normmat.cpp

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

                              sqrt(k*


                                  pow(epsc1, 


                                    2)*(3*k*pow(epsc1, 2)*


                                        pow(-2*as2*ch*e0c*epschr2 + 


                                        d*(-n0 + e0c*(as1*(-epschr2 + epsn) + 


                                        as2*(epschr2 + epsn))), 2) - 


                                      2*(as2*ch + as1*d)*


                                        e0c*(b*pow(d, 2)*fc*


                                        pow(epschr2 + epsn, 


                                        2)*(4*(-1 + k)*epschr2 + (6 - 9*k)*


                                        epsc1 + 4*(-1 + k)*epsn) + 


                                        6*k*epschr2*


                                        pow(epsc1, 


                                        2)*(as2*ch*e0c*epschr2 + 


                                        d*(n0 - e0c*(as1*epsn + 


                                        as2*(epschr2 + epsn))))))))/(6.*(as2*


                                  ch + as1*d)*e0c*k*pow(epsc1, 2)))))/(k*


            pow(epsc1, 2)*


            pow(epschr2 - 


                1/(6.*(as2*ch + as1*d)*e0c*k*pow(epsc1, 2))*(6*as2*ch*e0c*k*


                        epschr2*pow(epsc1, 2) + 


                      3*d*k*pow(epsc1, 


                          2)*(n0 + as1*e0c*(epschr2 - epsn) - 


                            as2*e0c*(epschr2 + epsn)) + 


                      sqrt(3.)*


                        sqrt(k*


                            pow(epsc1, 


                              2)*(3*k*pow(epsc1, 2)*


                                  pow(-2*as2*ch*e0c*epschr2 + 


                                      d*(-n0 + 


                                        e0c*(as1*(-epschr2 + epsn) + 


                                        as2*(epschr2 + epsn))), 2) - 


                                2*(as2*ch + as1*d)*


                                  e0c*(b*pow(d, 2)*fc*


                                        pow(epschr2 + epsn, 


                                        2)*(4*(-1 + k)*epschr2 + (6 - 9*k)*


                                        epsc1 + 4*(-1 + k)*epsn) + 


                                      6*k*epschr2*


                                        pow(epsc1, 


                                        2)*(as2*ch*e0c*epschr2 + 


                                        d*(n0 - e0c*(as1*epsn + 


                                        as2*(epschr2 + epsn)))))))), 2))) + e0c*(-(as1*(-cd + h/2.)) + as2*(-ch + h/2.))*epsn;





  }





  else{





    mhr2=1000000000.0;





  }


  return mhr2;


 }





 


 //TLACENA VYZTUZ + NORMALOVA SILA + TECENI V As2 + x < h





//pretvoreni betonu, kdy dochazi k teceni vyztuze As2, ale netece As1 a ani nedochazi k drceni betonu, x < h


double normmat::compute_epschr3 ()


{


  double ac1,ac2,ac3,epschr3;





