- #1
chandran
- 139
- 1
i have put this question in other forum also.
I have understood the stiffness matrix generation for a single rectangular element as below. I consider each node having 2 translational dofs
each in x and y coord system. There are 4 nodes in this rectangular plate element and hence 8 dofs overall.
K11U1+K12U2+K13U3+K14U4+K15U5+K16U6+K17U7+K18U8= F1
K21U1+K22U2+K23U3+K24U4+K25U5+K26U6+K27U7+K28U8= F2
K31U1+K32U2+K33U3+K34U4+K35U5+K36U6+K37U7+K38U8= F3
K41U1+K42U2+K43U3+K44U4+K45U5+K46U6+K47U7+K48U8= F4
K51U1+K52U2+K53U3+K54U4+K55U5+K56U6+K57U7+K58U8= F5
K61U1+K62U2+K63U3+K64U4+K65U5+K66U6+K67U7+K68U8= F6
K71U1+K72U2+K73U3+K74U4+K75U5+K76U6+K77U7+K78U8= F7
K81U1+K82U2+K83U3+K84U4+K85U5+K86U6+K87U7+K88U8= F8
where K(IJ) is the stiffness influence coefficient saying the force at ith dof due to a unit displacement at jth dof.
U1,U2,U3 ETC is the displacement at ith dof.
F1,F2,F3 ETC is the force at the ith dof.
Now i have a question. In nastran or other fea packages how this K(IJ) is calculated for rectangular elements. I know that for rod element it is
AE/L where A is the rod area,E youngs modulus and
L is the length of the rod. But for solid elements and plane elements how this is calculated.
One more question regarding rod or truss elements. There is a line of 10mm length horizontal to x axis. Why shouldn't i divide the
line into 10 rod or truss elements. What will be the error? Can i divide the line with 10 beam elements?
I have understood the stiffness matrix generation for a single rectangular element as below. I consider each node having 2 translational dofs
each in x and y coord system. There are 4 nodes in this rectangular plate element and hence 8 dofs overall.
K11U1+K12U2+K13U3+K14U4+K15U5+K16U6+K17U7+K18U8= F1
K21U1+K22U2+K23U3+K24U4+K25U5+K26U6+K27U7+K28U8= F2
K31U1+K32U2+K33U3+K34U4+K35U5+K36U6+K37U7+K38U8= F3
K41U1+K42U2+K43U3+K44U4+K45U5+K46U6+K47U7+K48U8= F4
K51U1+K52U2+K53U3+K54U4+K55U5+K56U6+K57U7+K58U8= F5
K61U1+K62U2+K63U3+K64U4+K65U5+K66U6+K67U7+K68U8= F6
K71U1+K72U2+K73U3+K74U4+K75U5+K76U6+K77U7+K78U8= F7
K81U1+K82U2+K83U3+K84U4+K85U5+K86U6+K87U7+K88U8= F8
where K(IJ) is the stiffness influence coefficient saying the force at ith dof due to a unit displacement at jth dof.
U1,U2,U3 ETC is the displacement at ith dof.
F1,F2,F3 ETC is the force at the ith dof.
Now i have a question. In nastran or other fea packages how this K(IJ) is calculated for rectangular elements. I know that for rod element it is
AE/L where A is the rod area,E youngs modulus and
L is the length of the rod. But for solid elements and plane elements how this is calculated.
One more question regarding rod or truss elements. There is a line of 10mm length horizontal to x axis. Why shouldn't i divide the
line into 10 rod or truss elements. What will be the error? Can i divide the line with 10 beam elements?