Consider the mapping in 2-D only = X1 +7X2 = X1+ uz *2 = (1+e)X2 = X2+ Uz. (1) 1. In terms of y and a compute F, i.c. the Fij's and then compute the Cy = FF.; recall F = F. Now do the following. 2. Take two fibers, viz. dX = e; and dY = e2, that is two fibers of unit length along the e, and ez axes, respectively in the reference state. Compute the stretch of dX and dY. 3. Compute the small strains from this mapping with u = X2 and uz = eX, from above. What would these small strains suggest for the change in lengths of dX and dY?

Consider the mapping in 2-D only = X1 +7X2 = X1+ uz *2 = (1+e)X2 = X2+ Uz. (1) 1. In terms of y and a compute F, i.c. the Fij's and then compute the Cy = FF.; recall F = F. Now do the following. 2. Take two fibers, viz. dX = e; and dY = e2, that is two fibers of unit length along the e, and ez axes, respectively in the reference state. Compute the stretch of dX and dY. 3. Compute the small strains from this mapping with u = X2 and uz = eX, from above. What would these small strains suggest for the change in lengths of dX and dY?

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: 2. Frame {2} is rotated with respect to frame {1} about the x-axis by an angle of 60°. the position…

Q: A force-couple system is acting on the frame as shown. Use A-100N, B-600N, C-100N, and M- 60N.m. The…

A: *As per our guidelines we are supposed to answer first three sub-parts of the question. Kindly…

Q: Frame {2} is rotated with respect to frame {1} about the x-axis by an angle of 600. the position of…

A: Given data: Angle of rotation = 60 degrees. 1D2 = [9 7 9]T 2P = [4 6 8]T

Q: Design a four bar linkage to generate the function y=x²-1 for values of x between 1 and 5. Use…

A: To solve this problem, we need to design a four-bar linkage that generates the function the for…

Q: For the given 2D element shown in the diagram with positions A = 5 m and B = 5 m, answer the…

Q: Find p¹ and matrix R₂.

A: The preceding method entails applying linear algebra techniques to the issue of determining the…

Q: he following polar equations by equivalent Cartesian , then describe or identify the graphs:

Q: List the vertices of the polygon above when it is represented using a vector data model.

A: Writing the vertices for vector data model for this closed figure as: - (0,0) (2,1) (2,0) (0,0)

Q: 7. Show position datums and coordinates and write constraint equations for the following systems.…

A: Solution: Given Data: To Find: Constraint equations.

Q: Last digit is =0

Q: H.W: replace the following polar equations by equivalent Cartesian equation, then describe or…

Q: Position of a particle in a rectangular- co-ordinate system is (5, 2, 3). Then its position vector…

A: Given data: Coordinates=5,2,3 Need to determine the position vector.

Q: 3- Find the eigenvalues and eigenvectors of the matrix -4.0 4.0 -1.6 A 1.2

A: To find: The Eigen values and Eigen values of the matrix. Given: The matrix is A=-44-1.61.2. Formula…

Q: Prob The link lengths and the value of 0, for some four Table P4-1.

A: Row Link1 Link2 Link3 Link4 θ2 a 6 2 7 9 30 b 7 9 3 8 85 c 3 10 6 8 45 d 8 5 7 6 25 e…

Q: Kinematičs for the robot, and compute the matrix with 1= 0.325m. %3D *[: ] K CoR Tmin Ackermann…

A: We have given

Q: 7. Given a square matrix -2 | A = -3 -1 4 0 1

Q: F will do work on a particle only when the particle undergoes a nt in the direction of the force.…

A: we have to establish the relationship in between force and work

Q: 4. 2 2.

Q: Q6: The distance between projections of the points C and D is 6.5 cm, for the line CD. C (xc, 1.5) &…

Q: Compute the inverse of matrix A with 1 1 A =0 1 V2 1 1

A: For a square matrix, A-1=1AAdjA and A≠0 If A=0, then the matrix is non singular and inverse…

Q: 3- A 2-mm by 1-mm rectangular domain is modeled using two linear triangular elements as shown below.…

A: according to the given details

Q: Position of a particle in a rectangular coordinate system is (3, 2, 5). Then its position vector…

Q: Q2) In a design, a triangle object is constructed by connecting three points A(12.66025, 11), B(4,…

A: as given in the above question that to design a triangle object is constructed by connecting three…

Q: Help!! Solve part D correctly.

Q: Find the 3D transformation matrix that represents a rotation by 60° about the z-axis?