  ac1 =((12*sqrt(3.)*e0c*((-8*b*(as2*ch + as1*d)*e0c*fc*(epsc1 - epsn)*


                        pow(epsc1 + 2*epsn, 2) + 


                      k*(12*pow(n0, 2)*pow(epsc1, 2) - 


                            12*(as1 + as2)*e0c*n0*


                              pow(epsc1, 2)*(epsc1 + 2*epsn) + 


                            e0c*(3*pow(as2, 2)*e0c*pow(epsc1, 2) + 


                                  2*as2*(3*as1*e0c*pow(epsc1, 2) + 


                                        b*ch*fc*(7*epsc1 - 4*epsn)) + 


                                  as1*(3*as1*e0c*pow(epsc1, 2) + 


                                        2*b*d*fc*(7*epsc1 - 4*epsn)))*


                              pow(epsc1 + 2*epsn, 2)))*(pow(as2, 2)*e0c*k*


                        pow(epsc1, 2) + 


                      2*as2*(as1*e0c*k*pow(epsc1, 2) + 


                            b*ch*fc*(k*epsc1 + 4*epsn - 4*k*epsn)) + 


                      as1*(as1*e0c*k*pow(epsc1, 2) + 


                            2*b*d*fc*(k*epsc1 + 4*epsn - 4*k*epsn))) - 


                3*e0c*pow(pow(as2, 2)*e0c*k*pow(epsc1, 2)*(epsc1 + 2*epsn) + 


                      as1*(2*b*d*


                              fc*(epsc1 + 2*epsn)*((-1 + 2*k)*epsc1 - 


                                  2*(-1 + k)*epsn) + 


                            k*pow(epsc1, 


                                2)*(-2*n0 + as1*e0c*(epsc1 + 2*epsn))) + 


                      2*as2*(b*ch*


                              fc*(epsc1 + 2*epsn)*((-1 + 2*k)*epsc1 - 


                                  2*(-1 + k)*epsn) + 


                            k*pow(epsc1, 2)*(-n0 + as1*e0c*(epsc1 + 2*epsn))),


                     2))*sqrt(k*


                pow(epsc1, 


                  2)*(3*k*pow(epsc1, 2)*


                      pow(as2*ch*e0c*


                            epsc1 + (d*(2*n0 + 


                                    e0c*(as1*(epsc1 - 2*epsn) - 


                                        as2*(epsc1 + 2*epsn))))/2., 2) - 


                    2*(as2*ch + as1*d)*


                      e0c*(-(b*pow(d, 2)*fc*


                                  pow(epsc1 + 2*epsn, 


                                    2)*((-4 + 7*k)*epsc1 - 4*(-1 + k)*epsn))/


                            4. + 3*k*


                            pow(epsc1, 


                              3)*((as2*ch*e0c*epsc1)/2. + 


                                d*(n0 - (e0c*(as2*epsc1 + 2*as1*epsn + 


                                        2*as2*epsn))/2.))))))/((as2*ch + 


                as1*d)*k*


            pow(-8*b*(as2*ch + as1*d)*e0c*fc*(epsc1 - epsn)*


                  pow(epsc1 + 2*epsn, 2) + 


                k*(12*pow(n0, 2)*pow(epsc1, 2) - 


                      12*(as1 + as2)*e0c*n0*pow(epsc1, 2)*(epsc1 + 2*epsn) + 


                      e0c*(3*pow(as2, 2)*e0c*pow(epsc1, 2) + 


                            2*as2*(3*as1*e0c*pow(epsc1, 2) + 


                                  b*ch*fc*(7*epsc1 - 4*epsn)) + 


                            as1*(3*as1*e0c*pow(epsc1, 2) + 


                                  2*b*d*fc*(7*epsc1 - 4*epsn)))*


                        pow(epsc1 + 2*epsn, 2)), 2)) - 


      4*epsc1*((6*(-ch + d)*e0c)/


              ch + (3*e0c*(2*as2*ch*k*pow(epsc1, 2) + (as1 - as2)*d*k*


                        pow(epsc1, 


                          2) + (2*


                            sqrt(3.)*(pow(as2, 2)*e0c*k*


                                  pow(epsc1, 2)*(epsc1 + 2*epsn) + 


                                as1*(2*b*d*


                                        fc*(epsc1 + 


                                        2*epsn)*((-1 + 2*k)*epsc1 - 


                                        2*(-1 + k)*epsn) + 


                                      k*pow(epsc1, 


