static value problems

static value problems - EN224: Linear Elasticity Division...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
EN224: Linear Elasticity Division of Engineering 3. 3D Static Boundary Value Problems Objective: Find elastostatic states in 3D solids with prescribed boundary conditions This is very difficult to do in general! A few useful techniques: (1) Represent the solution in terms of harmonic potentials . We can then generate elastostatic states from any harmonic function, and if we’re very lucky we find the solution to the problem we are interested in. Many useful solutions have been found this way, but the chances of finding a new one are small! (2) Try superposition and the method of images. This will only solve rather simple problems, but it’s worth a shot. (3) Use the reciprocal theorem. This is a good way of solving dislocation problems. If you’re very lucky it will give you a general solution for your region, but you need to solve a tricky singular problem first. (4) Transforms . This is the most powerful approach, as it gives you a formal procedure to follow. Examples include Fourier transforms (good for half-space problems and for the infinite solid), Hankel transforms (good for axisymmetric problems), Mellin transforms (good for quarter-space problems), among others. (5) Approximate the solution . If the 3D boundary value problem can’t be solved, one can sometimes make progress by reducing the problem to 2D. Examples include plane problems in elasticity, Saint Venant torsion, plates and shell theory. (6)
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 01/10/2010 for the course EN 224 taught by Professor Allenbower during the Spring '05 term at Brown.

Page1 / 5

static value problems - EN224: Linear Elasticity Division...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online