hbeam_interp.cc File Reference

#include "mbconfig.h"
#include "matvecexp.h"
#include "Rot.hh"
#include "hbeam_interp.h"

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Enumerations
enum	{ NODE1 = 0, NODE2 = 1, NUMNODES = 2 }

Functions
void	Compute (const Vec3 *const node_pos, const Mat3x3 *const node_or, const Vec3 *const node_f, const doublereal xi, const doublereal dexi_des, Vec3 &pos, Mat3x3 &orient, Vec3 &F, Vec3 &om, MatExp &A1, MatExp &A2, MatExp &A12, MatExp &A_tilde, MatExp &Theta_r_I, MatExp &Theta_tilde, MatExp &A_xi, VecExp &eta_r, VecExp &kappa, VecExp &eta_tilde)
void	ComputeInterpolation (const Vec3 *const node_pos, const Mat3x3 *const node_or, const Vec3 *const node_f, const doublereal xi, const doublereal dexi_des, Vec3 &pos, Mat3x3 &orient, Vec3 &F, Vec3 &om)
void	ComputeFullInterpolation (const Vec3 *const node_pos, const Mat3x3 *const node_or, const Vec3 *const node_f, const doublereal xi, const doublereal dexi_des, Vec3 &pos, Mat3x3 &orient, Mat3x3 *const or_delta_w_or, Mat3x3 *const delta_pos_w_or, Mat3x3 *const delta_pos_w_pos, Vec3 &F, Vec3 &om, Mat3x3 *const delta_om_ws_or, Mat3x3 *const delta_F_ws_or, Mat3x3 *const delta_F_ws_pos)

Enumeration Type Documentation

anonymous enum

Enumerator
NODE1
NODE2
NUMNODES

Definition at line 85 of file hbeam_interp.cc.

     {
        NODE1 = 0,
        NODE2 = 1,
        NUMNODES = 2    /* serve eventualmente per dimensionare arrays */
};

Function Documentation

void Compute ( const Vec3 *const  node_pos, const Mat3x3 *const  node_or, const Vec3 *const  node_f, const doublereal  xi, const doublereal  dexi_des, Vec3 &  pos, Mat3x3 &  orient, Vec3 &  F, Vec3 &  om, MatExp &  A1, MatExp &  A2, MatExp &  A12, MatExp &  A_tilde, MatExp &  Theta_r_I, MatExp &  Theta_tilde, MatExp &  A_xi, VecExp &  eta_r, VecExp &  kappa, VecExp &  eta_tilde  )

inline

Definition at line 92 of file hbeam_interp.cc.

References Vec3::Cross(), grad::Cross(), RoTrManip::DRoTr_I(), VecExp::GetMom(), MatExp::GetMom(), VecExp::GetVec(), MatExp::GetVec(), RoTrManip::Helix(), NODE1, NODE2, RoTrManip::RoTrAndDRoTr(), MatExp::Transpose(), and Mat3x3::Transpose().

Referenced by ComputeFullInterpolation(), and ComputeInterpolation().

                  {
        A1 = MatExp(node_or[NODE1], node_pos[NODE1].Cross(node_or[NODE1]));
        A2 = MatExp(node_or[NODE2], node_pos[NODE2].Cross(node_or[NODE2]));
        A12 = A2*(A1.Transpose());
        //VecExp e1(0.);
        eta_r = RoTrManip::Helix(A12);
        Theta_r_I = RoTrManip::DRoTr_I(eta_r);
        eta_tilde = eta_r*xi;
        RoTrManip::RoTrAndDRoTr(eta_tilde,A_tilde,Theta_tilde);
        A_xi = A_tilde*A1;
                //extract interpolated orientation and position
                orient = A_xi.GetVec();
                pos = (A_xi.GetMom()*(orient.Transpose())).Ax();

        kappa = Theta_tilde*eta_r*dexi_des;
                //extract interpolated curvature and def. gradient
                om = kappa.GetVec();
                F = kappa.GetMom();
                F -= pos.Cross(om); /* :) */
};

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void ComputeFullInterpolation	(	const Vec3 *const	node_pos,
		const Mat3x3 *const	node_or,
		const Vec3 *const	node_f,
		const doublereal	xi,
		const doublereal	dexi_des,
		Vec3 &	pos,
		Mat3x3 &	orient,
		Mat3x3 *const	or_delta_w_or,
		Mat3x3 *const	delta_pos_w_or,
		Mat3x3 *const	delta_pos_w_pos,
		Vec3 &	F,
		Vec3 &	om,
		Mat3x3 *const	delta_om_ws_or,
		Mat3x3 *const	delta_F_ws_or,
		Mat3x3 *const	delta_F_ws_pos
	)

Definition at line 148 of file hbeam_interp.cc.

References Compute(), Vec3::Cross(), RoTrManip::Elle(), Eye3, MatExp::GetMom(), VecExp::GetVec(), MatExp::GetVec(), MatCross, NODE1, NODE2, and NUMNODES.

Referenced by HBeam::AssStiffnessMat().

