scholarly journals Explicit difference schemes for a pseudoparabolic equation with an integral condition

2012 ◽  
Vol 53 ◽  
Author(s):  
Justina Jachimavičienė
Keyword(s):  
Boundary Conditions ◽  
Integral Condition ◽  
Numerical Results ◽  
Difference Schemes ◽  
Pseudoparabolic Equation ◽  
Different Boundary Conditions ◽  
Explicit Schemes ◽  
Explicit Difference Schemes

The aim of this paper is to analyze three layer explicit schemes for a pseudoparabolic equation with different boundary conditions, including nonlocal ones. The numerical results are presented.

Exact Elasticity Solutions for Stresses and Deflections in Curved Beams and Rings of Exponential and T-Sections

1991 ◽  
Author(s):  
Cemil Bagci
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Plane Stress ◽  
Numerical Results ◽  
Neutral Axis ◽  
Curved Beams ◽  
Equilibrium Stress ◽  
Different Boundary Conditions ◽  
Stress Functions ◽  
Elasticity Solutions

Abstract Exact elasticity solutions for stresses and deflections (displacements) in curved beams and rings of varying thicknesses are developed using polar elasticity and state of plane stress. Basic forms of differential equations of equilibrium, stress functions, and differential equations of compatibility are given. They are solved to develop expressions for radial, tangential, and shearing stresses for moment, force, and combined loadings. Neutral axis location for each type of loading is determined. Expressions for displacements are developed utilizing strain-displacement relationships of polar elasticity satisfying boundary conditions on displacements. In case of full rings stresses are as in curved beams with properly defined moment loading, but displacements differ satisfying different boundary conditions. The developments for constant thicknesses are used to develop solutions for curved beams and rings with T-sections. Comparative numerical results are given.

Buckling Analysis of Shells with a Circumferential Crack

2006 ◽  
Vol 306-308 ◽  
pp. 55-60
Author(s):  
I.S. Putra ◽  
T. Dirgantara ◽  
Firmansyah ◽  
M. Mora
Keyword(s):  
Boundary Conditions ◽  
Cylindrical Shells ◽  
Buckling Analysis ◽  
Numerical Results ◽  
Buckling Load ◽  
Numerical Analyses ◽  
Radius Of Curvature ◽  
Critical Buckling Load ◽  
Different Boundary Conditions ◽  
Circumferential Crack

In this paper, buckling analysis of cylindrical shells with a circumferential crack is presented. The analyses were performed both numerically using FEM and experimentally. The numerical analyses and experiments were conducted for several crack lengths and radius of curvature, and two different boundary conditions were applied, i.e. simply support and clamp in all sides. The results show the effect of the presence of crack to the critical buckling load of the shells. There are good agreements between experimental and numerical results.

The Effect of Graded Strength on Damage Propagation in Continuously Nonhomogeneous Materials

2003 ◽  
Vol 125 (4) ◽  
pp. 412-417 ◽  
Author(s):  
Priya Thamburaj ◽  
Michael H. Santare ◽  
George A. Gazonas
Keyword(s):  
Finite Element ◽  
Boundary Conditions ◽  
Damage Model ◽  
Numerical Results ◽  
Finite Element Code ◽  
Different Boundary Conditions ◽  
One Dimensional ◽  
Damage Propagation ◽  
Dynamic Finite Element ◽  
Nonhomogeneous Materials

A damage model developed by Johnson and Holmquist is implemented into a dynamic finite element code. This is then used to study the effect of grading of the phenomenological damage parameters on the propagation of damage through the material. The numerical results for two one-dimensional example problems with different boundary conditions are presented, wherein the effect of a gradient in the intact strength of the material on damage propagation is studied. The results show that introducing different strength gradients can alter the location of the site of maximum damage. This may have important implications in the design of impact resistant materials and structures.

