Example 1: (i) Find the compatibility condition for the strain tensor e; if e1 ,e22 , e12 are independent of x3 and e31 = e32 = e33 = 0.(ii) Find the condition under which the following are possible straincomponents.eii= k(x,? – x2), e12 = k' x1 x2 , e22 = k x1 X2 ,%3De31 = e32 = e33 = 0, k & k' are constants(iii) when eij given above are possible strain componentscorresponding displacements , given that u; = 0.find the

if e11 , Example 1: (i) Find the compatibility condition for the strain tensor e22 , e12 are independent of x3 and e31 = e32 = e33 = 0. eij (ii) Find the condition under which the following are possible strain components. en = k(x? – x2), e12 = k' x1 X2 , e22 = k x1 X2 , e31 = e32 = e33 = 0 , k & k' are constants (iii) when ej given above are possible strain components corresponding displacements , given that uz = find the 0.

if e11 , Example 1: (i) Find the compatibility condition for the strain tensor e22 , e12 are independent of x3 and e31 = e32 = e33 = 0. eij (ii) Find the condition under which the following are possible strain components. en = k(x? – x2), e12 = k' x1 X2 , e22 = k x1 X2 , e31 = e32 = e33 = 0 , k & k' are constants (iii) when ej given above are possible strain components corresponding displacements , given that uz = find the 0.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

See similar textbooks

Related questions

Q: Given the following state of stress at a point in a continuum, [X₁ X₂ X₂² 2 0 2 [0] = x₂² 0 2 X2X3…

Q: gages to measure a 2D strain field on the surface of a material, which you find to be €xx = 5 + x² +…

Q: Q1 The state of stress at a point of an elastic solid is given in the x-y-z coordinates by: 0 0 XX…

A: The stress along x-direction, σx = 100 MPaThe stress along y-direction, σy = -90 MPaThe stress along…

Q: Evaluate the effective Young's modulus (E) along direction 1 for a sandwich composite material…

A: And stiffness is proportional to the youngs modulus of the spring.So we write:

Q: Consider the four bar suspension linkage shown in the figure. Use the given dimensions from the…

A: Draw the given diagram for four bar suspension linkage with x-y coordinates. Write the given data.…

Q: a) The principal stresses for the given stress tensors. b) The directions of principal stresses. Г18…

A: For solution refer below images.

Q: 3.3 The displacement field at a point in a body is specified as follows: ux = 0.06x + 0.05y - 0.01z…

A: Given:The displacement field at a point in a body is specified as follows;The coordinate of one…

Q: Calculate the stiffness matrix for the Q8 element shown below. Make use of the shape functions in…

Q: 1. (a) If the displacement field is given by u kxy, u, = kxy, u, 2K(x + у)z where k is a constant…

A: u= ux= kxy v= uy= kxy w= uz= 2k(x+y)z Normal stress along X axis and X direction= εxx= du/dx= ky…

Q: Consider that l'm pulling a material with a 5N force as below: Material Hanging 5N mass And I get…

A: Since you have posted a question with multiple sub-parts, we will solve the first three subparts for…

Q: A finite element model of a rod (bar), with two quadratic elements as shown below is considered. The…

A: Given the length of the bar. Required: Value of a

Q: σ = 5 0 0 -6 0 -12 0 -12 Pa 1

Q: The state of stress in a steel component at the critical location for the maximum load condition is…

Q: A force F = 10 sin at N acts on a displacement of x = 2 sin (t – n16)m. Determine (a) the work done…

Q: A strain gauges system mounted at a point on a structural member that is subjected to multiaxial…

Q: The wedge shaped bar shown in Figure Q1 is to be analysed using a single one dimensional quadratic…

A: Given data: a) Calculate the strain shape function matrix. [B], for the element.b) Using the strain…

Q: Consider the following 2 equations: • x+ 2y = 3 • 4x - 5y =6 What is the value of y? 0.9452 -0.1748…

A: Given Two equations x + 2y = 3 4x – 5y =6 To find The value of y

Question

Example 1: (i) Find the compatibility condition for the strain tensor e; if e1 ,
e22 , e12 are independent of x3 and e31 = e32 = e33 = 0.
(ii) Find the condition under which the following are possible strain
components.
eii
= k(x,? – x2), e12 = k' x1 x2 , e22 = k x1 X2 ,
%3D
e31 = e32 = e33 = 0, k & k' are constants
(iii) when eij given above are possible strain components
corresponding displacements , given that u; = 0.
find the

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.

Similar questions

The state of stress at a point in an engine piston is given in the x-y-z coordinates by: 90 180 XX ху [o]= 180 240 0 MPa yx yy yz 120 zy Calculate the deviatoric invariants for the original state of stress, Calculate the principal stresses and the absolute maximum shear stress at the point. What are the stress invariants and the characteristic equation for the transformed state of stress, C. d. e
These are corrects 100%, but please tell me how to solve that.
When you buy a strain gauge, you have to pay attention to the GAUGE FACTOR, G. What is this gauge factor? Paragraph く BI U く A + v Lato (Recom... v 19px... v 5
Q1
The stress tensor for a three-dimensional system for some x, y z axis system is 1. 30 20 -15] 0 30 MPa 20 [-15 30 (a) Verify that one of the principal stresses is 40 MPa, and hence find the other two principal stresses. (b) Find the directional cosines of the plane on which the principal stress of 40 MPa acts.
Find the x and y components of the forces on B and C.
Analyse the statically determinate bar illustrated below by expressing the loading as a single function using Macaulay brackets and the Dirac delta, integrating to find th axial force and integrating again to find the displacements, applying the boundary conditions appropriately. Find the axial force in the bar at point A and the displaceme at point B. The cross section of the bar is constant with EA = 18000 kN. a = 4 m, b = 2 m, c = 2 m and d = 4 m. w1 = 12 kN/m, w2 = 17 kN/m,, P1 = 12 kN and P2 = 19kN. a W1 L/2 W2 Multiple Choice Answers Multiple Choice Answer: Axial force at point A (kN, tension positive): a. 3.31 b. 31.97 c. 37.33 d. 31 Multiple Choice Answer: Displacement at point B (mm, positive to right): a. 0.0061 b. 0.0395 c. 0.0193 d. 0.0261 Axial force at point A (kN, tension positive): Displacement at point B (mm, positive to right): L/2 P1 P2 (type in your multiple choice answer, e.g. a, b, c or d) (type in your multiple choice answer, e.g. a, b, c or d)
I have been stuck on this problem for while thar area is 779.1 mm^2 sigma_x is 120.6497159 sigma_y is 0 and tau_xy is 0. Beta is 20 degrees
3.56. Check whether or not the following distribution of the state of strain satisfies the compatibility conditions: where k = 10-4. XX+XX₁X3 0 [E]=k|x² + x3 Kinematics of a Continuum 169 X₁ X1Xx3 X₁ X²