normmat_new.cpp

Finite element program for mechanical problem. It can solve various problem in solid problem

m = List(-(fp*Power(lp, 2))/128. - (lp*z1)/8. - 
        z2, (-9*fp*Power(lp, 2))/128. - (3*lp*z1)/8. - 
        z2, (-25*fp*Power(lp, 2))/128. - (5*lp*z1)/8. - 
        z2, (-49*fp*Power(lp, 2))/128. - (7*lp*z1)/8. - z2)

mp = List(Abs(-(fp*Power(lp, 2))/128. - (lp*z1)/8. - z2), 
      Abs((-9*fp*Power(lp, 2))/128. - (3*lp*z1)/8. - z2), 
      Abs((-25*fp*Power(lp, 2))/128. - (5*lp*z1)/8. - z2), 
      Abs((-49*fp*Power(lp, 2))/128. - (7*lp*z1)/8. - z2))

\[CurlyEpsilon]n = (-2*A*fc*\[CurlyEpsilon]c1 + 3*A*fc*k*\[CurlyEpsilon]c1 + 
        As1*E0c*k*Power(\[CurlyEpsilon]c1, 2) + 
        As2*E0c*k*Power(\[CurlyEpsilon]c1, 2) - 
        Sqrt(Power(\[CurlyEpsilon]c1, 
                2)*(-8*A*fc*(-1 + k)*k*N0 + 
                  Power(A*fc*(-2 + 3*k) + (As1 + As2)*E0c*k*\[CurlyEpsilon]c1,
                       2))))/(4.*A*fc*(-1 + k))

If(Power(6*b*fc*Power(h, 2)*\[CurlyEpsilon]c1 - 
              9*b*fc*Power(h, 2)*k*\[CurlyEpsilon]c1 + 
              6*As2*ch*E0c*k*Power(\[CurlyEpsilon]c1, 2) + 
              6*As1*d*E0c*k*Power(\[CurlyEpsilon]c1, 2) - 
              6*As1*E0c*h*k*Power(\[CurlyEpsilon]c1, 2) - 
              6*As2*E0c*h*k*Power(\[CurlyEpsilon]c1, 2) - 
              8*b*fc*Power(h, 2)*\[CurlyEpsilon]n + 
              8*b*fc*Power(h, 2)*k*\[CurlyEpsilon]n, 2) - 
        4*b*fc*Power(h, 
            2)*(-4 + 4*k)*(6*h*k*N0*Power(\[CurlyEpsilon]c1, 2) + 
              6*b*fc*Power(h, 2)*\[CurlyEpsilon]c1*\[CurlyEpsilon]n - 
              9*b*fc*Power(h, 2)*k*\[CurlyEpsilon]c1*\[CurlyEpsilon]n + 
              6*As2*ch*E0c*k*Power(\[CurlyEpsilon]c1, 2)*\[CurlyEpsilon]n + 
              6*As1*d*E0c*k*Power(\[CurlyEpsilon]c1, 2)*\[CurlyEpsilon]n - 
              6*As1*E0c*h*k*Power(\[CurlyEpsilon]c1, 2)*\[CurlyEpsilon]n - 
              6*As2*E0c*h*k*Power(\[CurlyEpsilon]c1, 2)*\[CurlyEpsilon]n - 
              4*b*fc*Power(h, 2)*Power(\[CurlyEpsilon]n, 2) + 
              4*b*fc*Power(h, 2)*k*Power(\[CurlyEpsilon]n, 2)) >= 
