For the axisymmetric case, the Papkovich functions reduced to the Boussinesq potentials B and A z defined

Question:

For the axisymmetric case, the Papkovich functions reduced to the Boussinesq potentials B and A_z defined by relations (13.4.11). Show that the general forms for the displacements and stresses in cylindrical coordinates are given by:

18 Az Mr = 2 r (8+ (1=), Ms = 0, Mc= 4(1-v), Or= 0 V Azz V Az 06--1-27 (4(1-) + 1-2, -1 (0+1)) B+ 2v z r r

Equation 13.4.11

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Elasticity Theory Applications And Numerics

ISBN: 9780128159873

4th Edition

Authors: Martin H. Sadd Ph.D.

See More Books

Question Posted: Jan 15, 2024 05:03 AM

See More Questions

Using the results of Exercise 13.14, verify that the displacement and stress fields for the Boussinesq problem of Example 13.4 are given by (13.4.20) and (13.4.21). Note the interesting behavior of...
The following additional information is available for the Dr. Ivan and Irene Incisor family from Chapters 1-5. Ivan's grandfather died and left a portfolio of municipal bonds. In 2012, they pay Ivan...
List three specific parts of the Case Guide, Objectives and Strategy Section (See below) that you had the most difficulty understanding. Describe your current understanding of these parts. Provide...
Provide a brief description of the seven basic steps to use JDBC.
Figure shows an approximate plot of force magnitude F versus time t during the collision of a 58g super ball with a wall. The initial velocity of the ball is 34 m/s perpendicular to the wall; the...
Arnot Internationals bonds have a current market price of $1,200. The bonds have an 11% annual coupon payment, a $1,000 face value, and 10 years left until maturity. The bonds may be called in 5...
The rigid bar is supported by the pin-connected rod CB that has a cross-sectional area of 500 mm2 and is made of A-36 steel. Determine the vertical displacement of the bar at B when the load is...
Ethylene oxide is produced by the catalytic oxidation of ethylene: C 2 H 4 (g) + O 2 (g) C 2 H 4 O (g) an undesired competing reaction is the combustion of ethylene to CO 2 . The feed to a reactor...
The following information is from the annual financial statements of Raheem Company. Net sales Accounts receivable, net (year-end) Year 3 $ 430,000 28,400 Year 2 $ 361,000 26,200 Year 1 $ 420,000...
The displacement field for the Boussinesq problem was given by (13.4.20). For this case, construct a displacement vector distribution plot, similar to the two-dimensional case shown in Fig. 8.22. For...
Explicitly justify that the Papkovich functions A and B satisfy relations (13.4.9). Equation 13.4.9 VA -2F, VB = R.F 2(1-v)
CoastalView Magazine issued $600,000 of 15-year, 5% callable bonds payable on July 31, 2018, at 94. On July 31, 2021, CoastalView called the bonds at 101. Assume annual interest payments....
Write both serial code and parallel code to find a maximum number stored in 2dimensional array. Plot execution times of several runs with a different number of threads and to see the speed up.
Four identical charged particles are constrained along an $x$ axis. Identify one possible configuration of the particles that would leave one of them at rest at the origin when the others are fixed...
If electrons move easily in electrical conductors, why aren't pieces of metal usually negatively charged on the bottom and positively charged on top, due to gravitational settling of the electrons?
Metals are often good thermal conductors as well as good electrical conductors. In fact, usually the better a metal is as a thermal conductor, the better it is as an electrical conductor. Give a...
Someone has challenged you in a friendly bet that, given a set of six charged spheres with three carrying positive charge and three carrying negative charge, you can't place any three of them in a...
NAFTA (North American Free Trade Agreement) is an agreement among the United States, Canada, and Mexico to reduce trade barriers and promote the free flow of goods and services across borders. Many...
One study found that the elderly who do not have children dissave at about the same rate as the elderly who do have children. What might this finding imply about the reason the elderly do not dissave...
Compute the expressions for dp 2 /dx, d(p 1 p 2 )/dx, and d( p 2 /p 1 )/dx for p 1 = 5x 2 + 7 and p 2 = 5x 2 6x + 7.
Plot the contour plot and the gradient (shown by arrows) for the function f(x, y) = -x 2 + 2xy + 3y 2
Plot the solution of the equation 6y + y = f(t) if f (t) = 0 for t + 0 and f(t) = 15 for t 0. The initial condition is y(0) = 7.
7)A certain city covers an area of 62.294 mil 2 . How many square kilometers is this ?Use the conversion factor 1 mile = 1.61 km 8) A projectile is fired at 422.8 mi/hr. How fast is that in meters...
What is its unit price? Let's think of a batch of 100 baked goods...what is its total price? Speculate how much is the cost to bake (AND sell) that 1 batch (100 units)? Calculate its related gross...
1. What is the slope of the Aggregate-Supply curve in the short run? In the long run? What shifts the AS curve(s)? 2. How does the interest-rate effect help explain the slope of the aggregate-demand...

For the axisymmetric case, the Papkovich functions reduced to the Boussinesq potentials B and A z defined

Question:

Step by Step Answer:

General Papkovich Representation 2nAVB Axisymmetric ...View the full answer

Elasticity Theory Applications And Numerics

Students also viewed these Engineering questions