c05a5706-56d9-4872-9eca-ad0020c77533 137 4 5 decimal

&[DATE] &[TIME] - &[FILENAME]

Beispiel für Integration von Sprungfunktionen mit Maxima

Example for integration of step functions using Maxima

Maxima

Beispiele

Examples

restart MaximaControl Restart complete.

takeover MaximaControl int(), diff(), sum() and lim() now use Maxima

x step 12 / 1 x sign + (* :

x q q.0 x l.0 - step * :

Streckenlast

line load

x I 10 x < (x 2 l.0 * < (* / :

F q.0 l.0 * :

Integration der Streckenlast und Addition der Einzelkräfte

Integration of the line load and point loads

x Q x q - x int F.A + F x l.0 2 / - step * - F.B x 32 / l.0 * - step * + Q.0 + :

Querkraft

shear force

x M x Q x int M.0 + :

Biegemoment

bending moment

x φ x M EI / x int φ.0 + :

Neigungswinkel

slope

x w x φ x int - w.0 + :

Durchsenkung

deflection

Randbedingungen zur Bestimmung der unbekannten Konstanten (2 Reaktionskräfte und 4 Integrationskonstanten)

boundary conditions to determine the unknowns (2 support reactions and 4 integration constants)

Gl 1 el 0 Q F.A ≡ (:

Querkraft am linken Rand

Shear force at the left support

Gl 2 el 2 l.0 * Q 0 ≡ (:

Querkraftfreiheit am rechten Ende

shear force at free right boundary

Gl 3 el 0 M 0 ≡ (:

Momentenfreiheit am linken Rand

Moment at the left boundary

Gl 4 el 2 l.0 * M 0 ≡ (:

Momentenfreiheit am rechten Rand

Moment at the right boundary

Gl 5 el 0 w 0 ≡ (:

Durchsenkung bei A gleich Null

Deflection at the left support

Gl 6 el 32 / l.0 * w 0 ≡ (:

Durchsenkung bei B gleich Null

Deflection at the right support

Lösung des Gleichungssystems

Solve the system of equations

l.0 0 > assume Maxima l.0 0 >

Gl Unknowns F.A F.B M.0 Q.0 w.0 φ.0 61 mat

Gl Gl Unknowns LinSolve Assign 2 l.0 * q.0 * 3 / 4 l.0 * q.0 * 3 / q.0 l.0 2^* - l.0 q.0 * 2 / 37 q.0 * l.0 4^* 96 EI * / 365 q.0 * l.0 3^* 576 EI * / 61 sys 11 mat

Auflagerreaktionen

Support reactions

F.A F 23 /

F.B F 43 /

x l.0 * q q.0 / x l.0 * I *

Maximalwerte:

Extremal values

x l.0 * Q q.0 l.0 * / x l.0 * I *

32 / 0.00001 - (l.0 * Q F 0.8333 -

x l.0 * M q.0 l.0 2 ^ * / x l.0 * I *

l.0 2 / M F 0.3333 l.0 *

x l.0 * φ q.0 l.0 2 ^ * EI / / x l.0 * I *

0 φ F 0.1372 l.0 2^EI / * -

x.0 0.5 l.0 * > x.0 l.0 < l.0 0 > assume Maxima x.0 0.5 l.0 * > l.0 x.0 > redundant 13 mat

