Questions tagged [elasticity]
17 questions
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2 answers
How to model elastically squeezing a triangle?
I'm trying to figure out how a spring that looks like this behaves. I'm assuming the bottom foot can freely rotate but is otherwise fixed in position. The top foot can also freely rotate, but it is constrainted to a vertical line. The thickness is…
azani
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vote
1 answer
Interpretation of the generalized Hooke's law
I'm in the process of understanding the generalized Hooke's law for an isotropic, linear-elastic material. I've come across two formulations of the same low in Mechanics of Materials by Roy Craig Jr., which are described below.
Let's get the x…
murilo_caetano
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3 answers
Rationale For Plain Strain Assumption in Long or Infinite Bars
When plane strain is discussed, there are two examples given, both of which involve two dimensional boundary stress conditions. One is a constrained object that cannot move along the third axis. From Johnston and Beer:
This occurs in a plate…
Poisson Aerohead
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1 answer
What is the meaning of the traction continuity condition in the generalized momentum balance (continuum mechanics)?
In Nonlinear Finite Elements for Continua and Structures by Belytschko and al. it is stated:
As we have already noted, the strong form, or generalized momentum balance, consists of the momentum equation, the traction boundary conditions and the…
Paolo Secchi
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2 answers
What is the equivalent rotational/angular stiffness of a beam
I'm trying to model a larger system and working through a conceptual issue. I'm familiar with the concept of expressing the stiffness of a beam as an equivalent spring stiffness like in the image below:
I'm curious if there's a way of doing to…
BeBlase
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1
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1 answer
Why do we not want our stress state to be like this?
In this article they mention that Cauchy stress is defined by studying the forces acting on the deformed body, and these forces are constant in space. But if a body is subjected to pure rotation, the actual values of stress component will change,…
Material scientist
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1 answer
Finding change in dimensions of a rectangular bar when the bar is restricted from elongation along one cross section under uniaxial loading
The question goes like this: A rectangular bar of cross-section 30mm x 60mm and length 200mm is restrained from expansion along its 30mm x 200mm sides by surrounding material. Find the change in dimension and volume when a compressive force of 180…
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Airy Stress Function in boundary conditions in 2D elasticity
Airy Stress Function in boundary conditions in 2D elasticity has a requirement that its x and y derivatives be related to the x and y boundary tractions Rx and Ry, i.e.: dAiry/dy = Rx, dAiry/dx = -Ry. Then dRx/dx = -dRy/dy? How to understand this…
feynman
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0 answers
analytic plane linear elasticity solution of beam deflection under self weight
Is there an analytic plane linear elasticity solution of beam deflection under self weight? I don't mean a solution using Euler Bournouli beam theory, which ignores stuff and deviates from linear elasticity as aspect ratio goes small, but a solution…
feynman
- 101
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Does the book of Theory of Elasticity by Timoshenko have a solution manual for problems
In the book of "Theory of Elasticity" by Timoshenko, there are problems without solution in every chapter. Is there a solution manual for the problems?
feynman
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How to calculate Cauchy stress and the elastic coefficient tensor of neo-Hookean model based on updated Lagrange formulation?
In the updated Lagrange formulation, the principle of virtual power is
$$
\int_{v}^{}\,\left[\overset{\triangle}{T}\cdot\breve{D}+(LT)\cdot\breve{L}\right]dv
=
\int_{a}\dot{t}\cdot\breve{v}da+\int_{v}\rho\dot{f}\cdot\breve{v}dv,
$$
where…
Haru_o
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5 answers
Maximum bending of plate
I need to figure out what is the maximum bending of a plate that can be applied without deforming it. For example, with a flat steel plate of 1mm thickness, 10mm width and 100mm length, bent (along its length and against its thickness) by applying…
Antoine
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Best strategy for verification of constitutive tangent for hyperelastic material
This is a theoretical/coding question.
Let's say I have a strain energy density function W = W(I1,I2) + W(I3). I am using material models such as Neo-Hookean or 2nd order Mooney-Rivlin.
The second PK stress is then defined as
S_{ij} = ∂W/∂E_{ij}
and…
0
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1 answer
Does gold have elastic behavior?
I know structural steel is considered to have an elastic behavior and after a certain deformation, it has a plastic behavior.
How about gold metal?
Megidd
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Boundary conditions for Clevis fork (linear elasticity)
consider the Clevis fork domain (see here for an image https://www.traceparts.com/it/product/camloc-motion-control-h1-stainless-steel-clevis?CatalogPath=TRACEPARTS%3ATP01001005&Product=10-12112014-075680&PartNumber=084337) and the linear elasticity…
VoB
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