Q: 1. Compute the dot product for the following two vectors. A=51+3) and = 31-10)

A: We will answer the first question since the exact one was not specified. Please submit a new…

Q: Subject Date : الموافق Q/Find the domain f the function Y=DIn (2x+X-6-6)

Q: Find the eigenvalues, eigenvectors, and the matrix X that diagonalizes the given matrix via a…

A: Ans Given Now make a new matrix by subtracting from the diagonal entries of the given matrix A…

Q: 0 2. As a traffic engineer, you have been asked to investigate the dynamic response of the road sign…

Q: Write down any two methods of calculating product of a vector v and p

A: Two methods of product of vector v and p are as follow 1. Based on the notation we employ, the first…

Q: Define: cartesian space Forward kinematics Matrix

Concept explainers

The Space Lattice and Unit Cells

Every matter consists of atoms, molecules, and ions. If these atoms, molecules, and ions (micro-particles) are represented in a three-dimensional space-occupying certain specific points in space, then these arrangements are termed as space lattices and the specific points which are being occupied by atoms, molecules and ions are termed as lattice points. The atoms, molecules, and ions at the lattice points are generally grouped in a regular fashion and repeat periodically at the three-dimensional space.

Question

Topic: Calculation of stretch: small es. finite deformation
Consider the mapping in 2-D only
21 = X1 +7X2 = X1+ u1
82 = (1+e)X2 = X2 + Uz.
(1)
1. In terms of y and a compute F, i.e. the Fij's and then compute the Cj = FF.j; recall
F = Fi. Now do the following.
%3D
2. Take two fibers, viz. dX = e and dY = e2, that is two fibers of unit length along the ej
and ez axes, respectively in the reference state. Compute the stretch of dX and dY.
3. Compute the small strains from this mapping with u = 7X2 and ur = eX¡ from above.
What would these small strains suggest for the change in lengths of dX and dY?
4. Comment on what you found from the results of 2. and 3. You may want to sketch the
deformed state to explain your comments.

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

part 1).

VIEW

part 2)

VIEW

part 3).

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps with 3 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Principal Metallic Crystal Structures and Crystal Structure Analysis

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

I need detailed solution in handwritten format. Don't use chatgpt
I'm confused on starting the problem and I'm lost. Please help
1a
Find the transformation matrix for the following rotations: 1) Rotate a about the original x-axis (in frame 0). (Xo, Yo, Zo) → (X₁,Y₁,Z₁); 2) Followed by a rotation of B about current z-axis (in frame 1). (X₁,Y₁,Z₁)→ (X₂, X₂, Z₂); 3) Followed by a rotation of y about Xo -axis (in frame 0). (X2, Y, Z₂)→ (X3, Y, Z3); 4) Followed by a rotation of about Z3 - axis (in frame 3). (X3, X3,Z3) → (X,Y4, Z4). E F3 $ R F F4 Q Search DII % 5 F5 T F6 6 Y PRE F7 & H 7 PrtScn F8 U 8 Home End
The vector expressions for the position vectors for cables “AC” and “AD” are given by: rAC = -3i - j - 6k ft and rAD = 2i + 3j - 6k ft respectively. What is the length of cable “AD”?
Multiply, if possible, matrices B and C
Given the following vectors: S = 3i - j+ 5k P = 2i + 4j - 6k %3D Q = -7i + 2j + 9k %3D Obtain the following operations: 1. QxP 2. SxQ 3. PxS
Learning Goal: To use the dot product to find the components of forces acting in arbitrary directions. A three-legged structure is shown below. It is attached to the ground at points B= (4.68,0,0) and C=(-4.68.0.0) and connected to the ceiling at point A = (-5.54,3.10.4.47). The three legs connect at point D = (0,2.49, 4.00). where two forces, F and P. act. Force F is given by F= 6.00 i 12.5j + 26.2 k N: P has Figure 1 of 1 D Important: If you use this answer in later parts, use the full unrounded value in your calculations. ▾ Part D - Finding the component of a force perpendicular to a direction Given F 6.00 i 12.5j +26.2 kN, find the component of F that acts perpendicular to member DA such that the vector addition of the perpendicular and parallel components of F (F=F+F) with respect to DA equals F. Express your answer in component form. Express your answers, separated by commas, to three significant figures. View Available Hint(s) FIDA Submit VAXtvec Previous Answers * Incorrect;…
1
Given frames {A}, {B} and {C} as shown below, find transformation matrix from B to A, and from C to A. 30° Yc 60 ZA 2 units YA ZB XA YB 3 units
Question 2: The 3x3 matrices A and B are defined in term of a constant k by: [1 -3 [k A = 15 9. 27 1 0. and B = -1 -1 11 [4 1 1 a) Find an expression for det A, in terms of k. e N b) Find the possible values of k given that AB is singular.
write vector loop equation(s) theta2=57 also if a new length is constructed find its value. 02 57° 30° X L₁= 162 L2=40 L4=122 L3=96 0₁