      0, \[CurlyEpsilon]c = 
      1/(2.*b*fc*Power(h, 2)*(-4 + 4*k))*(-6*b*fc*
              Power(h, 2)*\[CurlyEpsilon]c1 + 
            9*b*fc*Power(h, 2)*k*\[CurlyEpsilon]c1 - 
            6*As2*ch*E0c*k*Power(\[CurlyEpsilon]c1, 2) - 
            6*As1*d*E0c*k*Power(\[CurlyEpsilon]c1, 2) + 
            6*As1*E0c*h*k*Power(\[CurlyEpsilon]c1, 2) + 
            6*As2*E0c*h*k*Power(\[CurlyEpsilon]c1, 2) + 
            8*b*fc*Power(h, 2)*\[CurlyEpsilon]n - 
            8*b*fc*Power(h, 2)*k*\[CurlyEpsilon]n - 
            Sqrt(Power(6*b*fc*Power(h, 2)*\[CurlyEpsilon]c1 - 
                        9*b*fc*Power(h, 2)*k*\[CurlyEpsilon]c1 + 
                        6*As2*ch*E0c*k*Power(\[CurlyEpsilon]c1, 2) + 
                        6*As1*d*E0c*k*Power(\[CurlyEpsilon]c1, 2) - 
                        6*As1*E0c*h*k*Power(\[CurlyEpsilon]c1, 2) - 
                        6*As2*E0c*h*k*Power(\[CurlyEpsilon]c1, 2) - 
                        8*b*fc*Power(h, 2)*\[CurlyEpsilon]n + 
                        8*b*fc*Power(h, 2)*k*\[CurlyEpsilon]n, 2) - 
                  4*b*fc*Power(h, 
                      2)*(-4 + 4*k)*(6*h*k*N0*Power(\[CurlyEpsilon]c1, 2) + 
                        6*b*fc*
                          Power(h, 2)*\[CurlyEpsilon]c1*\[CurlyEpsilon]n - 
                        9*b*fc*Power(h, 2)*
                          k*\[CurlyEpsilon]c1*\[CurlyEpsilon]n + 
                        6*As2*ch*E0c*k*
                          Power(\[CurlyEpsilon]c1, 2)*\[CurlyEpsilon]n + 
                        6*As1*d*E0c*k*
                          Power(\[CurlyEpsilon]c1, 2)*\[CurlyEpsilon]n - 
                        6*As1*E0c*h*k*
                          Power(\[CurlyEpsilon]c1, 2)*\[CurlyEpsilon]n - 
                        6*As2*E0c*h*k*
                          Power(\[CurlyEpsilon]c1, 2)*\[CurlyEpsilon]n - 
                        4*b*fc*Power(h, 2)*Power(\[CurlyEpsilon]n, 2) + 
                        4*b*fc*Power(h, 2)*k*
                          Power(\[CurlyEpsilon]n, 
                            2)))), \[CurlyEpsilon]c = -1)