                                        2)*(-2*n0 + 


                                        as1*e0c*(epsc1 + 2*epsn))) + 


                                2*as2*(b*ch*


                                        fc*(epsc1 + 


                                        2*epsn)*((-1 + 2*k)*epsc1 - 


                                        2*(-1 + k)*epsn) + 


                                      k*pow(epsc1, 


                                        2)*(-n0 + as1*e0c*(epsc1 + 2*epsn))))*


                            sqrt(k*


                                pow(epsc1, 


                                  2)*(3*k*pow(epsc1, 2)*


                                      pow(as2*ch*e0c*


                                        epsc1 + (d*(2*n0 + 


                                        e0c*(as1*(epsc1 - 2*epsn) - 


                                        as2*(epsc1 + 2*epsn))))/2., 2) - 


                                    2*(as2*ch + as1*d)*


                                      e0c*(-(b*pow(d, 2)*fc*


                                        pow(epsc1 + 2*epsn, 


                                        2)*((-4 + 7*k)*epsc1 - 


                                        4*(-1 + k)*epsn))/4. + 


                                        3*k*pow(epsc1, 


                                        3)*((as2*ch*e0c*epsc1)/2. + 


                                        d*(n0 - (e0c*(as2*epsc1 + 


                                        2*as1*epsn + 2*as2*epsn))/


                                        2.))))))/(-8*b*(as2*ch + as1*d)*e0c*


                              fc*(epsc1 - epsn)*pow(epsc1 + 2*epsn, 2) + 


                            k*(12*pow(n0, 2)*pow(epsc1, 2) - 


                                  12*(as1 + as2)*e0c*n0*


                                    pow(epsc1, 2)*(epsc1 + 2*epsn) + 


                                  e0c*(3*pow(as2, 2)*e0c*pow(epsc1, 2) + 


                                        2*as2*(3*as1*e0c*pow(epsc1, 2) + 


                                        b*ch*fc*(7*epsc1 - 4*epsn)) + 


                                        as1*(3*as1*e0c*pow(epsc1, 2) + 


                                        2*b*d*fc*(7*epsc1 - 4*epsn)))*


                                    pow(epsc1 + 2*epsn, 2)))))/((as2*ch + 


                      as1*d)*k*pow(epsc1, 2))) + (4*(3*as2*ch*d*k*


                  pow(epsc1, 2)*(4*fy + e0c*(epsc1 + 2*epsn)) + 


                3*as1*d*k*


                  pow(epsc1, 


                    2)*(-(ch*e0c*(epsc1 + 2*epsn)) + 


                      2*d*(2*fy + e0c*epsc1 + 2*e0c*epsn)) + 


                2*ch*(3*d*k*n0*pow(epsc1, 2) + 


                      sqrt(3.)*


                        sqrt(k*


                            pow(epsc1, 


                              2)*(3*k*pow(epsc1, 2)*


                                  pow(as2*ch*e0c*


                                        epsc1 + (d*(2*n0 + 


                                        e0c*(as1*(epsc1 - 2*epsn) - 


                                        as2*(epsc1 + 2*epsn))))/2., 2) - 


                                2*(as2*ch + as1*d)*


                                  e0c*(-(b*pow(d, 2)*fc*


                                        pow(epsc1 + 2*epsn, 


                                        2)*(-4*epsc1 + 7*k*epsc1 + 4*epsn - 


                                        4*k*epsn))/4. + 


                                      3*k*pow(epsc1, 


                                        3)*((as2*ch*e0c*epsc1)/2. + 


                                        d*(n0 - (e0c*(as2*epsc1 + 


                                        2*as1*epsn + 2*as2*epsn))/


                                        2.))))))))/(ch*(as2*ch + as1*d)*k*


            pow(epsc1, 2)))/(48.*e0c);