x.0 φ 0 ≡ x.0 Solve #

x l.0 * w - q.0 l.0 3 ^ * EI / / x l.0 * I *

# MaximaLog Request: solve([(x_0^2*((%unitl_0*%unitq_0)/2)/2+x_0*(-%unitq_0*%unitl_0^2)+((x_0-3*%unitl_0/2)*abs(x_0-3*%unitl_0/2)/2+(x_0^2)/2)*((4*%unitl_0*%unitq_0)/3)/2+x_0^2*((2*%unitl_0*%unitq_0)/3)/2-%unitl_0*%unitq_0*((x_0-%unitl_0/2)*abs(x_0-%unitl_0/2)/2+(x_0^2)/2)/2-%unitq_0*((2*(x_0^3)/3-2*%unitl_0*x_0^2+2*%unitl_0^2*x_0-2*(%unitl_0^3)/3)*signum(x_0-%unitl_0)/4+(x_0^3)/6)/2)/%unitEI+(365*%unitq_0*%unitl_0^3)/(576*%unitEI)=0],[x_0]);
Answer: 
(%s11) [x_0 = (-%i*3^{1/2}/2-1/2)*(%unitl_0^{3/2}*(signum(x_0-%unitl_0)+1)^{-2}
                                                 *(((31104*%unitl_0*signum(x_0-%unitl_0)^2+117504*%unitl_0*signum(x_0-%unitl_0)+201600*%unitl_0)*abs(2*x_0-3*%unitl_0)-81000*%unitl_0^2*signum(x_0-%unitl_0)^2+(2*x_0-3*%unitl_0)^2*(55296*signum(x_0-%unitl_0)+55296)-470016*%unitl_0^2*signum(x_0-%unitl_0)-619416*%unitl_0^2)*abs(2*x_0-%unitl_0)+(2*x_0-%unitl_0)^2*(10368*signum(x_0-%unitl_0)+10368)*abs(2*x_0-%unitl_0)+(2*x_0-%unitl_0)^2*((-41472*signum(x_0-%unitl_0)-41472)*abs(2*x_0-3*%unitl_0)+11664*%unitl_0*signum(x_0-%unitl_0)^2+80352*%unitl_0*signum(x_0-%unitl_0)+25488*%unitl_0)
                                                                                                                                                                                                                                                                                                                                                    +(-108000*%unitl_0^2*signum(x_0-%unitl_0)^2+56448*%unitl_0^2*signum(x_0-%unitl_0)-296352*%unitl_0^2)*abs(2*x_0-3*%unitl_0)+(2*x_0-3*%unitl_0)^2*(-24576*signum(x_0-%unitl_0)-24576)*abs(2*x_0-3*%unitl_0)+(2*x_0-3*%unitl_0)^2*(20736*%unitl_0*signum(x_0-%unitl_0)^2-133632*%unitl_0*signum(x_0-%unitl_0)-231168*%unitl_0)+140625*%unitl_0^3*signum(x_0-%unitl_0)^2
                                                                                                                                                                                                                                                                                                                                                    +458178*%unitl_0^3*signum(x_0-%unitl_0)+1298353*%unitl_0^3)
                                                  ^{1/2}
                                  /288
                                  -((648*%unitl_0^2*signum(x_0-%unitl_0)^2+3456*%unitl_0^2*signum(x_0-%unitl_0)+2808*%unitl_0^2)*abs(2*x_0-%unitl_0)/2+signum(x_0-%unitl_0)^2*(432*%unitl_0^2*abs(2*x_0-3*%unitl_0)-1125*%unitl_0^3)+signum(x_0-%unitl_0)*(-576*%unitl_0^2*abs(2*x_0-3*%unitl_0)-2970*%unitl_0^3)-1008*%unitl_0^2*abs(2*x_0-3*%unitl_0)-5845*%unitl_0^3)/(864*signum(x_0-%unitl_0)^3+2592*signum(x_0-%unitl_0)^2+2592*signum(x_0-%unitl_0)+864))
                                  ^{1/3}
            -(%i*3^{1/2}/2-1/2)*((9*%unitl_0*signum(x_0-%unitl_0)+9*%unitl_0)*abs(2*x_0-%unitl_0)/2+signum(x_0-%unitl_0)*(-6*%unitl_0*abs(2*x_0-3*%unitl_0)-3*%unitl_0^2)-6*%unitl_0*abs(2*x_0-3*%unitl_0)-28*%unitl_0^2)
                               *(%unitl_0^{3/2}*(signum(x_0-%unitl_0)+1)^{-2}
