MT-1620 al.2002 Summarizing what we've looked at in elasticity, we have 15 equations In 15 unknowns 3 equilibrium 6 strains 6 strain-displacement 3 displacements 6 stress-strain 6 stresses These must be solved for a generic body under some generic loading subject to the prescribed boundary conditions(BCs There are two types of boundary conditions 1. Normal(stress prescribed) 2. Geometric(displacement prescribed) you must have one or the other To solve this system of equations subject to such constraints over the continuum of a generic body is, in general, quite a challenge. There are basically two solution procedures 1. Exact--satisfy all the equations and the B.C.s 2. Numerical --come as close as possible"(energy methods, etc. Paul A Lagace @2001 Unit 8-p. 2MIT - 16.20 Fall, 2002 Summarizing what we’ve looked at in elasticity, we have: 15 equations in 15 unknowns - 3 equilibrium - 6 strains - 6 strain-displacement - 3 displacements - 6 stress-strain - 6 stresses These must be solved for a generic body under some generic loading subject to the prescribed boundary conditions (B.C.’s) There are two types of boundary conditions: 1. Normal (stress prescribed) 2. Geometric (displacement prescribed) --> you must have one or the other To solve this system of equations subject to such constraints over the continuum of a generic body is, in general, quite a challenge. There are basically two solution procedures: 1. Exact -- satisfy all the equations and the B.C.’s 2. Numerical -- come as “close as possible” (energy methods, etc.) Paul A. Lagace © 2001 Unit 8 - p. 2