	ac2 =(-2 + (2*d)/


        ch - (2*sqrt(3.)*((-8*b*(as2*ch + as1*d)*e0c*fc*(epsc1 - epsn)*


                        pow(epsc1 + 2*epsn, 2) + 


                      k*(12*pow(n0, 2)*pow(epsc1, 2) - 


                            12*(as1 + as2)*e0c*n0*


                              pow(epsc1, 2)*(epsc1 + 2*epsn) + 


                            e0c*(3*pow(as2, 2)*e0c*pow(epsc1, 2) + 


                                  2*as2*(3*as1*e0c*pow(epsc1, 2) + 


                                        b*ch*fc*(7*epsc1 - 4*epsn)) + 


                                  as1*(3*as1*e0c*pow(epsc1, 2) + 


                                        2*b*d*fc*(7*epsc1 - 4*epsn)))*


                              pow(epsc1 + 2*epsn, 2)))*(pow(as2, 2)*e0c*k*


                        pow(epsc1, 2) + 


                      2*as2*(as1*e0c*k*pow(epsc1, 2) + 


                            b*ch*fc*(k*epsc1 + 4*epsn - 4*k*epsn)) + 


                      as1*(as1*e0c*k*pow(epsc1, 2) + 


                            2*b*d*fc*(k*epsc1 + 4*epsn - 4*k*epsn))) - 


                3*e0c*pow(pow(as2, 2)*e0c*k*pow(epsc1, 2)*(epsc1 + 2*epsn) + 


                      as1*(2*b*d*


                              fc*(epsc1 + 2*epsn)*((-1 + 2*k)*epsc1 - 


                                  2*(-1 + k)*epsn) + 


                            k*pow(epsc1, 


                                2)*(-2*n0 + as1*e0c*(epsc1 + 2*epsn))) + 


                      2*as2*(b*ch*


                              fc*(epsc1 + 2*epsn)*((-1 + 2*k)*epsc1 - 


                                  2*(-1 + k)*epsn) + 


                            k*pow(epsc1, 2)*(-n0 + as1*e0c*(epsc1 + 2*epsn))),


                     2))*sqrt(k*


                pow(epsc1, 


                  2)*(3*k*pow(epsc1, 2)*


                      pow(as2*ch*e0c*


                            epsc1 + (d*(2*n0 + 


                                    e0c*(as1*(epsc1 - 2*epsn) - 


                                        as2*(epsc1 + 2*epsn))))/2., 2) - 


                    2*(as2*ch + as1*d)*


                      e0c*(-(b*pow(d, 2)*fc*


                                  pow(epsc1 + 2*epsn, 


                                    2)*((-4 + 7*k)*epsc1 - 4*(-1 + k)*epsn))/


                            4. + 3*k*


                            pow(epsc1, 


                              3)*((as2*ch*e0c*epsc1)/2. + 


                                d*(n0 - (e0c*(as2*epsc1 + 2*as1*epsn + 


                                        2*as2*epsn))/2.))))))/((as2*ch + 


                as1*d)*k*epsc1*


            pow(-8*b*(as2*ch + as1*d)*e0c*fc*(epsc1 - epsn)*


                  pow(epsc1 + 2*epsn, 2) + 


                k*(12*pow(n0, 2)*pow(epsc1, 2) - 


                      12*(as1 + as2)*e0c*n0*pow(epsc1, 2)*(epsc1 + 2*epsn) + 


                      e0c*(3*pow(as2, 2)*e0c*pow(epsc1, 2) + 


                            2*as2*(3*as1*e0c*pow(epsc1, 2) + 


                                  b*ch*fc*(7*epsc1 - 4*epsn)) + 


                            as1*(3*as1*e0c*pow(epsc1, 2) + 


                                  2*b*d*fc*(7*epsc1 - 4*epsn)))*


                        pow(epsc1 + 2*epsn, 2)), 2)) + (2*as2*ch*k*


              pow(epsc1, 2) + (as1 - as2)*d*k*


              pow(epsc1, 


                2) + (2*


                  sqrt(3.)*(pow(as2, 2)*e0c*k*pow(epsc1, 2)*(epsc1 + 2*epsn) + 


                      as1*(2*b*d*


                              fc*(epsc1 + 2*epsn)*((-1 + 2*k)*epsc1 - 


                                  2*(-1 + k)*epsn) + 


                            k*pow(epsc1, 


                                2)*(-2*n0 + as1*e0c*(epsc1 + 2*epsn))) + 


                      2*as2*(b*ch*


                              fc*(epsc1 + 2*epsn)*((-1 + 2*k)*epsc1 - 


                                  2*(-1 + k)*epsn) + 


                            k*pow(epsc1, 


                                2)*(-n0 + as1*e0c*(epsc1 + 2*epsn))))*


                  sqrt(k*pow(epsc1, 


                        2)*(3*k*pow(epsc1, 2)*


                            pow(as2*ch*e0c*


                                  epsc1 + (d*(2*n0 + 


                                        e0c*(as1*(epsc1 - 2*epsn) - 


                                        as2*(epsc1 + 2*epsn))))/2., 2) - 


                          2*(as2*ch + as1*d)*


                            e0c*(-(b*pow(d, 2)*fc*


                                        pow(epsc1 + 2*epsn, 


                                        2)*((-4 + 7*k)*epsc1 - 


                                        4*(-1 + k)*epsn))/4. + 


                                3*k*pow(epsc1, 


                                    3)*((as2*ch*e0c*epsc1)/2. + 


                                      d*(n0 - (e0c*(as2*epsc1 + 2*as1*epsn + 


                                        2*as2*epsn))/2.))))))/(-8*


                    b*(as2*ch + as1*d)*e0c*fc*(epsc1 - epsn)*


                    pow(epsc1 + 2*epsn, 2) + 


                  k*(12*pow(n0, 2)*pow(epsc1, 2) -