1) If the deformation mapping of a body is given by x(X)=(X, + AX, )e, +(X, + BX, )e, + X3zez where A and B are constants. Determine (a) the displacement components in the material description (b) the displacement components in the spatial description (c) the components of the Green strain tensor (d) the components of the small strain tensor under the condition of small displacement gradients

1) If the deformation mapping of a body is given by x(X)=(X, + AX, )e, +(X, + BX, )e, + X3zez where A and B are constants. Determine (a) the displacement components in the material description (b) the displacement components in the spatial description (c) the components of the Green strain tensor (d) the components of the small strain tensor under the condition of small displacement gradients

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

Similar questions

Please show all work for a & b.
of tion A particle is subjected to two forces F₁ = -40i +65j -70k (N) and F₂ =80i +50j -60k (N) The magnitude of the resultant force is The magnitude of projection of force F2 along z-axis is The angle between F₁ and F₂ is 178.11 103.56 121.8 147.81 60 -60 -70 70 68.46 79.18 108.57 85.13
STATICS OF RIGID BODIES PRODUCTS OF VECTOR VECTOR CROSS AND DOT PRODUCT
Q1 ( shown. * The stresses in a bracket were obtained from a 3D finite element analysis as (a) [A] = 0 (c) [σA] = [20 0 15 (e) [σA] = Which of the following stress tensors [A] correctly corresponds to the stress state at point A, as represented by the infinitesimal cube above. (All units in MPa.) 10 25 L15 25 -30] [-20 0 15 0 -10 -25 15 -25 -30 20 20 0 -15] 0 10 25 -15 25 -30] 30 15 25 25 Y [20 15 0 10 -25 -25 -30. (b) [A] = 15 LO (f) [A] = [20 (d) [A] = 0 L15 0 15 10 -25 -25 -30] OH O 0 [-20 -15] 0 -25 -15 -25 -30] -10
If n1 is an eigenvector for a strain tensor, show it is also a principal direction for the stress tensor
The opposite figure is composed of a rectangle (b=12.2 , h=6.1 m , density 4 kg/m² ) and a triangle (b=12.2, a=3.05 m , density 8 kg/m² ). E a D h x b/4 h/3 А В
(Dimensional Analysis) If the velocity V in a fluid flow depends on a dimension 1, the fluid density p, and the viscosity µ, show that this implies that the Reynolds number Vlp/µ is constant.
ZA 50 N 3 m y 300 Nm 70 N 2 m 3 m 40 N 2 m 12md 30 N Questions: (a) Reduce the system of forces and moments acting on the structure to a single resultant force (Fro) and a couple (Mro) acting at the origin of coordinates. (b) Determine the "parallel component” (M) of the couple (Mro), i.e., the compo- nent lying parallel to (F). State (M) in vector form. (c) Determine the corresponding "perpendicular component" (M₁). State (M₁) in vector form. (d) Reduce the force and couple at the origin to a "wrench resultant" and determine a precise and complete description of the line of action of the "wrench resultant."
force in three dimensions is given by (a) F = FO(yx^ - xy^) (b) F= FO(yx^ + xy ^) where x^ and y^ are the cartesian basic vectors and F0 is a constant. Find if possible the corresponding potential energy
i need the answer quickly