This preview shows pages 1–4. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Mechanics of Aircraft structures C.T. Sun 2.1 Consider a unit cube of a solid occupying the region 1 x , 1 y , 1 z After loads are applied, the displacements are given by x u = y v = = w (a) Sketch the deformed shape for 03 . = , 01 . = . (b) Calculate the six strain components. (c) Find the volume change V [ V = V (the volume after deformation) V 0 (the original volume) ] for this unit cube. Show that V zz yy xx + + . Solution: (a) Since , there is no deformation in the zdirection and the deformation can be represented in the xy plane. = w The new position of point B after deformation is given by 03 . 1 1 03 . 1  1 ' , 1 = + = + = = = y x u x ) 01 . (  ' , 1 = + = + = = = y x v y New coordinates of B = ( 1.03 , 0 ) Similarly, new positions of A, C, D can be obtained as follows: A = ( 0 , 0 ) C = ( 1.03, 0.99 ) D = ( 0 , 0.99 )  ANS A, A B 1 B 1.03 D, 1 D 0.99 C C x y A=(0,0) A=(0,0) B=(1,0) B=(1.03,0) C=(1,1) C=(1.03,0.99) D=(0,1) D=(0,0.99) 2.1.1 AAE 352 S08 HW #3 Solutions Mechanics of Aircraft structures C.T. Sun (b) Strain components are: nents, Normal strain compo 03 . = = = x u xx 01 . = = = y v yy = = z w zz Shear strain components, = + = = v u x y yx xy = + = = x w z u zx xz = + = = y w z v zy yz  ANS (c) The volume change is defined by 03 . 1 1 ' z ' y ' x V V V 0197 . 1 1 1 1 99 . = = = = Also, 0197 . 02 . ) 01 . ( 03 . = = + + = + + V zz yy xx  ANS It can also be verified by: zz yy xx zz yy zz xx yy xx zz yy xx zz yy xx zz yy zz xx yy xx zz yy xx zz yy + + + + + + = + + + + + + + = + + Since the deformation is very small, we have ) ( V ) 1 1 ( V 1 1 1 1 ) 1 ( 1 ) 1 ( 1 ) 1 ( V V V xx + = = 1 << => higher order terms can be dropped. Therefore we have V V zz yy xx zz yy xx + + = + + ) ( , since V 0 = 1 2.1.2 Mechanics of Aircraft structures C.T. Sun 2.2 Consider the following displacement field: y u = x v = = w Sketch the displaced configuration of a unit cube with the faces originally perpendicular to the axes, respectively. This displacement field does not yield perpendicular to the axes, respectively....
View
Full
Document
This note was uploaded on 04/11/2008 for the course AAE 352 taught by Professor Chen during the Spring '08 term at Purdue UniversityWest Lafayette.
 Spring '08
 Chen

Click to edit the document details