/* [wxMaxima batch file version 1] [ DO NOT EDIT BY HAND! ]*/ /* [ Created with wxMaxima version 0.8.7 ] */ /* [wxMaxima: input start ] */ kill(all); /* [wxMaxima: input end ] */ /* [wxMaxima: comment start ] equilibrium equations [wxMaxima: comment end ] */ /* [wxMaxima: input start ] */ eqtrx : UA = 0; eqtry : VD = 0; eqtrz : -F+WA+WD = 0; /* [wxMaxima: input end ] */ /* [wxMaxima: input start ] */ eqrOx : ThetaD +0*VD +b*WD -c*F ; /* [wxMaxima: input end ] */ /* [wxMaxima: input start ] */ eqrOy : PhiA + a*F -a*WA + 0*UA ; /* [wxMaxima: input end ] */ /* [wxMaxima: input start ] */ eqrOz : 0 = 0 ; /* [wxMaxima: input end ] */ /* [wxMaxima: comment start ] blindly solve the equations [wxMaxima: comment end ] */ /* [wxMaxima: input start ] */ linsolve( [ eqtrx , eqtry, eqtrz , eqrOx , eqrOy, eqrOz ], [UA,PhiA, WD,VD,ThetaD] ) , globalsolve=True; /* [wxMaxima: input end ] */ /* [wxMaxima: comment start ] the WA unknown reaction force has been removed from the unknowns list, thus obtaining a parametric representation of the reaction forces and moments, with WA as a parameter (like F) [wxMaxima: comment end ] */ /* [wxMaxima: comment start ] to obtain the actual value of WA, the deflection in the z direction of the A point has to be evaluated and zeroed. Castigliano's Theorem fits. [wxMaxima: comment end ] */ /* [wxMaxima: input start ] */ N : 0; Sx : -VD; Sy : -WD; /* [wxMaxima: input end ] */ /* [wxMaxima: comment start ] equilibrium with respect to rotation along the local Cz axis [wxMaxima: comment end ] */ /* [wxMaxima: input start ] */ linsolve( Mt + ThetaD - e*WD + f*VD , Mt) ,globalsolve=true; /* [wxMaxima: input end ] */ /* [wxMaxima: comment start ] equilibrium with respect to rotation along the local Gx and Gy axes [wxMaxima: comment end ] */ /* [wxMaxima: input start ] */ linsolve( Mx +WD*s =0, Mx), globalsolve=True; /* [wxMaxima: input end ] */ /* [wxMaxima: input start ] */ linsolve ( My - VD*s =0,My ), globalsolve=true; /* [wxMaxima: input end ] */ /* [wxMaxima: comment start ] Internal energy for the DB beam [wxMaxima: comment end ] */ /* [wxMaxima: input start ] */ U : integrate( (Jyy*Mx^2+Jxx*My^2+2*Jxy*Mx*My) / (2*E*(Jxx*Jyy-Jxy^2)) + N^2/2/E/A + ( chix * Sx^2 + chiy * Sy^2 + chixy * Sx*Sy ) / (2*G*A) + Mt^2/2/G/Kt ,s,0,a); /* [wxMaxima: input end ] */ /* [wxMaxima: comment start ] Castigliano's Theorem is now applied to obtain the z deflection at A [wxMaxima: comment end ] */ /* [wxMaxima: input start ] */ linsolve( diff( U , WA ) = 0, WA ), globalsolve=true; /* [wxMaxima: input end ] */ /* [wxMaxima: input start ] */ U : ev(U); /* [wxMaxima: input end ] */ /* [wxMaxima: comment start ] I check that all the WA terms hidden within U are now expressed as functions of F [wxMaxima: comment end ] */ /* [wxMaxima: input start ] */ diff( U , 'WA) ; /* [wxMaxima: input end ] */ /* [wxMaxima: comment start ] the z deflection at the L point is evaluated for the quarter ladder frame structure, constrained according to two skew-symm planes [wxMaxima: comment end ] */ /* [wxMaxima: input start ] */ d : diff(U , F); /* [wxMaxima: input end ] */ /* [wxMaxima: input start ] */ dw : diff(4*U , F); /* [wxMaxima: input end ] */ /* Maxima can't load/batch files which end with a comment! */ "Created with wxMaxima"$