shapefnc.cc

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/* $Header: /var/cvs/mbdyn/mbdyn/mbdyn-1.0/mbdyn/struct/shapefnc.cc,v 1.31 2017/01/12 14:46:43 masarati Exp $ */
/* 
 * MBDyn (C) is a multibody analysis code. 
 * http://www.mbdyn.org
 *
 * Copyright (C) 1996-2017
 *
 * Pierangelo Masarati  <masarati@aero.polimi.it>
 * Paolo Mantegazza     <mantegazza@aero.polimi.it>
 *
 * Dipartimento di Ingegneria Aerospaziale - Politecnico di Milano
 * via La Masa, 34 - 20156 Milano, Italy
 * http://www.aero.polimi.it
 *
 * Changing this copyright notice is forbidden.
 *
 * This program is free software; you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
 * the Free Software Foundation (version 2 of the License).
 * 
 *
 * This program is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU General Public License for more details.
 *
 * You should have received a copy of the GNU General Public License
 * along with this program; if not, write to the Free Software
 * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
 */

#include "mbconfig.h"           /* This goes first in every *.c,*.cc file */

#include <limits>
#include <cfloat>
#include <limits>

#include "matvec3.h"
#include "shapefnc.h"

/* Funzioni di forma e loro derivate */
const doublereal dN2_1 = .5;            /* ShapeFunc2N(0., 1, 0) */
const doublereal dN2_2 = .5;            /* ShapeFunc3N(0., 2, 0) */

const doublereal dN2P_1 = -.5;          /* ShapeFunc2N(0., 1, 1) */
const doublereal dN2P_2 = .5;           /* ShapeFunc2N(0., 2, 1) */

const doublereal dN2PP_1 = 0.;          /* ShapeFunc2N(0., 1, 2) */
const doublereal dN2PP_2 = 0.;          /* ShapeFunc2N(0., 2, 2) */

/* Per l'interpolazione piu' compatta */
const doublereal dN2[2] = {
        dN2_1, dN2_2
};

const doublereal dN2P[2] = {
        dN2P_1, dN2P_2
};

const doublereal dN2PP[2] = {
        dN2PP_1, dN2PP_2
};

/* Funzioni di interpolazione */
doublereal 
ShapeFunc2N(doublereal d, integer iNode, enum Order Ord)
{
        ASSERT(iNode == 1 || iNode == 2);
        
        switch (Ord) {
        case ORD_ALG:
                switch (iNode) {
                case 1:
                        return .5*(1.-d);
                        
                case 2:
                        return .5*(1.+d);
                        
                default:
                        throw ErrGeneric(MBDYN_EXCEPT_ARGS);
                }
                
        case ORD_D1:
                switch (iNode) {
                case 1:         
                        return -.5;
                        
                case 2:
                        return .5;
                        
                default:
                        throw ErrGeneric(MBDYN_EXCEPT_ARGS);
                }
                
        case ORD_D2:
                switch (iNode) {
                case 1:         
                        return 0.;
                        
                case 2:
                        return 0.;
                        
                default:
                        throw ErrGeneric(MBDYN_EXCEPT_ARGS);
                }
        }
        
        /* Per evitare warnings */
        return 0.;
}

doublereal
DxDcsi2N(doublereal d, const Vec3& X1, const Vec3& X2)
{
        doublereal dN1p = ShapeFunc2N(d, 1, ORD_D1);
        doublereal dN2p = ShapeFunc2N(d, 2, ORD_D1);
        Vec3 DXDcsi(X1*dN1p+X2*dN2p);
        doublereal dd = DXDcsi.Dot();

        if (dd > std::numeric_limits<doublereal>::epsilon()) {
                return std::sqrt(dd);
        }

        return 0.;
}

/* Punto di valutazione */
const doublereal dS = 1./sqrt(3.);