If(-(fy/E0c) - \[CurlyEpsilon]n > ((-ch + h)*\[CurlyEpsilon]c)/
        h, \[CurlyEpsilon]c = -1, 1)

\[CurlyEpsilon]chr1 = \[CurlyEpsilon]c

If(\[CurlyEpsilon]c < 0 && \[CurlyEpsilon]c != -1, 
    mhr1 = 0.08333333333333333*(6*As1*
              E0c*(-2*cd + h)*(\[CurlyEpsilon]n + 
                  1/(6.*(As2*ch + As1*d)*E0c*k*
                          Power(\[CurlyEpsilon]c1, 2))*(6*As2*ch*E0c*
                          k*\[CurlyEpsilon]c*Power(\[CurlyEpsilon]c1, 2) + 
                        3*d*k*Power(\[CurlyEpsilon]c1, 
                            2)*(N0 + 
                              As1*E0c*(\[CurlyEpsilon]c - \[CurlyEpsilon]n) - 
                              As2*E0c*(\[CurlyEpsilon]c + \[CurlyEpsilon]n)) +
                         Sqrt(3)*
                          Sqrt(k*
                              Power(\[CurlyEpsilon]c1, 
                                2)*(3*k*Power(\[CurlyEpsilon]c1, 2)*
                                    Power(-2*As2*ch*E0c*\[CurlyEpsilon]c + 
                                        d*(-N0 + 
                                        E0c*(As1*(-\[CurlyEpsilon]c + \
\[CurlyEpsilon]n) + As2*(\[CurlyEpsilon]c + \[CurlyEpsilon]n))), 2) - 
                                  2*(As2*ch + As1*d)*
                                    E0c*(b*Power(d, 2)*fc*
                                        Power(\[CurlyEpsilon]c + \
\[CurlyEpsilon]n, 2)*(4*(-1 + k)*\[CurlyEpsilon]c + (6 - 
                                        9*k)*\[CurlyEpsilon]c1 + 
                                        4*(-1 + k)*\[CurlyEpsilon]n) + 
                                        6*k*\[CurlyEpsilon]c*
                                        Power(\[CurlyEpsilon]c1, 
                                        2)*(As2*ch*E0c*\[CurlyEpsilon]c + 
                                        d*(N0 - E0c*(As1*\[CurlyEpsilon]n + 
                                        As2*(\[CurlyEpsilon]c + \
\[CurlyEpsilon]n))))))))) - 
            6*As2*E0c*(-2*ch + 
                  h)*(\[CurlyEpsilon]c - (ch*\[CurlyEpsilon]c)/
                    d + \[CurlyEpsilon]n + (ch*(6*As2*ch*E0c*
                              k*\[CurlyEpsilon]c*
                              Power(\[CurlyEpsilon]c1, 2) + 
                            3*d*k*Power(\[CurlyEpsilon]c1, 
                                2)*(N0 + 
                                  As1*E0c*(\[CurlyEpsilon]c - \
\[CurlyEpsilon]n) - As2*E0c*(\[CurlyEpsilon]c + \[CurlyEpsilon]n)) + 
                            Sqrt(3)*
                              Sqrt(k*
                                  Power(\[CurlyEpsilon]c1, 
                                    2)*(3*k*Power(\[CurlyEpsilon]c1, 2)*
                                        Power(-2*As2*ch*E0c*\[CurlyEpsilon]c +
                                         d*(-N0 + 
                                        E0c*(As1*(-\[CurlyEpsilon]c + \
\[CurlyEpsilon]n) + As2*(\[CurlyEpsilon]c + \[CurlyEpsilon]n))), 2) - 
                                      2*(As2*ch + As1*d)*
                                        E0c*(b*Power(d, 2)*fc*
                                        Power(\[CurlyEpsilon]c + \
\[CurlyEpsilon]n, 2)*(4*(-1 + k)*\[CurlyEpsilon]c + (6 - 
                                        9*k)*\[CurlyEpsilon]c1 + 
                                        4*(-1 + k)*\[CurlyEpsilon]n) + 
                                        6*k*\[CurlyEpsilon]c*
                                        Power(\[CurlyEpsilon]c1, 
                                        2)*(As2*ch*E0c*\[CurlyEpsilon]c + 
                                        d*(N0 - E0c*(As1*\[CurlyEpsilon]n + 
                                        As2*(\[CurlyEpsilon]c + \
\[CurlyEpsilon]n)))))))))/(6.*d*(As2*ch + As1*d)*E0c*k*
                        Power(\[CurlyEpsilon]c1, 2))) - (b*d*fc*
                  Power(\[CurlyEpsilon]c + \[CurlyEpsilon]n, 
                    2)*(2*d*(\[CurlyEpsilon]c + \[CurlyEpsilon]n)*((-1 + 
                                  k)*\[CurlyEpsilon]c + (2 - 
                                  3*k)*\[CurlyEpsilon]c1 + (-1 + 
                                  k)*\[CurlyEpsilon]n) - 
                      h*(4*(-1 + k)*\[CurlyEpsilon]c + (6 - 
                                  9*k)*\[CurlyEpsilon]c1 + 
                            4*(-1 + 
                                  k)*\[CurlyEpsilon]n)*(\[CurlyEpsilon]c - (6*
                                    As2*ch*E0c*k*\[CurlyEpsilon]c*
