1. Historical Background Before 1860 the United States had begun to change into an industrial and urban society. In the years preceding the Civil War relatively few volumes of imaginative literature were published in the Us. But as the century progressed
1. Historical Background 1607 Jamestown Colony, in Virginia. 1620 Plymouth Colony 1630 Massachusetts Bay Colony 1640 The Bay Psalm Book, the first publication in America
What do you think the eigenvectors of the element stiff- ness matrix represent? 1. a basis in which the stiffness matrix would be diago- nal (if rotated to that basis) 2. a set of nodal displacements for the element corre-
How many zero eigenvalues do you think any element stiffness matrix (regardless of the type of finite element nterpolation should have in 2D and 3D, respectively?
Why is the element stiffness matrix singular in a finite element formulation? 1. So that it can accomodate rigid element dis- placements without introducing spurious nodal 2 Because we made a mistake in the formula- tion the stiffness matrix should not be sin- g 3. Because we havent enforced any displace ment boundary conditions(it's a variational approach after all) Statement(1)
By looking at the potential energy of an element, what can you conclude about the properties required for the basis functions of an euler -bernoulli beam element? They should be differentiable twice
The finite element method In FEMi we derale finite element equations fro PVD swe- SWe and obtained: K0=R:=4…n waere n:number of element nodal p Ue: elenent nodal displace ents
he finite element Metnod Overcome limitations of Rita Simple basis functions( ow order polyuouisls) Basisfonctians supported in sdo domains(fuite elemnet Basis functions constructed to provide interpolant of proximate soluton Undetermined beraweters represent vales of dead