                                               *(((31104*%unitl_0*signum(x_0-%unitl_0)^2+117504*%unitl_0*signum(x_0-%unitl_0)+201600*%unitl_0)*abs(2*x_0-3*%unitl_0)-81000*%unitl_0^2*signum(x_0-%unitl_0)^2+(2*x_0-3*%unitl_0)^2*(55296*signum(x_0-%unitl_0)+55296)-470016*%unitl_0^2*signum(x_0-%unitl_0)-619416*%unitl_0^2)*abs(2*x_0-%unitl_0)+(2*x_0-%unitl_0)^2*(10368*signum(x_0-%unitl_0)+10368)*abs(2*x_0-%unitl_0)+(2*x_0-%unitl_0)^2*((-41472*signum(x_0-%unitl_0)-41472)*abs(2*x_0-3*%unitl_0)+11664*%unitl_0*signum(x_0-%unitl_0)^2+80352*%unitl_0*signum(x_0-%unitl_0)+25488*%unitl_0)
                                                                                                                                                                                                                                                                                                                                                  +(-108000*%unitl_0^2*signum(x_0-%unitl_0)^2+56448*%unitl_0^2*signum(x_0-%unitl_0)-296352*%unitl_0^2)*abs(2*x_0-3*%unitl_0)+(2*x_0-3*%unitl_0)^2*(-24576*signum(x_0-%unitl_0)-24576)*abs(2*x_0-3*%unitl_0)+(2*x_0-3*%unitl_0)^2*(20736*%unitl_0*signum(x_0-%unitl_0)^2-133632*%unitl_0*signum(x_0-%unitl_0)-231168*%unitl_0)+140625*%unitl_0^3*signum(x_0-%unitl_0)^2
                                                                                                                                                                                                                                                                                                                                                  +458178*%unitl_0^3*signum(x_0-%unitl_0)+1298353*%unitl_0^3)
                                                ^{1/2}
                                /288
                                -((648*%unitl_0^2*signum(x_0-%unitl_0)^2+3456*%unitl_0^2*signum(x_0-%unitl_0)+2808*%unitl_0^2)*abs(2*x_0-%unitl_0)/2+signum(x_0-%unitl_0)^2*(432*%unitl_0^2*abs(2*x_0-3*%unitl_0)-1125*%unitl_0^3)+signum(x_0-%unitl_0)*(-576*%unitl_0^2*abs(2*x_0-3*%unitl_0)-2970*%unitl_0^3)-1008*%unitl_0^2*abs(2*x_0-3*%unitl_0)-5845*%unitl_0^3)/(864*signum(x_0-%unitl_0)^3+2592*signum(x_0-%unitl_0)^2+2592*signum(x_0-%unitl_0)+864))
                                ^{-1/3}
             /(9*signum(x_0-%unitl_0)^2+18*signum(x_0-%unitl_0)+9)+(3*%unitl_0*signum(x_0-%unitl_0)+8*%unitl_0)/(3*(signum(x_0-%unitl_0)+1)),
        x_0 = (%i*3^{1/2}/2-1/2)*(%unitl_0^{3/2}*(signum(x_0-%unitl_0)+1)^{-2}
                                                *(((31104*%unitl_0*signum(x_0-%unitl_0)^2+117504*%unitl_0*signum(x_0-%unitl_0)+201600*%unitl_0)*abs(2*x_0-3*%unitl_0)-81000*%unitl_0^2*signum(x_0-%unitl_0)^2+(2*x_0-3*%unitl_0)^2*(55296*signum(x_0-%unitl_0)+55296)-470016*%unitl_0^2*signum(x_0-%unitl_0)-619416*%unitl_0^2)*abs(2*x_0-%unitl_0)+(2*x_0-%unitl_0)^2*(10368*signum(x_0-%unitl_0)+10368)*abs(2*x_0-%unitl_0)+(2*x_0-%unitl_0)^2*((-41472*signum(x_0-%unitl_0)-41472)*abs(2*x_0-3*%unitl_0)+11664*%unitl_0*signum(x_0-%unitl_0)^2+80352*%unitl_0*signum(x_0-%unitl_0)+25488*%unitl_0)