                                    Power(\[CurlyEpsilon]c1, 2) + 
                                  3*d*k*
                                    Power(\[CurlyEpsilon]c1, 
                                      2)*(N0 + 
                                        As1*E0c*(\[CurlyEpsilon]c - \
\[CurlyEpsilon]n) - As2*E0c*(\[CurlyEpsilon]c + \[CurlyEpsilon]n)) + 
                                  Sqrt(3)*
                                    Sqrt(k*
                                        Power(\[CurlyEpsilon]c1, 
                                        2)*(3*k*Power(\[CurlyEpsilon]c1, 2)*
                                        Power(-2*As2*ch*E0c*\[CurlyEpsilon]c +
                                         d*(-N0 + 
                                        E0c*(As1*(-\[CurlyEpsilon]c + \
\[CurlyEpsilon]n) + As2*(\[CurlyEpsilon]c + \[CurlyEpsilon]n))), 2) - 
                                        2*(As2*ch + As1*d)*
                                        E0c*(b*Power(d, 2)*fc*
                                        Power(\[CurlyEpsilon]c + \
\[CurlyEpsilon]n, 2)*(4*(-1 + k)*\[CurlyEpsilon]c + (6 - 
                                        9*k)*\[CurlyEpsilon]c1 + 
                                        4*(-1 + k)*\[CurlyEpsilon]n) + 
                                        6*k*\[CurlyEpsilon]c*
                                        Power(\[CurlyEpsilon]c1, 
                                        2)*(As2*ch*E0c*\[CurlyEpsilon]c + 
                                        d*(N0 - E0c*(As1*\[CurlyEpsilon]n + 
                                        As2*(\[CurlyEpsilon]c + \
\[CurlyEpsilon]n))))))))/(6.*(As2*ch + As1*d)*E0c*k*
                                  Power(\[CurlyEpsilon]c1, 2)))))/(k*
                  Power(\[CurlyEpsilon]c1, 2)*
                  Power(\[CurlyEpsilon]c - 
                      1/(6.*(As2*ch + As1*d)*E0c*k*
                              Power(\[CurlyEpsilon]c1, 2))*(6*As2*ch*E0c*
                              k*\[CurlyEpsilon]c*
                              Power(\[CurlyEpsilon]c1, 2) + 
                            3*d*k*Power(\[CurlyEpsilon]c1, 
                                2)*(N0 + 
                                  As1*E0c*(\[CurlyEpsilon]c - \
\[CurlyEpsilon]n) - As2*E0c*(\[CurlyEpsilon]c + \[CurlyEpsilon]n)) + 
                            Sqrt(3)*
                              Sqrt(k*
                                  Power(\[CurlyEpsilon]c1, 
                                    2)*(3*k*Power(\[CurlyEpsilon]c1, 2)*
                                        Power(-2*As2*ch*E0c*\[CurlyEpsilon]c +
                                         d*(-N0 + 
                                        E0c*(As1*(-\[CurlyEpsilon]c + \
\[CurlyEpsilon]n) + As2*(\[CurlyEpsilon]c + \[CurlyEpsilon]n))), 2) - 
                                      2*(As2*ch + As1*d)*
                                        E0c*(b*Power(d, 2)*fc*
                                        Power(\[CurlyEpsilon]c + \
\[CurlyEpsilon]n, 2)*(4*(-1 + k)*\[CurlyEpsilon]c + (6 - 
                                        9*k)*\[CurlyEpsilon]c1 + 
                                        4*(-1 + k)*\[CurlyEpsilon]n) + 
                                        6*k*\[CurlyEpsilon]c*
                                        Power(\[CurlyEpsilon]c1, 
                                        2)*(As2*ch*E0c*\[CurlyEpsilon]c + 
                                        d*(N0 - E0c*(As1*\[CurlyEpsilon]n + 
                                        As2*(\[CurlyEpsilon]c + \
\[CurlyEpsilon]n)))))))), 2))), mhr1 = 1000000000)

Null

If(mhr1 == 1000000000 || 
      E0c*(3*E0c*
                Power(k*
                      Power(\[CurlyEpsilon]c1, 
                        2)*(-2*As2*ch*fy - As1*d*fy + As2*d*fy + d*N0 + 
                          2*As2*(ch - d)*E0c*\[CurlyEpsilon]n) + 
                    b*Power(d, 2)*
                      fc*(-2*(-1 + k)*
                            Power(\[CurlyEpsilon]c1, 
                              2) + (2 - 
                                3*k)*\[CurlyEpsilon]c1*\[CurlyEpsilon]n + 
                          2*(-1 + k)*Power(\[CurlyEpsilon]n, 2)), 
                  2) - (2*As2*(-ch + d)*E0c*k*Power(\[CurlyEpsilon]c1, 2) - 
                    b*Power(d, 2)*
                      fc*((-2 + k)*\[CurlyEpsilon]c1 + 
                          4*(-1 + k)*\[CurlyEpsilon]n))*(-6*As2*k*