Transcription of Lecture 8: Energy Methods in Elasticity - MIT …
{{id}} {{{paragraph}}}
Example: biology
Lecture 8: Energy Methods in Elasticity - MIT …
Structural Mechanics Lecture 8 Semester Yr Lecture 8: Energy Methods in Elasticity The Energy Methods provide a powerful tool for deriving exact and approximate solutions to many structural problems. The concept of Potential Energy From high school physics you must recall two equations 1. E = M v 2 kinematic Energy ( ). 2. W = mgH potential Energy ( ). where H is the hight of a mass m from a certain reference level Ho , and g stands for the earth acceleration. The reference level could be the center of the earth, the sea level or any surface from which H is measured. m F = mg H x x H Ho Ho F. Figure : Gravitational potential Energy . We seldom measure H from the center of earth.
Structural Mechanics 2.080 Lecture 8 Semester Yr q z dx w x z w H Ho q(x) Figure 8.2: Potential energy of a beam element and the entire beam. In the above de nition Wis negative. The concept of the energy stored elastically Uhas been introduced earlier. For a 3-D body U= Z V 1 2 ˙ ij ijdv (8.5) and for a beam U= Z l 0 1 2 MKdx+ Z l 0 1 2 N dx ...
Loading..
Tags:
Information
Domain:
Source:
Link to this page:
Please notify us if you found a problem with this document: