normmat_new.cpp

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

                  As1*(2*b*d*
                          fc*(\[CurlyEpsilon]c1 + 
                              2*\[CurlyEpsilon]n)*((-1 + 
                                    2*k)*\[CurlyEpsilon]c1 - 
                              2*(-1 + k)*\[CurlyEpsilon]n) + 
                        k*Power(\[CurlyEpsilon]c1, 
                            2)*(-2*N0 + 
                              As1*E0c*(\[CurlyEpsilon]c1 + 
                                    2*\[CurlyEpsilon]n))) + 
                  2*As2*(b*ch*
                          fc*(\[CurlyEpsilon]c1 + 
                              2*\[CurlyEpsilon]n)*((-1 + 
                                    2*k)*\[CurlyEpsilon]c1 - 
                              2*(-1 + k)*\[CurlyEpsilon]n) + 
                        k*Power(\[CurlyEpsilon]c1, 
                            2)*(-N0 + 
                              As1*E0c*(\[CurlyEpsilon]c1 + 
                                    2*\[CurlyEpsilon]n))), 2))*
        Sqrt(k*Power(\[CurlyEpsilon]c1, 
              2)*(3*k*Power(\[CurlyEpsilon]c1, 2)*
                  Power(As2*ch*
                        E0c*\[CurlyEpsilon]c1 + (d*(2*N0 + 
                                E0c*(As1*(\[CurlyEpsilon]c1 - 
                                        2*\[CurlyEpsilon]n) - 
                                      As2*(\[CurlyEpsilon]c1 + 
                                        2*\[CurlyEpsilon]n))))/2., 2) - 
                2*(As2*ch + As1*d)*
                  E0c*(-(b*Power(d, 2)*fc*
                              Power(\[CurlyEpsilon]c1 + 2*\[CurlyEpsilon]n, 
                                2)*((-4 + 7*k)*\[CurlyEpsilon]c1 - 
                                  4*(-1 + k)*\[CurlyEpsilon]n))/4. + 
                      3*k*Power(\[CurlyEpsilon]c1, 
                          3)*((As2*ch*E0c*\[CurlyEpsilon]c1)/2. + 
                            d*(N0 - (E0c*(As2*\[CurlyEpsilon]c1 + 
                                        2*As1*\[CurlyEpsilon]n + 
                                        2*As2*\[CurlyEpsilon]n))/
                                    2.))))))/((As2*ch + As1*d)*k*
        Power(\[CurlyEpsilon]c1, 2)*
        Power(-8*b*(As2*ch + As1*d)*E0c*
              fc*(\[CurlyEpsilon]c1 - \[CurlyEpsilon]n)*
              Power(\[CurlyEpsilon]c1 + 2*\[CurlyEpsilon]n, 2) + 
            k*(12*Power(N0, 2)*Power(\[CurlyEpsilon]c1, 2) - 
                  12*(As1 + As2)*E0c*N0*
                    Power(\[CurlyEpsilon]c1, 
                      2)*(\[CurlyEpsilon]c1 + 2*\[CurlyEpsilon]n) + 
                  E0c*(3*Power(As2, 2)*E0c*Power(\[CurlyEpsilon]c1, 2) + 
                        2*As2*(3*As1*E0c*Power(\[CurlyEpsilon]c1, 2) + 
                              b*ch*fc*(7*\[CurlyEpsilon]c1 - 
                                    4*\[CurlyEpsilon]n)) + 
                        As1*(3*As1*E0c*Power(\[CurlyEpsilon]c1, 2) + 
                              2*b*d*fc*(7*\[CurlyEpsilon]c1 - 
                                    4*\[CurlyEpsilon]n)))*
                    Power(\[CurlyEpsilon]c1 + 2*\[CurlyEpsilon]n, 2)), 2))

\[CurlyEpsilon]c = (-ac2 + Sqrt(Power(ac2, 2) - 4*ac1*ac3))/(2.*ac3)

\[CurlyEpsilon]chr3 = \[CurlyEpsilon]c

mhr3 = (6*As1*
          E0c*(-2*cd + 
              h)*(\[CurlyEpsilon]n + (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))) - 
        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 - (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)), 2)))/12.

Null

ac1 = (-(ch*E0c*\[CurlyEpsilon]c1)/2. + 
          d*(fy + (E0c*\[CurlyEpsilon]c1)/2. + E0c*\[CurlyEpsilon]n))/(ch*
          E0c) + (Sqrt(3)*b*fc*h*(-1 + k)*
            Power(\[CurlyEpsilon]c1, 
              4)*(Power(b, 2)*Power(fc, 2)*Power(h, 4)*Power(2 - 3*k, 2) + 
                4*Power(E0c, 
                    2)*(Power(As2, 
                          2)*(3*Power(ch, 2) - 3*ch*h + Power(h, 2)) + 
                      Power(As1, 2)*(3*Power(d, 2) - 3*d*h + Power(h, 2)) + 
                      As1*As2*(6*ch*d - 3*ch*h - 3*d*h + 2*Power(h, 2)))*
                  Power(k, 2)*Power(\[CurlyEpsilon]c1, 2) - 
                2*b*fc*Power(h, 3)*
                  k*(4*(-1 + k)*N0 - (As1 + As2)*
                        E0c*(-2 + 3*k)*\[CurlyEpsilon]c1))*
            Sqrt(Power(d, 
                  2)*(12*Power(As2*ch + As1*d, 2)*Power(E0c, 2)*Power(k, 2)*
                      Power(\[CurlyEpsilon]c1, 4) + 
                    Power(b, 2)*Power(fc, 2)*
                      Power(h, 
                        4)*((-4 + 7*k)*\[CurlyEpsilon]c1 - 
                          4*(-1 + k)*\[CurlyEpsilon]n)*((-4 + 
                                5*k)*\[CurlyEpsilon]c1 + 
                          4*(-1 + k)*\[CurlyEpsilon]n) + 
                    4*b*fc*Power(h, 2)*k*
                      Power(\[CurlyEpsilon]c1, 
                        2)*(3*(As2*ch + As1*d)*
                            E0c*(k*(\[CurlyEpsilon]c1 - 4*\[CurlyEpsilon]n) + 
                                4*\[CurlyEpsilon]n) + 
                          8*h*(-1 + 
                                k)*(-N0 + (As1 + As2)*
                                  E0c*(\[CurlyEpsilon]c1/
                                        2. + \[CurlyEpsilon]n))))))/
        Power(12*Power(As2*ch + As1*d, 2)*Power(E0c, 2)*Power(k, 2)*
            Power(\[CurlyEpsilon]c1, 4) + 
          Power(b, 2)*Power(fc, 2)*
            Power(h, 
              4)*((16 - 48*k + 35*Power(k, 2))*Power(\[CurlyEpsilon]c1, 2) + 
                8*(-1 + k)*k*\[CurlyEpsilon]c1*\[CurlyEpsilon]n -