機械工程中常用的數值分析方法- 2

1、Finite Element & Numerical Optimization in Mechanical EngineeringByProfs. Ji-Hong ZHU & Tong Gao1Episode 3Properties of Stiffness Matrix2SingularityRigid Body Motion3Items4ItemsA unit displacement on 1st DOF generates the reaction forces.5ItemsA unit displacement on 2nd DOF generates the reaction fo

2、rces.6ItemsAn easy way to obtain stiffness matrixA unit displacement on jth DOF generates the reaction force on ith DOF.7Items8Symmetry9Symmetry10SymmetryA unit displacement on jth DOF generates a reaction force on ith DOFA unit displacement on ith DOF generates a reaction force on jth DOF11Episode

3、4FEM of Beams1213Why beamsSpringBarBeam14Stiffness matrix of beam (6DOFs)15Stiffness matrix of beam (6DOFs)16Stiffness matrix of beam (6DOFs)17Stiffness matrix of beam (6DOFs)18Stiffness matrix of beam (9DOFs)1,2,34,5,67,8,91,2,3,4,5,64,5,6,7,8,9K11K12K13K14K15K16000K21K22K23K24K25K26000K31K32K33K34

4、K35K36000K41K42K43K44K45K46K47K48K49K51K52K53K54K55K56K57K58K59K61K62K63K64K65K66K67K68K69000K74K75K76K77K78K79000K84K85K86K87K88K89000K94K95K96K97K98K9919Stiffness matrix of beam (9DOFs)1,2,34,5,67,8,91,2,3,4,5,64,5,6,7,8,9K11K12K13K14K15K16000K21K22K23K24K25K26000K31K32K33K34K35K36000K41K42K43K44K

5、45K46K47K48K49K51K52K53K54K55K56K57K58K59K61K62K63K64K65K66K67K68K69000K74K75K76K77K78K79000K84K85K86K87K88K89000K94K95K96K97K98K9920More Problems1,2,34,5,67,8,91,2,34,5,6?21Episode 5Coordinate Transformation22Local and Global Coordinate1,2,34,5,6xy1,2,34,5,6x*y*Local CoordinateGlobal Coordinate23Lo

6、cal and Global Coordinate1,2,34,5,6xy1,2,34,5,6x*y*Local CoordinateGlobal Coordinate24Local and Global Coordinatexyx*y*xy25Local and Global Coordinatexyx*y*26Local and Global Coordinate27Local and Global Coordinate28Local and Global Coordinate1,2,34,5,67,8,9K11K12K13K14K15K16000K21K22K23K24K25K26000

7、K31K32K33K34K35K36000K41K42K43K44K45K46K47K48K49K51K52K53K54K55K56K57K58K59K61K62K63K64K65K66K67K68K69000K74K75K76K77K78K79000K84K85K86K87K88K89000K94K95K96K97K98K9929Local and Global Coordinate1,2,34,5,67,8,9K11K12K13K14K15K16000K21K22K23K24K25K26000K31K32K33K34K35K36000K41K42K43K44K45K46K47K48K49K51K52K53K54K55K56K57K58K59K61K62K63K64K65K66K67K68K69000K74K75K76K77K78K79000K84K85K86K87K88K89000K94K95K96K97K98K99301/ Stiffness Matr