                                                      {
        MatExp A1, A2, A12, A_tilde, Theta_r_I, Theta_tilde, A_xi;
        VecExp eta_r, kappa, eta_tilde;
        Compute(node_pos,node_or, node_f,xi,dexi_des,pos,orient,F,om,
                A1,A2,A12,A_tilde,Theta_r_I,Theta_tilde,A_xi,eta_r, 
                kappa,eta_tilde);

        MatExp eta_xi_delta_2(Theta_tilde*Theta_r_I*xi);
        MatExp eta_xi_delta_1(A_tilde);
                eta_xi_delta_1-=Theta_tilde*Theta_r_I*A2*xi;
        //compute traslation wrenches at xi and at the nodes:
        MatExp Trasl_n[NUMNODES];
        Trasl_n[NODE1] = MatExp(Eye3, Mat3x3(MatCross, node_pos[NODE1]));
        Trasl_n[NODE2] = MatExp(Eye3, Mat3x3(MatCross, node_pos[NODE2]));
        MatExp Trasl_xi_bak(Eye3, Mat3x3(MatCross, -pos));
        //compute delta_kappa_i
        MatExp Lambda(RoTrManip::Elle(eta_tilde,eta_r*dexi_des));
        MatExp delta_kappa_2(Lambda*xi);
                delta_kappa_2+=Theta_tilde*dexi_des;
                delta_kappa_2 = delta_kappa_2*Theta_r_I;
        MatExp delta_kappa_1(delta_kappa_2*A2*-1);
        
        //transform eta_xi_delta_i to deltapos_ordelta_xi_i
        MatExp dpos_ord_xi_1(Trasl_xi_bak*eta_xi_delta_1);
        MatExp dpos_ord_xi_2(Trasl_xi_bak*eta_xi_delta_2);
        //project to nodes delta_pos, or_delta:
        MatExp dpos_ord_dpos_ord_1(dpos_ord_xi_1*Trasl_n[NODE1]);
        MatExp dpos_ord_dpos_ord_2(dpos_ord_xi_2*Trasl_n[NODE2]);
        //extract or_delta_w_or, delta_pos_w_or and delta_pos_w_pos
        or_delta_w_or[NODE1] = dpos_ord_dpos_ord_1.GetVec();
        or_delta_w_or[NODE2] = dpos_ord_dpos_ord_2.GetVec();
        delta_pos_w_or[NODE1] = dpos_ord_dpos_ord_1.GetMom();
        delta_pos_w_or[NODE2] = dpos_ord_dpos_ord_2.GetMom();
        delta_pos_w_pos[NODE1] = dpos_ord_dpos_ord_1.GetVec();
        delta_pos_w_pos[NODE2] = dpos_ord_dpos_ord_2.GetVec();
        //project delta_kappa_1 to nodes delta_pos, or_delta:
        MatExp dkappa_dpos_ord_1(delta_kappa_1*Trasl_n[NODE1]);
        MatExp dkappa_dpos_ord_2(delta_kappa_2*Trasl_n[NODE2]);
        //extract delta_om_ws_or, delta_F_ws_or and delta_F_ws_pos
        delta_om_ws_or[NODE1] = dkappa_dpos_ord_1.GetVec();
        delta_om_ws_or[NODE2] = dkappa_dpos_ord_2.GetVec();
        //delta kappa.Mom()
        delta_F_ws_or[NODE1] = dkappa_dpos_ord_1.GetMom();
        delta_F_ws_pos[NODE1] = dkappa_dpos_ord_1.GetVec();
        delta_F_ws_or[NODE2] = dkappa_dpos_ord_2.GetMom();
        delta_F_ws_pos[NODE2] = dkappa_dpos_ord_2.GetVec();
        //x cross delta kappa.Vec()
        delta_F_ws_or[NODE1] -= pos.Cross(dkappa_dpos_ord_1.GetVec());
        delta_F_ws_or[NODE2] -= pos.Cross(dkappa_dpos_ord_2.GetVec());
        //kappa.Vec() x delta_pos
        delta_F_ws_or[NODE1] += kappa.GetVec().Cross(delta_pos_w_or[NODE1]);
        delta_F_ws_pos[NODE1] += kappa.GetVec().Cross(delta_pos_w_pos[NODE1]);
        delta_F_ws_or[NODE2] += kappa.GetVec().Cross(delta_pos_w_or[NODE2]);
        delta_F_ws_pos[NODE2] += kappa.GetVec().Cross(delta_pos_w_pos[NODE2]);

        //tarocco per l'aggiunta dell'offset f
        //le curvature e le posizioni invece sono giuste perche' 
        //viene passato node_pos=x_node+node_or*f
        Mat3x3 fodo;
        
        fodo = node_f[NODE1].Cross(or_delta_w_or[NODE1]);
        delta_pos_w_or[NODE1] -= delta_pos_w_pos[NODE1]*fodo;
        delta_F_ws_or[NODE1] -= delta_F_ws_pos[NODE1]*fodo;
        
        fodo = node_f[NODE2].Cross(or_delta_w_or[NODE2]);
        delta_pos_w_or[NODE2] -= delta_pos_w_pos[NODE2]*fodo;
        delta_F_ws_or[NODE2] -= delta_F_ws_pos[NODE2]*fodo;
}

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void ComputeInterpolation	(	const Vec3 *const	node_pos,
		const Mat3x3 *const	node_or,
		const Vec3 *const	node_f,
		const doublereal	xi,
		const doublereal	dexi_des,
		Vec3 &	pos,
		Mat3x3 &	orient,
		Vec3 &	F,
		Vec3 &	om
	)

Definition at line 132 of file hbeam_interp.cc.

References Compute().

Referenced by HBeam::AssStiffnessVec(), and HBeam::DsDxi().

                                  {
        MatExp A1, A2, A12, A_tilde, Theta_r_I, Theta_tilde, A_xi;
        VecExp eta_r, kappa, eta_tilde;
        Compute(node_pos,node_or, node_f,xi,dexi_des,pos,orient,F,om,
                A1,A2,A12,A_tilde,Theta_r_I,Theta_tilde,A_xi,eta_r, 
                kappa,eta_tilde);
};

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