/* Funzioni di forma e loro derivate - punto I */
const doublereal dN1_I = (1.+sqrt(3.))/6.;       /* ShapeFunc3N(-dS, 1) */
const doublereal dN2_I = 2./3.;                  /* ShapeFunc3N(-dS, 2) */
const doublereal dN3_I = (1.-sqrt(3.))/6.;       /* ShapeFunc3N(-dS, 3) */

const doublereal dN1P_I = -(2.*sqrt(3.)+3.)/6.;  /* ShapeFunc3N(-dS, 1, 1) */
const doublereal dN2P_I = 2./sqrt(3.);           /* ShapeFunc3N(-dS, 2, 1) */
const doublereal dN3P_I = -(2.*sqrt(3.)-3.)/6.;  /* ShapeFunc3N(-dS, 3, 1) */

const doublereal dN1PP_I = 1.;                   /* ShapeFunc3N(-dS, 1, 2) */
const doublereal dN2PP_I = -2.;                  /* ShapeFunc3N(-dS, 2, 2) */
const doublereal dN3PP_I = 1.;                   /* ShapeFunc3N(-dS, 3, 2) */

/* Funzioni di forma e loro derivate - punto II */
const doublereal dN1II = dN3_I;
const doublereal dN2II = dN2_I;
const doublereal dN3II = dN1_I;

const doublereal dN1PII = -dN3P_I;
const doublereal dN2PII = -dN2P_I;
const doublereal dN3PII = -dN1P_I;

const doublereal dN1PPII = dN3PP_I;
const doublereal dN2PPII = dN2PP_I;
const doublereal dN3PPII = dN1PP_I;

/* Per l'interpolazione piu' compatta */
const doublereal dN3[2][3] = {
        { dN1_I, dN2_I, dN3_I },
        { dN1II, dN2II, dN3II }
};

const doublereal dN3P[2][3] = {
        { dN1P_I, dN2P_I, dN3P_I },
        { dN1PII, dN2PII, dN3PII }
};

const doublereal dN3PP[2][3] = {
        { dN1PP_I, dN2PP_I, dN3PP_I },
        { dN1PPII, dN2PPII, dN3PPII }
};

doublereal 
ShapeFunc3N(doublereal d, integer iNode, enum Order Ord)
{
        ASSERT(iNode == 1 || iNode == 2 || iNode == 3);
        
        switch (Ord) {
        case ORD_ALG:
                switch (iNode) {
                case 1:         
                        return .5*d*(d-1.);
                        
                case 2:         
                        return 1.-d*d;
                        
                case 3:         
                        return .5*d*(d+1.);
                        
                default:
                        throw ErrGeneric(MBDYN_EXCEPT_ARGS);
                }
                
        case ORD_D1:
                switch (iNode) {
                case 1:         
                        return d-.5;
                        
                case 2:
                        return -2.*d;
                        
                case 3:
                        return d+.5;
                        
                default:
                        throw ErrGeneric(MBDYN_EXCEPT_ARGS);
                }
        case ORD_D2:
                switch (iNode) {
                case 1:         
                        return 1.;
                        
                case 2:
                        return -2.;
                        
                case 3:
                        return 1.;
                        
                default:
                        throw ErrGeneric(MBDYN_EXCEPT_ARGS);
                }
        }
        
        /* Per evitare warnings */
        return 0.;
}

doublereal
DxDcsi3N(doublereal d, const Vec3& X1, const Vec3& X2, const Vec3& X3)
{
        doublereal dN1p = ShapeFunc3N(d, 1, ORD_D1);
        doublereal dN2p = ShapeFunc3N(d, 2, ORD_D1);
        doublereal dN3p = ShapeFunc3N(d, 3, ORD_D1);
        Vec3 DXDcsi(X1*dN1p+X2*dN2p+X3*dN3p);
        doublereal dd = DXDcsi.Dot();

        if (dd > std::numeric_limits<doublereal>::epsilon()) {
                return std::sqrt(dd);
        }

        return 0.;
}