                                                                                                                                                                                                                                                                                                                                                   +(-108000*%unitl_0^2*signum(x_0-%unitl_0)^2+56448*%unitl_0^2*signum(x_0-%unitl_0)-296352*%unitl_0^2)*abs(2*x_0-3*%unitl_0)+(2*x_0-3*%unitl_0)^2*(-24576*signum(x_0-%unitl_0)-24576)*abs(2*x_0-3*%unitl_0)+(2*x_0-3*%unitl_0)^2*(20736*%unitl_0*signum(x_0-%unitl_0)^2-133632*%unitl_0*signum(x_0-%unitl_0)-231168*%unitl_0)+140625*%unitl_0^3*signum(x_0-%unitl_0)^2
                                                                                                                                                                                                                                                                                                                                                   +458178*%unitl_0^3*signum(x_0-%unitl_0)+1298353*%unitl_0^3)
                                                 ^{1/2}
                                 /288
                                 -((648*%unitl_0^2*signum(x_0-%unitl_0)^2+3456*%unitl_0^2*signum(x_0-%unitl_0)+2808*%unitl_0^2)*abs(2*x_0-%unitl_0)/2+signum(x_0-%unitl_0)^2*(432*%unitl_0^2*abs(2*x_0-3*%unitl_0)-1125*%unitl_0^3)+signum(x_0-%unitl_0)*(-576*%unitl_0^2*abs(2*x_0-3*%unitl_0)-2970*%unitl_0^3)-1008*%unitl_0^2*abs(2*x_0-3*%unitl_0)-5845*%unitl_0^3)/(864*signum(x_0-%unitl_0)^3+2592*signum(x_0-%unitl_0)^2+2592*signum(x_0-%unitl_0)+864))
                                 ^{1/3}
            -(-%i*3^{1/2}/2-1/2)*((9*%unitl_0*signum(x_0-%unitl_0)+9*%unitl_0)*abs(2*x_0-%unitl_0)/2+signum(x_0-%unitl_0)*(-6*%unitl_0*abs(2*x_0-3*%unitl_0)-3*%unitl_0^2)-6*%unitl_0*abs(2*x_0-3*%unitl_0)-28*%unitl_0^2)
                                *(%unitl_0^{3/2}*(signum(x_0-%unitl_0)+1)^{-2}
                                                *(((31104*%unitl_0*signum(x_0-%unitl_0)^2+117504*%unitl_0*signum(x_0-%unitl_0)+201600*%unitl_0)*abs(2*x_0-3*%unitl_0)-81000*%unitl_0^2*signum(x_0-%unitl_0)^2+(2*x_0-3*%unitl_0)^2*(55296*signum(x_0-%unitl_0)+55296)-470016*%unitl_0^2*signum(x_0-%unitl_0)-619416*%unitl_0^2)*abs(2*x_0-%unitl_0)+(2*x_0-%unitl_0)^2*(10368*signum(x_0-%unitl_0)+10368)*abs(2*x_0-%unitl_0)+(2*x_0-%unitl_0)^2*((-41472*signum(x_0-%unitl_0)-41472)*abs(2*x_0-3*%unitl_0)+11664*%unitl_0*signum(x_0-
Received bytes: 8192
SMath get: [x,0≡(-i*3^{1/2}/2-1/2)*('l,0^{3/2}*(sign(x,0-'l,0)+1)^{-2}*(((31104*'l,0*sign(x,0-'l,0)^2+117504*'l,0*sign(x,0-'l,0)+201600*'l,0)*abs(2*x,0-3*'l,0)-81000*'l,0^2*sign(x,0-'l,0)^2+(2*x,0-3*'l,0)^2*(55296*sign(x,0-'l,0)+55296)-470016*'l,0^2*sign(x,0-'l,0)-619416*'l,0^2)*abs(2*x,0-'l,0)+(2*x,0-'l,0)^2*(10368*sign(x,0-'l,0)+10368)*abs(2*x,0-'l,0)+(2*x,0-'l,0)^2*((-41472*sign(x,0-'l,0)-41472)*abs(2*x,0-3*'l,0)+11664*'l,0*sign(x,0-'l,0)^2+80352*'l,0*sign(x,0-'l,0)+25488*'l,0)+(-108000*'l,0^2*sign(x,0-'l,0)^2+56448*'l,0^2*sign(x,0-'l,0)-296352*'l,0^2)*abs(2*x,0-3*'l,0)+(2*x,0-3*'l,0)^2*(-24576*sign(x,0-'l,0)-24576)*abs(2*x,0-3*'l,0)+(2*x,0-3*'l,0)^2*(20736*'l,0*sign(x,0-'l,0)^2-133632*'l,0*sign(x,0-'l,0)-231168*'l,0)+140625*'l,0^3*sign(x,0-'l,0)^2+458178*'l,0^3*sign(x,0-'l,0)+1298353*'l,0^3)^{1/2}/288-((648*'l,0^2*sign(x,0-'l,0)^2+3456*'l,0^2*sign(x,0-'l,0)+2808*'l,0^2)*abs(2*x,0-'l,0)/2+sign(x,0-'l,0)^2*(432*'l,0^2*abs(2*x,0-3*'l,0)-1125*'l,0^