Exact Elasticity Solutions for Stresses and Deflections in Curved Beams and Rings of Exponential and T-Sections

1993 ◽  
Vol 115 (3) ◽  
pp. 346-358 ◽  
Author(s):  
C. Bagci
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Plane Stress ◽  
Numerical Results ◽  
Neutral Axis ◽  
Curved Beams ◽  
Equilibrium Stress ◽  
Different Boundary Conditions ◽  
Stress Functions ◽  
Elasticity Solutions

Exact elasticity solutions for stresses and deflections (displacements) in curved beams and rings of varying thicknesses are developed using polar elasticity and state of plane stress. Basic forms of differential equations of equilibrium, stress functions, and differential equations of compatibility are given. They are solved to develop expressions for radial, tangential, and shearing stresses for moment, force, and combined loadings. Neutral axis location for each type of loading is determined. Expressions for displacements are developed utilizing strain-displacement relationships of polar elasticity satisfying boundary conditions on displacements. In case of full rings stresses are as in curved beams with properly defined moment loading, but displacements differ satisfying different boundary conditions. The developments for constant thicknesses are used to develop solutions for curved beams and rings with T-sections. Comparative numerical results are given.

scholarly journals Mechanics of tubular helical assemblies: ensemble response to axial compression and extension

2021 ◽  
Author(s):  
Jacopo Quaglierini ◽  
Alessandro Lucantonio ◽  
Antonio DeSimone
Keyword(s):  
Boundary Conditions ◽  
Elastic Properties ◽  
Central Region ◽  
Mechanical Response ◽  
Different Boundary Conditions ◽  
Kirchhoff Rods ◽  
Model Versus ◽  
The Individual ◽  
Opposite Chirality

Abstract Nature and technology often adopt structures that can be described as tubular helical assemblies. However, the role and mechanisms of these structures remain elusive. In this paper, we study the mechanical response under compression and extension of a tubular assembly composed of 8 helical Kirchhoff rods, arranged in pairs with opposite chirality and connected by pin joints, both analytically and numerically. We first focus on compression and find that, whereas a single helical rod would buckle, the rods of the assembly deform coherently as stable helical shapes wound around a common axis. Moreover, we investigate the response of the assembly under different boundary conditions, highlighting the emergence of a central region where rods remain circular helices. Secondly, we study the effects of different hypotheses on the elastic properties of rods, i.e., stress-free rods when straight versus when circular helices, Kirchhoff’s rod model versus Sadowsky’s ribbon model. Summing up, our findings highlight the key role of mutual interactions in generating a stable ensemble response that preserves the helical shape of the individual rods, as well as some interesting features, and they shed some light on the reasons why helical shapes in tubular assemblies are so common and persistent in nature and technology. Graphic Abstract We study the mechanical response under compression/extension of an assembly composed of 8 helical rods, pin-jointed and arranged in pairs with opposite chirality. In compression we find that, whereas a single rod buckles (a), the rods of the assembly deform as stable helical shapes (b). We investigate the effect of different boundary conditions and elastic properties on the mechanical response, and find that the deformed geometries exhibit a common central region where rods remain circular helices. Our findings highlight the key role of mutual interactions in the ensemble response and shed some light on the reasons why tubular helical assemblies are so common and persistent.

The Bending, Buckling, and Flexural Vibration of Simply Supported Polygonal Plates by Point-Matching

1961 ◽  
Vol 28 (2) ◽  
pp. 288-291 ◽  
Author(s):  
H. D. Conway
Keyword(s):  
Hydrostatic Pressure ◽  
Boundary Conditions ◽  
Flexural Vibration ◽  
Frequency Equation ◽  
Numerical Results ◽  
Special Technique ◽  
Point Matching ◽  
Buckling Loads ◽  
Simply Supported ◽  
Flexural Vibrations

The bending by uniform lateral loading, buckling by two-dimensional hydrostatic pressure, and the flexural vibrations of simply supported polygonal plates are investigated. The method of meeting the boundary conditions at discrete points, together with the Marcus membrane analog [1], is found to be very advantageous. Numerical examples include the calculation of the deflections and moments, and buckling loads of triangular square, and hexagonal plates. A special technique is then given, whereby the boundary conditions are exactly satisfied along one edge, and an example of the buckling of an isosceles, right-angled triangle plate is analyzed. Finally, the frequency equation for the flexural vibrations of simply supported polygonal plates is shown to be the same as that for buckling under hydrostatic pressure, and numerical results can be written by analogy. All numerical results agree well with the exact solutions, where the latter are known.

Sign in / Sign up

Export Citation Format

Share Document