a formalism that maps the two-dimensional (2D) elastic problem into that of nonlinear interaction of elastic charges. This approach offers an intuitive conceptual framework, qualitatively explaining the linear response, the onset of mechanical instability, and aspects of the postinstability state. Apart from intuition, the formalism also quantitatively reproduces full numeric simulations of several prototypical 2D structures. Possible applications of the tools developed in this work for the study of ordered and disordered 2D porous elastic metamaterials are discussed.

Stress Distribution Around Edge Slits in a Plate Loaded in Tension —the Effect of Finite Width of Plate

1962 ◽  
Vol 66 (617) ◽  
pp. 320-322 ◽  
Author(s):  
J. R. Dixon
Keyword(s):  
Stress Concentration ◽  
Stress Distribution ◽  
Flat Plate ◽  
Elastic Stress ◽  
Width Ratio ◽  
Finite Width ◽  
Two Dimensional ◽  
Finite Plate ◽  
Edge Slit ◽  
Plate Width

SummaryTwo-dimensional photoelastic tests have been carried out on uni-axially loaded flat-plate specimens with two collinear edge slits, to investigate the effect of finite plate width on the elastic stress distribution. It was found that the effect of slitlength/ plate-width ratio on the elastic stress concentration at the end of the edge slit of length l was virtually the same as that for a central slit of length 2l in a plate of the same width, and could be adequately expressed by existing theories.

Complex Analysis of Plane Problem of Two-Dimensional Quasicrystals

2012 ◽  
Vol 236-237 ◽  
pp. 52-54
Author(s):  
Lin Yang ◽  
Qin He ◽  
Shu Yong Zhou ◽  
Wu Li
Keyword(s):  
Stress Concentration ◽  
Plane Problem ◽  
Complex Potential ◽  
Fracture Behavior ◽  
Complex Analysis ◽  
Potential Method ◽  
Two Dimensional ◽  
Complex Potential Method ◽  
Important Significance

The fracture behavior of materials and structures are always caused by stress concentration near the defects in materials. This article describes the complex potential method for solving plane problems of quasicrystalline materials with defects. In order to prove effectiveness and success of the method, an example is given, and the results have very important significance in studying two-dimensional quasicrystals.

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