3)+sign(x,0-'l,0)*(-576*'l,0^2*abs(2*x,0-3*'l,0)-2970*'l,0^3)-1008*'l,0^2*abs(2*x,0-3*'l,0)-5845*'l,0^3)/(864*sign(x,0-'l,0)^3+2592*sign(x,0-'l,0)^2+2592*sign(x,0-'l,0)+864))^{1/3}-(i*3^{1/2}/2-1/2)*((9*'l,0*sign(x,0-'l,0)+9*'l,0)*abs(2*x,0-'l,0)/2+sign(x,0-'l,0)*(-6*'l,0*abs(2*x,0-3*'l,0)-3*'l,0^2)-6*'l,0*abs(2*x,0-3*'l,0)-28*'l,0^2)*('l,0^{3/2}*(sign(x,0-'l,0)+1)^{-2}*(((31104*'l,0*sign(x,0-'l,0)^2+117504*'l,0*sign(x,0-'l,0)+201600*'l,0)*abs(2*x,0-3*'l,0)-81000*'l,0^2*sign(x,0-'l,0)^2+(2*x,0-3*'l,0)^2*(55296*sign(x,0-'l,0)+55296)-470016*'l,0^2*sign(x,0-'l,0)-619416*'l,0^2)*abs(2*x,0-'l,0)+(2*x,0-'l,0)^2*(10368*sign(x,0-'l,0)+10368)*abs(2*x,0-'l,0)+(2*x,0-'l,0)^2*((-41472*sign(x,0-'l,0)-41472)*abs(2*x,0-3*'l,0)+11664*'l,0*sign(x,0-'l,0)^2+80352*'l,0*sign(x,0-'l,0)+25488*'l,0)+(-108000*'l,0^2*sign(x,0-'l,0)^2+56448*'l,0^2*sign(x,0-'l,0)-296352*'l,0^2)*abs(2*x,0-3*'l,0)+(2*x,0-3*'l,0)^2*(-24576*sign(x,0-'l,0)-24576)*abs(2*x,0-3*'l,0)+(2*x,0-3*'l,0)^2*(20736*'l,0*sign(x,0-'l,0)^2-133632*'l,0*sign(x,0-'l,0)-231168*'l,0)+140625*'l,0^3*sign(x,0-'l,0)^2+458178*'l,0^3*sign(x,0-'l,0)+1298353*'l,0^3)^{1/2}/288-((648*'l,0^2*sign(x,0-'l,0)^2+3456*'l,0^2*sign(x,0-'l,0)+2808*'l,0^2)*abs(2*x,0-'l,0)/2+sign(x,0-'l,0)^2*(432*'l,0^2*abs(2*x,0-3*'l,0)-1125*'l,0^3)+sign(x,0-'l,0)*(-576*'l,0^2*abs(2*x,0-3*'l,0)-2970*'l,0^3)-1008*'l,0^2*abs(2*x,0-3*'l,0)-5845*'l,0^3)/(864*sign(x,0-'l,0)^3+2592*sign(x,0-'l,0)^2+2592*sign(x,0-'l,0)+864))^{-1/3}/(9*sign(x,0-'l,0)^2+18*sign(x,0-'l,0)+9)+(3*'l,0*sign(x,0-'l,0)+8*'l,0)/(3*(sign(x,0-'l,0)+1));x,0≡(i*3^{1/2}/2-1/2)*('l,0^{3/2}*(sign(x,0-'l,0)+1)^{-2}*(((31104*'l,0*sign(x,0-'l,0)^2+117504*'l,0*sign(x,0-'l,0)+201600*'l,0)*abs(2*x,0-3*'l,0)-81000*'l,0^2*sign(x,0-'l,0)^2+(2*x,0-3*'l,0)^2*(55296*sign(x,0-'l,0)+55296)-470016*'l,0^2*sign(x,0-'l,0)-619416*'l,0^2)*abs(2*x,0-'l,0)+(2*x,0-'l,0)^2*(10368*sign(x,0-'l,0)+10368)*abs(2*x,0-'l,0)+(2*x,0-'l,0)^2*((-41472*sign(x,0-'l,0)-41472)*abs(2*x,0-3*'l,0)+11664*'l,0*sign(x,0-'l,0)^2+80352*'l,0*sign(x,0-'l,0)+25488*'l,0)+(-108000*'l,0^2*sign(x,0-'l,0)^2+56448*'l,0^2*sign(x,0-'l,0)-296352*'l,0^2)*abs(2*x,0-3*'l,0)+(2*x,0-3*'l,0)^2*(-24576*sign(x,0-'l,0)-24576)*abs(2*x,0-3*'l,0)+(2*x,0-3*'l,0)^2*(20736*'l,0*sign(x,0-'l,0)^2-133632*'l,0*sign(x,0-'l,0)-231168*'l,0)+140625*'l,0^3*sign(x,0-'l,0)^2+458178*'l,0^3*sign(x,0-'l,0)+1298353*'l,0^3)^{1/2}/288-((648*'l,0^2*sign(x,0-'l,0)^2+3456*'l,0^2*sign(x,0-'l,0)+2808*'l,0^2)*abs(2*x,0-'l,0)/2+sign(x,0-'l,0)^2*(432*'l,0^2*abs(2*x,0-3*'l,0)-1125*'l,0^3)+sign(x,0-'l,0)*(-576*'l,0^2*abs(2*x,0-3*'l,0)-2970*'l,0^3)-1008*'l,0^2*abs(2*x,0-3*'l,0)-5845*'l,0^3)/(864*sign(x,0-'l,0)^3+2592*sign(x,0-'l,0)^2+2592*sign(x,0-'l,0)+864))^{1/3}-(-i*3^{1/2}/2-1/2)*((9*'l,0*sign(x,0-'l,0)+9*'l,0)*abs(2*x,0-'l,0)/2+sign(x,0-'l,0)*(-6*'l,0*abs(2*x,0-3*'l,0)-3*'l,0^2)-6*'l,0*abs(2*x,0-3*'l,0)-28*'l,0^2)*('l,0^{3/2}*(sign(x,0-'l,0)+1)^{-2}*(((31104*'l,0*sign(x,0-'l,0)^2+117504*'l,0*sign(x,0-'l,0)+201600*'l,0)*abs(2*x,0-3*'l,0)-81000*'l,0^2*sign(x,0-'l,0)^2+(2*x,0-3*'l,0)^2*(55296*sign(x,0-'l,0)+55296)-470016*'l,0^2*sign(x,0-'l,0)-619416*'l,0^2)*abs(2*x,0-'l,0)+(2*x,0-'l,0)^2*(10368*sign(x,0-'l,0)+10368)*abs(2*x,0-'l,0)+(2*x,0-'l,0)^2*((-41472*sign(x,0-'l,0)-41472)*abs(2*x,0-3*'l,0)+11664*'l,0*sign(x,0

