美国麻省理工大学：《结构分析与设计技术》教学资源（讲义）notes122

Which of the following are real problems with the ritz method 1. Selection of basis functions for general ge- metres 2. Lack of systematic procedure to compute stiff atrix and forcing terms

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

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

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

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)

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?

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-

The finite element method(I for three-diwnensional robles Potential enery applied to one eleet

How many quadrature points do you need to integrate a polynomial of order p= 3 exactly using Gauss'method