scholarly journals Buckling of regular, chiral and hierarchical honeycombs under a general macroscopic stress state

2014 ◽  
Vol 470 (2167) ◽  
pp. 20130856 ◽  
Author(s):  
Babak Haghpanah ◽  
Jim Papadopoulos ◽  
Davood Mousanezhad ◽  
Hamid Nayeb-Hashemi ◽  
Ashkan Vaziri
Keyword(s):  
Finite Element ◽  
Stress State ◽  
Closed Form ◽  
Plane Stress ◽  
Plane Stress State ◽  
Cellular Structures ◽  
Two Dimensional ◽  
Buckling Strength ◽  
Macroscopic Stress ◽  
Unit Cells

An approach to obtain analytical closed-form expressions for the macroscopic ‘buckling strength’ of various two-dimensional cellular structures is presented. The method is based on classical beam-column end-moment behaviour expressed in a matrix form. It is applied to sample honeycombs with square, triangular and hexagonal unit cells to determine their buckling strength under a general macroscopic in-plane stress state. The results were verified using finite-element Eigenvalue analysis.

On Systematic Errors of Two-Dimensional Finite Element Modeling of Right Circular Planar Flexure Hinges

2004 ◽  
Vol 127 (4) ◽  
pp. 782-787 ◽  
Author(s):  
B. Zettl ◽  
W. Szyszkowski ◽  
W. J. Zhang
Keyword(s):  
Finite Element ◽  
Plane Strain ◽  
Plane Stress ◽  
Compliant Mechanisms ◽  
Three Dimensional ◽  
Systematic Errors ◽  
Plane Stress State ◽  
3D Analysis ◽  
Two Dimensional ◽  
Flexure Hinges

This paper discusses the finite element method (FEM) based modeling of the behavior of typical right circular flexure hinges used in planar compliant mechanisms. Such hinges have traditionally been approximated either by simple beams in the analytical approach or very often by two-dimensional (2D) plane stress elements when using the FEM. The three-dimensional (3D) analysis presented examines these approximations, focusing on systematic errors due to 2D modeling. It is shown that the 2D models provide only the lower (assuming the plane stress state) or the upper (assuming the plane strain state) limits of the hinge’s stiffness. The error of modeling a particular hinge by 2D elements (with either the plane stress or the plane strain assumptions) depends mainly on its depth-to-height ratio and may reach up to about 12%. However, this error becomes negligible for hinges with sufficiently high or sufficiently low depth-to-height ratios, in which either the plane strain or stress states dominate respectively. It is also shown that the computationally intensive 3D elements can be replaced, without sacrificing accuracy, by numerically efficient 2D elements if the material properties are appropriately manipulated.

scholarly journals Analytical Solution of the Problem of Symmetric Thermally Stressed State of Thick Plates Based on the 3D Elasticity Theory

2021 ◽  
Vol 24 (1) ◽  
pp. 36-41
Author(s):  
Viktor P. Revenko ◽  
Keyword(s):  
Stress State ◽  
Boundary Conditions ◽  
Plane Stress ◽  
Harmonic Functions ◽  
Three Dimensional ◽  
Thermoelastic Stress ◽  
Plane Stress State ◽  
Median Surface ◽  
Two Dimensional ◽  
Particular Solution

An important place among thermoelasticity problems is occupied by the plane elasticity problem obtained from the general three-dimensional problem after using plane stress state hypotheses for thin plates. In the two-dimensional formulation, this problem has become widespread in the study of the effect of temperature loads on the stress state of thin thermosensitive plates. The article proposes a general three-dimensional solution of the static problem of thermoelasticity in a form convenient for practical application. To construct it, a particular solution of the inhomogeneous equation, the thermoelastic displacement potential, was added by us to the general solution of Lamé's equations, the latter solution having been previously found by us in terms of three harmonic functions. It is shown that the use of the proposed solution allows one to satisfy the relation between the static three-dimensional theory of thermoelasticity and boundary conditions, and also to construct a closed system of partial differential equations for the introduced two-dimensional functions without using hypotheses about the plane stress state of a plate. The thermoelastic stress state of a thick or thin plate is divided into two parts. The first part takes into account the thermal effects caused by external heating and internal heat sources, while the second one is determined by a symmetrical force load. The thermoelastic stresses are expressed in terms of deformations and known temperature. A three-dimensional thermoelastic stress-strain state representation is used and the zero boundary conditions on the outer flat surfaces of the plate are precisely satisfied. This allows us to show that the introduced two-dimensional functions will be harmonic. After integrating along the thickness of the plate along the normal to the median surface, normal and shear efforts are expressed in terms of three unknown two-dimensional functions. The three-dimensional stress state of a symmetrically loaded thermosensitive plate was simplified to the two-dimensional state. For this purpose, we used only the hypothesis that the normal stresses perpendicular to the median surface are insignificant in comparison with the longitudinal and transverse ones. Displacements and stresses in the plate are expressed in terms of two two-dimensional harmonic functions and a particular solution, which is determined by a given temperature on the surfaces of the plate. The introduced harmonic functions are determined from the boundary conditions on the side surface of the thick plate. The proposed technique allows the solution of three-dimensional boundary value problems for thick thermosensitive plates to be reduced to a two-dimensional case.

scholarly journals Incremental Approach to the Nonlinear Analysis of Reinforcement Concrete with Cracks at Plane Stress State

2015 ◽  
Vol 111 ◽  
pp. 386-389 ◽  
Author(s):  
Nikolay I. Karpenko ◽  
Sergey N. Karpenko ◽  
Aleksey N. Petrov ◽  
Zakhar A. Voronin ◽  
Anna V. Evseeva
Keyword(s):  
Stress State ◽  
Nonlinear Analysis ◽  
Plane Stress ◽  
Plane Stress State ◽  
Incremental Approach
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