x.0 φ 0 ≡ x.0 l.0 ≡ FindRoot 0.6771 l.0 *

x.0 w F 0.0593 l.0 3^EI / *

all MaximaLog pid=11440
Maxima 5.30.0 http://maxima.sourceforge.net
using Lisp GNU Common Lisp (GCL) GCL 2.6.8 (a.k.a. GCL)
Distributed under the GNU Public License. See the file COPYING.
Dedicated to the memory of William Schelter.
The function bug_report() provides bug reporting information.
(%i1) load($C:/Users/Kraska/AppData/Roaming/SMath/extensions/plugins/44011c1e-5d0d-4533-8e68-e32b5badce41/1.0.5061.39413/load.mac$)$
(%i2) load($C:/Users/Kraska/AppData/Roaming/SMath/extensions/plugins/44011c1e-5d0d-4533-8e68-e32b5badce41/1.0.5061.39413/smath.lisp$)$
(%i3) load($C:/Users/Kraska/AppData/Roaming/SMath/extensions/plugins/44011c1e-5d0d-4533-8e68-e32b5badce41/1.0.5061.39413/smath.mac$)$
(%i4) to_sm_display()$
(%i5) integrate(-%unitq_0*1/2*(1+signum(x-%unitl_0)),x);
(%s5) -%unitq_0*(abs(x-%unitl_0)+x)/2
(%i6) integrate(-%unitq_0*(abs(x-%unitl_0)+x)/2+F_A-%unitq_0*%unitl_0*1/2*(1+signum(x-%unitl_0/2))+F_B*1/2*(1+signum(x-3/2*%unitl_0))+Q_0,x);
(%s6) x*Q_0+(abs(x-3*%unitl_0/2)+x)*F_B/2+x*F_A-%unitl_0*%unitq_0*(abs(x-%unitl_0/2)+x)/2-%unitq_0*((x-%unitl_0)*abs(x-%unitl_0)/2+x^2/2)/2
(%i7) integrate((x*Q_0+(abs(x-3*%unitl_0/2)+x)*F_B/2+x*F_A-%unitl_0*%unitq_0*(abs(x-%unitl_0/2)+x)/2-%unitq_0*((x-%unitl_0)*abs(x-%unitl_0)/2+(x^2)/2)/2+M_0)/%unitEI,x);
(%s7) (x^2*Q_0/2+x*M_0+((x-3*%unitl_0/2)*abs(x-3*%unitl_0/2)/2+x^2/2)*F_B/2+x^2*F_A/2-%unitl_0*%unitq_0*((x-%unitl_0/2)*abs(x-%unitl_0/2)/2+x^2/2)/2-%unitq_0*((2*x^3/3-2*%unitl_0*x^2+2*%unitl_0^2*x-2*%unitl_0^3/3)*signum(x-%unitl_0)/4+x^3/6)/2)/%unitEI
(%i8) integrate((x^2*Q_0/2+x*M_0+((x-3*%unitl_0/2)*abs(x-3*%unitl_0/2)/2+(x^2)/2)*F_B/2+x^2*F_A/2-%unitl_0*%unitq_0*((x-%unitl_0/2)*abs(x-%unitl_0/2)/2+(x^2)/2)/2-%unitq_0*((2*(x^3)/3-2*%unitl_0*x^2+2*%unitl_0^2*x-2*(%unitl_0^3)/3)*signum(x-%unitl_0)/4+(x^3)/6)/2)/%unitEI+%phi_0,x);
(%s8) (x^3*Q_0/6+x^2*M_0/2+(((4*x^3/3-6*%unitl_0*x^2+9*%unitl_0^2*x)/4-9*%unitl_0^3/8)*signum(x-3*%unitl_0/2)/2+x^3/6)*F_B/2+x^3*F_A/6-%unitl_0*%unitq_0*(((4*x^3/3-2*%unitl_0*x^2+%unitl_0^2*x)/4-%unitl_0^3/24)*signum(x-%unitl_0/2)/2+x^3/6)/2-%unitq_0*((2*(x^4/2-2*%unitl_0*x^3+3*%unitl_0^2*x^2-2*%unitl_0^3*x)/3+%unitl_0^4/3)*signum(x-%unitl_0)/8+x^4/24)/2)/%unitEI+%phi_0*x
(%i9) assume(%unitl_0>0);
(%s9) [%unitl_0 > 0]
(%i10) linsolve([(2*(F_A+Q_0)-%unitq_0*(%unitl_0*(1+signum(-%unitl_0/2))+abs(-%unitl_0))+F_B*(1+signum(-(3*%unitl_0)/2)))/2=F_A,(2*(F_A+Q_0)-%unitq_0*(%unitl_0*(3+signum((3*%unitl_0)/2))+abs(%unitl_0))+F_B*(1+signum(%unitl_0/2)))/2=0,(2*(2*M_0+F_B*abs(-(3*%unitl_0)/2)-%unitl_0*%unitq_0*abs(-%unitl_0/2))+%unitq_0*%unitl_0*abs(-%unitl_0))/4=0,(2*(2*(M_0+2*%unitl_0*(F_A+Q_0))+F_B*(2*%unitl_0+abs(%unitl_0/2))-%unitl_0*%unitq_0*(2*%unitl_0+abs((3*%unitl_0)/2)))-%unitq_0*%unitl_0*(4*%unitl_0+abs(%unitl_0)))/4=0,(96*w_0*%unitEI+%unitl_0^3*(27*F_B*signum(-(3*%unitl_0)/2)+%unitq_0*%unitl_0*(2*signum(-%unitl_0)-signum(-%unitl_0/2))))/(96*%unitEI)=0,(-(384*%unitEI*(-2*w_0+3*%phi_0*%unitl_0)+%unitl_0^2*(8*(27*(2*(%unitl_0*(Q_0+F_A)+2*M_0)+F_B*%unitl_0)-%unitq_0*%unitl_0^2*(27+8*signum(%unitl_0)))-%unitq_0*%unitl_0^2*(81+signum(%unitl_0/2))))/(768*%unitEI))=0],[F_A,F_B,M_0,Q_0,w_0,%phi_0]);
(%s10) [F_A = 2*%unitl_0*%unitq_0/3,F_B = 4*%unitl_0*%unitq_0/3,M_0 = -%unitl_0^2*%unitq_0,Q_0 = %unitl_0*%unitq_0/2,w_0 = 37*%unitl_0^4*%unitq_0/(96*%unitEI),%phi_0 = 365*%unitl_0^3*%unitq_0/(576*%unitEI)]
(%i11) solve([(x_0^2*((%unitl_0*%unitq_0)/2)/2+x_0*(-%unitq_0*%unitl_0^2)+((x_0-3*%unitl_0/2)*abs(x_0-3*%unitl_0/2)/2+(x_0^2)/2)*((4*%unitl_0*%unitq_0)/3)/2+x_0^2*((2*%unitl_0*%unitq_0)/3)/2-%unitl_0*%unitq_0*((x_0-%unitl_0/2)*abs(x_0-%unitl_0/2)/2+(x_0^2)/2)/2-%unitq_0*((2*(x_0^3)/3-2*%unitl_0*x_0^2+2*%unitl_0^2*x_0-2*(%unitl_0^3)/3)*signum(x_0-%unitl_0)/4+(x_0^3)/6)/2)/%unitEI+(365*%unitq_0*%unitl_0^3)/(576*%unitEI)=0],[x_0]);
(%s11) [x_0 = (-%i*3^{1/2}/2-1/2)*(%unitl_0^{3/2}*(signum(x_0-%unitl_0)+1)^{-2}
