the finite derwent meThod Ir position of boundary conditions(olis plcewent) We had obtained the aesewbed finite element eeve Kik2∞ Kht K Ki

The finite element melod I In FEM I We derived basis functions of arbitrary order for Hhe rod Model

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

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

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

清华大学出版社：高等院校应用型特色规划教材《冲压工艺与模具设计》课程教学资源（书籍教材）封面

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

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

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