properties of finite dement soltions Noded point equilibrio At a node, the sow of he elemeat nodal forces s in equilibriun with Hhe externed loads

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

Concept Question How many quadrature points do you need to integrate exactly the stiffness matrix of a lD finite element with quadratic interpolation for the displacements? gauss

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

cmaulenon o isoparametRic elemets (Bathes book Consider the uadriltersd denat shown in the 8oc nodd coordinates

Numerical integration Consider He 4-D integral =+(s 1 Seek n-point apploxiwisfions G~2M =1 are the weights and

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?

Finite element wodel of a beam(Euler-Bernollia- governing eQuations

The correct global local node mapping for the quadraticelement mesh in the figure is

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