                                                 *(((31104*%unitl_0*signum(x_0-%unitl_0)^2+117504*%unitl_0*signum(x_0-%unitl_0)+201600*%unitl_0)*abs(2*x_0-3*%unitl_0)-81000*%unitl_0^2*signum(x_0-%unitl_0)^2+(2*x_0-3*%unitl_0)^2*(55296*signum(x_0-%unitl_0)+55296)-470016*%unitl_0^2*signum(x_0-%unitl_0)-619416*%unitl_0^2)*abs(2*x_0-%unitl_0)+(2*x_0-%unitl_0)^2*(10368*signum(x_0-%unitl_0)+10368)*abs(2*x_0-%unitl_0)+(2*x_0-%unitl_0)^2*((-41472*signum(x_0-%unitl_0)-41472)*abs(2*x_0-3*%unitl_0)+11664*%unitl_0*signum(x_0-%unitl_0)^2+80352*%unitl_0*signum(x_0-%unitl_0)+25488*%unitl_0)
                                                                                                                                                                                                                                                                                                                                                    +(-108000*%unitl_0^2*signum(x_0-%unitl_0)^2+56448*%unitl_0^2*signum(x_0-%unitl_0)-296352*%unitl_0^2)*abs(2*x_0-3*%unitl_0)+(2*x_0-3*%unitl_0)^2*(-24576*signum(x_0-%unitl_0)-24576)*abs(2*x_0-3*%unitl_0)+(2*x_0-3*%unitl_0)^2*(20736*%unitl_0*signum(x_0-%unitl_0)^2-133632*%unitl_0*signum(x_0-%unitl_0)-231168*%unitl_0)+140625*%unitl_0^3*signum(x_0-%unitl_0)^2
                                                                                                                                                                                                                                                                                                                                                    +458178*%unitl_0^3*signum(x_0-%unitl_0)+1298353*%unitl_0^3)
                                                  ^{1/2}
                                  /288
                                  -((648*%unitl_0^2*signum(x_0-%unitl_0)^2+3456*%unitl_0^2*signum(x_0-%unitl_0)+2808*%unitl_0^2)*abs(2*x_0-%unitl_0)/2+signum(x_0-%unitl_0)^2*(432*%unitl_0^2*abs(2*x_0-3*%unitl_0)-1125*%unitl_0^3)+signum(x_0-%unitl_0)*(-576*%unitl_0^2*abs(2*x_0-3*%unitl_0)-2970*%unitl_0^3)-1008*%unitl_0^2*abs(2*x_0-3*%unitl_0)-5845*%unitl_0^3)/(864*signum(x_0-%unitl_0)^3+2592*signum(x_0-%unitl_0)^2+2592*signum(x_0-%unitl_0)+864))
                                  ^{1/3}
            -(%i*3^{1/2}/2-1/2)*((9*%unitl_0*signum(x_0-%unitl_0)+9*%unitl_0)*abs(2*x_0-%unitl_0)/2+signum(x_0-%unitl_0)*(-6*%unitl_0*abs(2*x_0-3*%unitl_0)-3*%unitl_0^2)-6*%unitl_0*abs(2*x_0-3*%unitl_0)-28*%unitl_0^2)
                               *(%unitl_0^{3/2}*(signum(x_0-%unitl_0)+1)^{-2}
                                               *(((31104*%unitl_0*signum(x_0-%unitl_0)^2+117504*%unitl_0*signum(x_0-%unitl_0)+201600*%unitl_0)*abs(2*x_0-3*%unitl_0)-81000*%unitl_0^2*signum(x_0-%unitl_0)^2+(2*x_0-3*%unitl_0)^2*(55296*signum(x_0-%unitl_0)+55296)-470016*%unitl_0^2*signum(x_0-%unitl_0)-619416*%unitl_0^2)*abs(2*x_0-%unitl_0)+(2*x_0-%unitl_0)^2*(10368*signum(x_0-%unitl_0)+10368)*abs(2*x_0-%unitl_0)+(2*x_0-%unitl_0)^2*((-41472*signum(x_0-%unitl_0)-41472)*abs(2*x_0-3*%unitl_0)+11664*%unitl_0*signum(x_0-%unitl_0)^2+80352*%unitl_0*signum(x_0-%unitl_0)+25488*%unitl_0)
                                                                                                                                                                                                                                                                                                                                                  +(-108000*%unitl_0^2*signum(x_0-%unitl_0)^2+56448*%unitl_0^2*signum(x_0-%unitl_0)-296352*%unitl_0^2)*abs(2*x_0-3*%unitl_0)+(2*x_0-3*%unitl_0)^2*(-24576*signum(x_0-%unitl_0)-24576)*abs(2*x_0-3*%unitl_0)+(2*x_0-3*%unitl_0)^2*(20736*%unitl_0*signum(x_0-%unitl_0)^2-133632*%unitl_0*signum(x_0-%unitl_0)-231168*%unitl_0)+140625*%unitl_0^3*signum(x_0-%unitl_0)^2
                                                                                                                                                                                                                                                                                                                                                  +458178*%unitl_0^3*signum(x_0-%unitl_0)+1298353*%unitl_0^3)
