scholarly journals Strain-energy bounds in finite-element analysis by slab analogy

1967 ◽  
Vol 2 (4) ◽  
pp. 265-271 ◽  
Author(s):  
B Fraeijs De Veubeke ◽  
O C Zienkiewicz
Keyword(s):  
Strain Energy ◽  
Energy Content ◽  
True Strain ◽  
Plane Elasticity ◽  
Stress Fields ◽  
Lower And Upper Bounds ◽  
Displacement Fields ◽  
Element Analysis ◽  
Energy Bounds ◽  
Elasticity Problems

It is well known that in approximate analysis of elasticity problems lower and upper bounds to the true strain-energy content can be obtained by the alternative assumptions of compatible displacement fields or of equilibrating stress fields. While formulations based on the first are relatively easy to achieve those based on the second present many difficulties. In this paper it is shown how by virtue of the analogy between plane-elasticity and slab-deflection problems compatible-displacement formulations in either one can be used to generate equilibrating formulations in the other. This should result in a direct application of existing programmes to a wider range of problems.

scholarly journals Finite elements with continuous stress fields in calculation of folded prismatic thin-walled rods and shells

2018 ◽  
Vol 196 ◽  
pp. 01018
Author(s):  
Sergey Nazarenko ◽  
Nina Blokhina
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Degrees Of Freedom ◽  
High Efficiency ◽  
Stress Fields ◽  
Displacement Fields ◽  
Element Analysis ◽  
The Finite Element Analysis ◽  
Shell Finite Element ◽  
Rectangular Shell

The article deals with methods of creating a rectangular wall-beam finite element with eight degrees of freedom per node and continuous stress fields along the boundaries. This effect is achieved by specifying displacement fields in the plane of the element in forms similar to those in finite elements of Bogner, Fox, and Schmitt plate. The article provides algebraic expressions for displacement forms; methods of forming reaction and stress matrices are also considered. Test calculations carried out with the help of “Computational mechanics” FEM complex have proved high efficiency of the finite element analysis performed. A rectangular shell finite element with twelve degrees of freedom per node was developed as a combination of membrane finite element and Bogner, Fox and Schmitt plate element.

Mixed-displacement finite-element analysis with particular application using plane-stress triangles

1972 ◽  
Vol 7 (4) ◽  
pp. 243-252 ◽  
Author(s):  
G M McNeice ◽  
S F Hunnisett
Keyword(s):  
Finite Elements ◽  
Plane Stress ◽  
Strain Energy ◽  
Degrees Of Freedom ◽  
High Strain ◽  
Energy Content ◽  
Three Dimensional ◽  
Triangular Grid ◽  
Element Analysis ◽  
Displacement Approach

Finite elements which have different displacement functions for each boundary are termed ‘mixed-displacement’ elements. The mixed-displacement approach to finite elements is applied to plane-stress problems in which mixed-strain triangles are formed from the linear-strain triangle. It is shown that by using these triangles in conjunction with existing linear- and constant-strain triangles, higher strain-energy content is produced with fewer active degrees of freedom than are otherwise necessary. A basic triangular grid is first assumed and any number of additional midside nodes can be inserted in regions of high strain gradients. Reference to three-dimensional isoparametric elements is given.

The Stress Fields Caused by a Circular Cylindrical Inclusion

1992 ◽  
Vol 59 (2S) ◽  
pp. S107-S114 ◽  
Author(s):  
Hisao Hasegawa ◽  
Ven-Gen Lee ◽  
Toshio Mura
Keyword(s):  
Exact Solutions ◽  
Strain Energy ◽  
Elastic Solid ◽  
Cylindrical Inclusion ◽  
Stress Fields ◽  
Axisymmetric Stress ◽  
Displacement Fields ◽  
Elastic Fields ◽  
Stress And Displacement Fields ◽  
Interior Points

Exact solutions are presented in closed forms for the axisymmetric stress and displacement fields caused by a solid or hollow circular cylindrical inclusion (with uniform axial eigenstrain prescribed) in an infinite elastic solid. The same expressions are obtained for the elastic fields for interior and exterior points of the inclusion. Although Eshelby’s solutions for ellipsoidal inclusions are uniform in the interior points, the present solutions do not show the uniformity. When the length of inclusion becomes infinite, the present solutions agree with Eshelby ’s results. The strain energy is also shown. The method of Green’s function is used.

scholarly journals Photogrammetric Process to Monitor Stress Fields Inside Structural Systems

