- #1
Ronankeating
- 63
- 0
hi,
I'm studying the book for elasticity theory and I stuck at one of the equation in that book, the stiffness matrix for elements(thin or thick plate) in bending is given in that form
ke= t∫∫BT*Db*B*det(J)dζdη+∫∫BT*Ds*B*det(J)dζdη
The question is:
Since I know that shape function(Ni = 1/4(1 + ξ*ξi )(1 + η*ηi)) is bilinear of ζ and η. B matrix is 1st order bilinear, so BT*Db*B yieleds 2nd order. Form of det(J) is also ζ and η dependant. Multiplication of all of this terms will result in at least 3 order form of equation , is that really can be solved with Gauss integration?
Regards,
I'm studying the book for elasticity theory and I stuck at one of the equation in that book, the stiffness matrix for elements(thin or thick plate) in bending is given in that form
ke= t∫∫BT*Db*B*det(J)dζdη+∫∫BT*Ds*B*det(J)dζdη
- B is the strain matrix(5x12) where the inner products include the shape function and derivation of shape function regarding the ζ and η.
- Db is the bending coefficient matrix (5x5) (scalar)
- Ds is the shear coefficient matrix (5x5) (scalar)
- det(J) is the determinant of Jacobian matrix (2x2)
The question is:
Since I know that shape function(Ni = 1/4(1 + ξ*ξi )(1 + η*ηi)) is bilinear of ζ and η. B matrix is 1st order bilinear, so BT*Db*B yieleds 2nd order. Form of det(J) is also ζ and η dependant. Multiplication of all of this terms will result in at least 3 order form of equation , is that really can be solved with Gauss integration?
Regards,