Problem 2 give the engineering notation stiffness matrix for...

Problem 2: Give the engineering notation stiffness matrix for an isotropic material in a form analogous to those given for a monoclinic material (see equation 5.3.22), an orthotropic material (see equation 5.3.24), and a transversely isotropic material (see equation 5.3.32). Present your result in terms of the Lamé constants.. ..10 Points

Transcript

00:01 Hello students a slippery biological material.

00:05 So this is a material in a ridge setup.

00:09 So this is the material so this is subjected to stress so sigma is a desert stress it is confined to to that position so it cannot be deformed cannot be moved along the any other axis except for the z -axis no moment in the x and y axis only in the z -axis it can it is able to move.

00:37 So the we need to calculate the determine the the normal stress develops in the y direction because of the confinement so the normal stress can be calculated normal stress sigma yy will be equal to so since it cannot deform in that direction, so there is no deformation in this direction so that means there is no the so force by area so that means that is that it cannot the experience of force experience per unit area of that surface so it will be some let's say why that is why is the displacement in the vice the the side length in the? y -axis, so that means it is force in the y direction divided by the y delta y or y square whatever the component is so that will be the the area now this the force experienced will be equally distributed.

01:47 So whatever the force is acting on down, so let's call this f force f force.

01:52 So f will be equally distributed across all these directions so based upon the area coordinate it will be distributed.

02:01 So f will be equal to f by the area of the z -plane said is that plane will be equal to f f x by area of the xx plane plus f y by area of the yy plane.

02:19 So that kind of balancing will be there now the sigma yy will be equal to this the force distributed so if it is equally distributed the area is equal then we can say that it will be 1 by 2 the force experienced by area of the yy plane so that will be the stress acting on that thing now the strain in this c direction we can calculate the strain...

Question

Please give Ace some feedback