22 Dec 2015
— Edited @ @
22 Dec 2015
I want to add aerodynamic forces into GEBT to analysis the aeroelastic response of composite rotor blade, so I dig into the details of GEBT source codes. The followings are the questions I encountered:
1. About the follower force and moment: In the source code, the follower applied force and moment are transformed into the global a frame by premultiplied matrix CT, should the transformation matrix be CTCab(CaB)?Or the follower appliced force F and moment M should be premultiplied by Cab first before input and then use CabF and CabM as input force and moment?
2. In preprocess.stiff.f90 line 213 and 214, it seems that one ndiv should be divided rather than two in order to obtain the linearly varying sectional properties?
3. In element.f90 line 281, the matrix tmp333 is used to express the derivatives of matrix -(I3-Tilde(theta*.5D0))/(1+tt4) with respect to theta,where tt4=DOT_PRODUCT(theta,theta)*0.25D0. I derived the derivative by hand and software mathematic, it seems that the expressions used in the code is wrong and the correct expression should be tmp333=(Tilde(I3(i,:)*0.5d0*(1+tt4))+theta(i)*0.5d0*(I3-Tilde(theta*0.5d0)))/ (1+tt4)**2?
4. In system.f90 subroutine PointFollowerJ, the unknown deflection u is always treated as locating before the unknown rotation theta for all key points. While for connection points this is the case, for boundary points the order of u and theta depends on the order of the prescribed forces and moments. So I think for the boundary points, PointFollowerJ should determine the order of u and theta first according to the prescribed forces and moments and then put the derivatives with respect to theta into the column corresponding to theta.
5. In system.f90 subroutine AssembleJacobian, for the connection points which have prescribed displacements, coef and rhs are modified correspondingly. How does the modification in the code work? It seems to me that by the modification in the code the delta of the prescribed displacement is set to the prescribed value not the prescribed displacement itself.
6. I followed professor Hodges and his students Shang’s paper”Finite Element Solution of Nonliear Intrinsic Equations for Curved Composite Beams” to understand the mathematic of GEBT. I used the method introcuded by professor Hodges in the appendix B of his book “Nonlinear composite beam theory” to derive the equations for fu,fpsi,fFi,fMi,fPi and fHi. By my derivation, I found that while fu,fpsi,fFi,fMi and fPi correspond to deltau, deltapsi,deltaF,deltaM and deltaP expressed in the gobal a frame, fHi used in GEBT(the same as Hodges and Shang’s paper)corresponds to deltaH expressed in the deformed B frame. Therefore, I think the connection of fHi between elements may have a problem in GEBT.