                                                ^{1/2}
                                /288
                                -((648*%unitl_0^2*signum(x_0-%unitl_0)^2+3456*%unitl_0^2*signum(x_0-%unitl_0)+2808*%unitl_0^2)*abs(2*x_0-%unitl_0)/2+signum(x_0-%unitl_0)^2*(432*%unitl_0^2*abs(2*x_0-3*%unitl_0)-1125*%unitl_0^3)+signum(x_0-%unitl_0)*(-576*%unitl_0^2*abs(2*x_0-3*%unitl_0)-2970*%unitl_0^3)-1008*%unitl_0^2*abs(2*x_0-3*%unitl_0)-5845*%unitl_0^3)/(864*signum(x_0-%unitl_0)^3+2592*signum(x_0-%unitl_0)^2+2592*signum(x_0-%unitl_0)+864))
                                ^{-1/3}
             /(9*signum(x_0-%unitl_0)^2+18*signum(x_0-%unitl_0)+9)+(3*%unitl_0*signum(x_0-%unitl_0)+8*%unitl_0)/(3*(signum(x_0-%unitl_0)+1)),
        x_0 = (%i*3^{1/2}/2-1/2)*(%unitl_0^{3/2}*(signum(x_0-%unitl_0)+1)^{-2}
                                                *(((31104*%unitl_0*signum(x_0-%unitl_0)^2+117504*%unitl_0*signum(x_0-%unitl_0)+201600*%unitl_0)*abs(2*x_0-3*%unitl_0)-81000*%unitl_0^2*signum(x_0-%unitl_0)^2+(2*x_0-3*%unitl_0)^2*(55296*signum(x_0-%unitl_0)+55296)-470016*%unitl_0^2*signum(x_0-%unitl_0)-619416*%unitl_0^2)*abs(2*x_0-%unitl_0)+(2*x_0-%unitl_0)^2*(10368*signum(x_0-%unitl_0)+10368)*abs(2*x_0-%unitl_0)+(2*x_0-%unitl_0)^2*((-41472*signum(x_0-%unitl_0)-41472)*abs(2*x_0-3*%unitl_0)+11664*%unitl_0*signum(x_0-%unitl_0)^2+80352*%unitl_0*signum(x_0-%unitl_0)+25488*%unitl_0)
                                                                                                                                                                                                                                                                                                                                                   +(-108000*%unitl_0^2*signum(x_0-%unitl_0)^2+56448*%unitl_0^2*signum(x_0-%unitl_0)-296352*%unitl_0^2)*abs(2*x_0-3*%unitl_0)+(2*x_0-3*%unitl_0)^2*(-24576*signum(x_0-%unitl_0)-24576)*abs(2*x_0-3*%unitl_0)+(2*x_0-3*%unitl_0)^2*(20736*%unitl_0*signum(x_0-%unitl_0)^2-133632*%unitl_0*signum(x_0-%unitl_0)-231168*%unitl_0)+140625*%unitl_0^3*signum(x_0-%unitl_0)^2
                                                                                                                                                                                                                                                                                                                                                   +458178*%unitl_0^3*signum(x_0-%unitl_0)+1298353*%unitl_0^3)
                                                 ^{1/2}
                                 /288
                                 -((648*%unitl_0^2*signum(x_0-%unitl_0)^2+3456*%unitl_0^2*signum(x_0-%unitl_0)+2808*%unitl_0^2)*abs(2*x_0-%unitl_0)/2+signum(x_0-%unitl_0)^2*(432*%unitl_0^2*abs(2*x_0-3*%unitl_0)-1125*%unitl_0^3)+signum(x_0-%unitl_0)*(-576*%unitl_0^2*abs(2*x_0-3*%unitl_0)-2970*%unitl_0^3)-1008*%unitl_0^2*abs(2*x_0-3*%unitl_0)-5845*%unitl_0^3)/(864*signum(x_0-%unitl_0)^3+2592*signum(x_0-%unitl_0)^2+2592*signum(x_0-%unitl_0)+864))
                                 ^{1/3}
            -(-%i*3^{1/2}/2-1/2)*((9*%unitl_0*signum(x_0-%unitl_0)+9*%unitl_0)*abs(2*x_0-%unitl_0)/2+signum(x_0-%unitl_0)*(-6*%unitl_0*abs(2*x_0-3*%unitl_0)-3*%unitl_0^2)-6*%unitl_0*abs(2*x_0-3*%unitl_0)-28*%unitl_0^2)
                                *(%unitl_0^{3/2}*(signum(x_0-%unitl_0)+1)^{-2}
                                                *(((31104*%unitl_0*signum(x_0-%unitl_0)^2+117504*%unitl_0*signum(x_0-%unitl_0)+201600*%unitl_0)*abs(2*x_0-3*%unitl_0)-81000*%unitl_0^2*signum(x_0-%unitl_0)^2+(2*x_0-3*%unitl_0)^2*(55296*signum(x_0-%unitl_0)+55296)-470016*%unitl_0^2*signum(x_0-%unitl_0)-619416*%unitl_0^2)*abs(2*x_0-%unitl_0)+(2*x_0-%unitl_0)^2*(10368*signum(x_0-%unitl_0)+10368)*abs(2*x_0-%unitl_0)+(2*x_0-%unitl_0)^2*((-41472*signum(x_0-%unitl_0)-41472)*abs(2*x_0-3*%unitl_0)+11664*%unitl_0*signum(x_0-