Sensors ◽  
2021 ◽  
Vol 21 (12) ◽  
pp. 4023
Author(s):  
Leonardo M. Honório ◽  
Milena F. Pinto ◽  
Maicon J. Hillesheim ◽  
Francisco C. de Araújo ◽  
Alexandre B. Santos ◽  
...  
Keyword(s):  
Boundary Element ◽  
Real Time ◽  
Stress Fields ◽  
Structural Systems ◽  
Unknown Boundary ◽  
Stress Distributions ◽  
Displacement Fields ◽  
Time Stress ◽  
Beam Surface ◽  
Measured Displacement

This research employs displacement fields photogrammetrically captured on the surface of a solid or structure to estimate real-time stress distributions it undergoes during a given loading period. The displacement fields are determined based on a series of images taken from the solid surface while it experiences deformation. Image displacements are used to estimate the deformations in the plane of the beam surface, and Poisson’s Method is subsequently applied to reconstruct these surfaces, at a given time, by extracting triangular meshes from the corresponding points clouds. With the aid of the measured displacement fields, the Boundary Element Method (BEM) is considered to evaluate stress values throughout the solid. Herein, the unknown boundary forces must be additionally calculated. As the photogrammetrically reconstructed deformed surfaces may be defined by several million points, the boundary displacement values of boundary-element models having a convenient number of nodes are determined based on an optimized displacement surface that best fits the real measured data. The results showed the effectiveness and potential application of the proposed methodology in several tasks to determine real-time stress distributions in structures.

On the Crack Initiated from the Bi-Material Notch Tip

2010 ◽  
Vol 452-453 ◽  
pp. 441-444 ◽  
Author(s):  
Tomáš Profant ◽  
Jan Klusák ◽  
Michal Kotoul
Keyword(s):  
Energy Density ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Local Minimum ◽  
Plane Elasticity ◽  
Mean Value ◽  
Tangential Stresses ◽  
Density Factor ◽  
The Mean ◽  
Energy Density Factor

The bi-material notch composed of two orthotropic parts is considered. The radial and tangential stresses and strain energy density is expressed using the Stroh-Eshelby-Lekhnitskii formalism for the plane elasticity. The potential direction of the crack initiation is determined from the maximum mean value of the tangential stresses and local minimum of the mean value of the generalized strain energy density factor in both materials. Matched asymptotic procedure is used to derive the change of potential energy for the debonding crack and the crack initiated in the determined direction.

Vibration-Based Crack Detection in L-Frames

2014 ◽  
Vol 658 ◽  
pp. 261-268
Author(s):  
Jean Louis Ntakpe ◽  
Gilbert Rainer Gillich ◽  
Florian Muntean ◽  
Zeno Iosif Praisach ◽  
Peter Lorenz
Keyword(s):  
Strain Energy ◽  
Crack Detection ◽  
Natural Frequencies ◽  
Vibration Modes ◽  
Structural Elements ◽  
Element Analysis ◽  
Accurate Localization ◽  
Mathematical Expressions ◽  
Measurement Results ◽  
Non Destructive

This paper presents a novel non-destructive method to locate and size damages in frame structures, performed by examining and interpreting changes in measured vibration response. The method bases on a relation, prior contrived by the authors, between the strain energy distribution in the structure for the transversal vibration modes and the modal changes (in terms of natural frequencies) due to damage. Using this relation a damage location indicator DLI was derived, which permits to locate cracks in spatial structures. In this paper an L-frame is considered for proving the applicability of this method. First the mathematical expressions for the modes shapes and their derivatives were determined and simulation result compared with that obtained by finite element analysis. Afterwards patterns characterizing damage locations were derived and compared with measurement results on the real structure; the DLI permitted accurate localization of any crack placed in the two structural elements.

Stress Field of Semi-Infinite Interface Crack Tip of Double Dissimilar Orthotropic Composite Materials

2010 ◽  
Vol 97-101 ◽  
pp. 1223-1226
Author(s):  
Jun Lin Li ◽  
Shao Qin Zhang
Keyword(s):  
Composite Material ◽  
Composite Materials ◽  
Interface Crack ◽  
Interfacial Crack ◽  
Crack Tip ◽  
Stress Fields ◽  
Displacement Fields ◽  
Orthotropic Composite ◽  
Stress Functions ◽  
Secular Equations

The problem of orthotropic composite materials semi-infinite interfacial crack was studied, by constructing new stress functions and employing the method of composite material complex. In the case that the secular equations’ discriminates the and theoretical solutions to the stress fields and the displacement fields near semi-infinite interface crack tip without oscillation and inter-embedding between the interfaces of the crack are obtained, a comparison with finite element example was done to verify the correction of theoretical solution.

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