Solid Mechanics - Revision history

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‎References

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‎NUmerical examples

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‎Case studies

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‎Case studies

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‎Case studies

2021-09-02T09:31:01Z

‎Plane stress with Lamé constants

2018-02-24T11:01:22Z

‎References

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‎References

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‎References

2017-10-08T16:33:18Z

‎Von Mises stress

← Older revision		Revision as of 17:33, 4 December 2022
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	* Theory of matrix structural analysis		* Theory of matrix structural analysis

−	'''This list might be incomplete, check also reference on the [[Main Page]].'''	+	'''This list might be incomplete, check also reference on the Main Page.'''

← Older revision		Revision as of 17:32, 4 December 2022
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−	= ~~NUmerical~~ examples =	+	= Numerical examples =

	The following pages describe several case studies in the field of elastostatics and elastodynamics. The subpages include the problem description (equations and boundary conditions), analytical solutions if obtainable and numerical results for given parameter values.		The following pages describe several case studies in the field of elastostatics and elastodynamics. The subpages include the problem description (equations and boundary conditions), analytical solutions if obtainable and numerical results for given parameter values.

← Older revision		Revision as of 20:01, 22 October 2022
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−	= ~~Case studies~~ =	+	= NUmerical examples =

	The following pages describe several case studies in the field of elastostatics and elastodynamics. The subpages include the problem description (equations and boundary conditions), analytical solutions if obtainable and numerical results for given parameter values.		The following pages describe several case studies in the field of elastostatics and elastodynamics. The subpages include the problem description (equations and boundary conditions), analytical solutions if obtainable and numerical results for given parameter values.

@@ Line 6: / Line 6: @@
 *[[Cantilever beam]]
 *[[Hertzian contact]]
-*[FWO case | Fretting fatigue contact]
+*[[FWO case | Fretting fatigue contact]]
 =Basic equations of elasticity=

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 *[[Cantilever beam]]
 *[[Hertzian contact]]
-*[[FWO case]]
+*[FWO case | Fretting fatigue contact]
 =Basic equations of elasticity=

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 \[E = \frac{\mu(3\lambda+2\mu)}{\lambda+\mu}\]
 \[\nu = \frac{\lambda}{2(\lambda+\mu)}\]
 === Plane strain ===

← Older revision		Revision as of 11:01, 24 February 2018
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	* Slak J., Kosec G.; Refined meshless local strong form solution of Cauchy-Navier equation on an irregular domain. Engineering analysis with boundary elements. 2018;11 ; [http://comms.ijs.si/~gkosec/data/papers/31107623.pdf manuscript]		* Slak J., Kosec G.; Refined meshless local strong form solution of Cauchy-Navier equation on an irregular domain. Engineering analysis with boundary elements. 2018;11 ; [http://comms.ijs.si/~gkosec/data/papers/31107623.pdf manuscript]
	* Theory of matrix structural analysis		* Theory of matrix structural analysis
		+
		+	'''This list might be incomplete, check also reference on the [[Main Page]].'''

← Older revision		Revision as of 10:49, 24 February 2018
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	=References=		=References=
		+	* Slak J., Kosec G.; Refined meshless local strong form solution of Cauchy-Navier equation on an irregular domain. Engineering analysis with boundary elements. 2018;11 ; [http://comms.ijs.si/~gkosec/data/papers/31107623.pdf manuscript]
	* Theory of matrix structural analysis		* Theory of matrix structural analysis

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 \sigma_\mathrm{v} = \sqrt{\sigma_{11}^2 - \sigma_{11}\sigma_{22}+\sigma_{22}^2 + 3\sigma_{12}^2}.
 \]
 =References=
 * Theory of matrix structural analysis

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 A more detailed explanation of the von Mises stress can be found on [https://en.wikipedia.org/wiki/Von_Mises_yield_criterion Wikipedia].
-In materials science and engineering the von Mises yield criterion can be also formulated in terms of the von Mises stress or equivalent tensile stress, $\sigma_v$. This is a scalar value of stress that can be computed from the Cauchy stress tensor $\boldsymbol{\sigma}$. In this case, a material is said to start yielding when the von Mises stress reaches a value known as yield strength, $\sigma_y$.
+In materials science and engineering the von Mises yield criterion can be also formulated in terms of the von Mises stress or equivalent tensile stress, $\sigma_\mathrm{v}$. This is a scalar value of stress that can be computed from the Cauchy stress tensor $\boldsymbol{\sigma}$. In this case, a material is said to start yielding when the von Mises stress reaches a value known as yield strength, $\sigma_\mathrm{y}$.
 Mathematically the von Mises yield criterion can be expressed as:
 \[
-   \sigma _{v}=\sigma _{y}={\sqrt {3J_{2}}},
+   \sigma _\mathrm{v}=\sigma_\mathrm{y}={\sqrt {3J_{2}}},
 \]
 where $J_2$ is the [https://en.wikipedia.org/wiki/Cauchy_stress_tensor#Stress_deviator_tensor second deviatoric stress invariant].
 =References=
 * Theory of matrix structural analysis