Stress tensor Definition and 119 Threads

Homework Statement Stress tensor at a point Q in a body has components: pij: | 1 -1 0 | |-1 2 1 | | 0 1 3 | (i) Calculate components of the stress force f across a small area of surface at Q normal to n = (2,1,-1). (ii) The component of f in the direction of n...

The following information is given: The Cartesian components of stress tensor are: \sigma_{ij}=m(\hat \lambda _{i}\hat \mu _{j}+\hat \lambda _{j}\hat \mu _{i}) , (i=1,2,3; \ j=1,2,3) . \hat \lambda _{i} and \hat \mu_{j} are the Cartesian components of the unit vectors \hat \lambda...

This hasn't been asked before, and I am more or less new to this subject. Therefore, I haven't done an attempt on the solution. Say we have a 2 dimensional square of sides "a". 2 forces "F" of equal magnitude and opposite direction act on the opposite ends of the square such that the square...

Hello, I perform FEA (finite element analysis) and write massive amounts of VBA code in Access in order to streamline heat exchanger designs and I have a Boss with no experience with Tensors and the ASME (American Society of Mechanical Engineers) Section VIII, Div. 2 requires one to calculate...

Well lately i have in mess for this. The problem is about the stress energy tensor. Well we know that T_mn = r0 U^m U^n where r0 is mass density and U is proper velocity. Ok now consider the local observer. For him except for U^0 other U^m will be jero. So for local observer. T_00 = r0 c^2...

Would someone please be able to run me through the different components of the Maxwell Stress Tensor equation. T_{ij} = \epsilon_0 \left( E_i E_j - \frac{1}{2} \delta_{ij} E^2 \right) + \frac{1}{\mu_0} \left( B_i B_j - \frac{1}{2} \delta_{ij} E^2 \right) I don't understand some of it and...

Hi all, I'm doing a MEMS project, I have a cantilever beam with a mass at its end, I need to calculate the stress tensor at the beam contact point, there is a piezoelectric matirial there, and I want to calculate the voltage it generates. somebody can please help me and explain how to calculate...

Hi all, I'm doing a MEMS project, I have a cantilever beam with a mass at its end, I need to calculate the stress tensor at the beam contact point, there is a piezoelectric matirial there, and I want to calculate the voltage it generates. somebody can please help me and explain how to calculate...

Consider a particle with charge q in an static, homogeneous electric field. Using the fact that the net force on the particle in the surface integral of the Maxwell Stress Tensor, and assuming the surface is a sphere around this particle: a) Find the net force on the particle (This part I...

Maxwell stress tensor: T_{ij} = \epsilon_0 \left( E_i E_j - \frac{1}{2} \delta_{ij} E^2 \right) + \frac{1}{\mu_0} \left( B_i B_j - \frac{1}{2} \delta_{ij} E^2 \right) We can interpret T as the force per unit area acting on the surface. But what surprises me is, T_{ij} = T_{ji}, i.e. the...

I am working through a set of notes on conformal field theory by Schellekens and want to show the conformal invariance of N=4 SYM theory in four dimensions. I start with the action S=\frac{1}{4g}\int d^Dx \sqrt{g}Tr\left(F_{\mu\nu}F^{\mu \nu}) There's only the metric in the action to worry...

Hello ! I'm having trouble with the symmetry of the stress tensor. What it means physically? In the demostration of the symmetry my book applies the angular momentum equation to a third material volume (a cube, length L). In the final step we have: 0 = \mathop {\lim }\limits_{L \to 0}...

Can we curl a stress tensor? What physically meaning will it be?

URGENT! Hi, I have a couple of urgent problems which are listed below. I am not sure what to do in either of them! If someone could help me as soon as possible that would be great! Cheers Problems: 1. Consider a linearly polarised plane wave incident normally on a slab of material...

what is a tensor. what is a stress tensor? what is a inertia tensor?

Can someone explain to me why the stress tensor is symmetrical. I understand that Sij=Sji , but can someone give me the assumption or the physical reason why this is true. Thanks.

I'm having some trouble with an example in griffiths book about using the stress tensor. The problem is to find the force on the northern hemisphere of a uniformly charged solid sphere by the southern hemisphere. Charge Q, radius R. I understand that we will only need the zx, zy, and zz...

Consider an infinite parallel plate capacitor with the lower plate (at z=-d/2) carrying the charge density- \sigma and the upper plate (at z=d/2) carrying the charge density \sigma. Determine all nine elements of the stress tensor in the region between the plates. Display your answer as a...

Consider a spherical volume of radius R filled with a uniform electric charge density p(rowe) a) Use Gauss' law to calculate the electric field E in the interior of the spherical charge b) Use the expression for the electric field to derive an expression for the Maxwell stress tensor...