normmat.cpp

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

        pow(epsc1, 


          4)*(sqrt(pow(epsc1, 


                    2)*(-8*a*fc*(-1 + k)*k*(fn*lp - z3) + 


                      pow(a*fc*(-2 + 3*k) + (as1 + as2)*e0c*k*epsc1, 2))) - 


            sqrt(pow(epsc1, 


                    2)*(8*a*fc*(-1 + k)*k*z3 + 


                      pow(a*fc*(-2 + 3*k) + (as1 + as2)*e0c*k*epsc1, 


                          2)))) + 


      2*pow(a, 3)*pow(fc, 3)*


        k*(-2 + 3*k)*(-60*pow(fn, 2)*pow(-1 + k, 2)*k*pow(lp, 2)*


              epsc1 + (-2 + 3*k)*(2*(-1 + k)*z3 + 


                  3*(as1 + as2)*e0c*(-2 + 3*k)*


                    epsc1)*(sqrt(pow(epsc1, 


                            2)*(-8*a*fc*(-1 + k)*k*(fn*lp - z3) + 


                              pow(a*fc*(-2 + 3*k) + (as1 + as2)*e0c*k*epsc1,


                                   2))) - 


                    sqrt(pow(epsc1, 


                            2)*(8*a*fc*(-1 + k)*k*z3 + 


                              pow(a*fc*(-2 + 3*k) + (as1 + as2)*e0c*k*epsc1,


                                   2))))\


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


              lp*(30*pow(k, 2)*epsc1*(2*z3 + 3*(as1 + as2)*e0c*epsc1) + 


                  2*sqrt(pow(epsc1, 


                          2)*(-8*a*fc*(-1 + k)*k*(fn*lp - z3) + 


                            pow(a*fc*(-2 + 3*k) + (as1 + as2)*e0c*k*epsc1, 


                                2))) - 


                  3*k*(20*z3*epsc1 + 20*as1*e0c*pow(epsc1, 2) + 


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


                        sqrt(pow(epsc1, 


                                2)*(-8*a*fc*(-1 + k)*k*(fn*lp - z3) + 


                                  pow(a*fc*(-2 + 3*k) + (as1 + as2)*e0c*k*


                                        epsc1, 2)))))) + 


      2*a*pow(as1 + as2, 2)*pow(e0c, 2)*fc*pow(k, 3)*


        pow(epsc1, 


          2)*(as1*e0c*


              epsc1*(60*fn*(-1 + k)*k*lp*epsc1 + 


                  13*(-2 + 


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


                                2)*(-8*a*fc*(-1 + k)*k*(fn*lp - z3) + 


                                  pow(a*fc*(-2 + 3*k) + (as1 + as2)*e0c*k*


                                        epsc1, 2))) - 


                        sqrt(pow(epsc1, 


                                2)*(8*a*fc*(-1 + k)*k*z3 + 


                                  pow(a*fc*(-2 + 3*k) + (as1 + as2)*e0c*k*


                                        epsc1, 2))))) + 


            as2*e0c*epsc1*(60*fn*(-1 + k)*k*lp*epsc1 + 


                  13*(-2 + 


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


                                2)*(-8*a*fc*(-1 + k)*k*(fn*lp - z3) + 


                                  pow(a*fc*(-2 + 3*k) + (as1 + as2)*e0c*k*


                                        epsc1, 2))) - 


                        sqrt(pow(epsc1, 


                                2)*(8*a*fc*(-1 + k)*k*z3 + 


                                  pow(a*fc*(-2 + 3*k) + (as1 + as2)*e0c*k*


                                        epsc1, 2))))) - 


            42*(-1 + 


                  k)*(fn*lp*


                    sqrt(pow(epsc1, 


                          2)*(-8*a*fc*(-1 + k)*k*(fn*lp - z3) + 


                            pow(a*fc*(-2 + 3*k) + (as1 + as2)*e0c*k*epsc1, 


                                2))) + 


                  z3*(-sqrt(pow(epsc1, 


                                2)*(-8*a*fc*(-1 + k)*k*(fn*lp - z3) + 


                                  pow(a*fc*(-2 + 3*k) + (as1 + as2)*e0c*k*


                                        epsc1, 2))) + 


                        sqrt(pow(epsc1, 


                                2)*(8*a*fc*(-1 + k)*k*z3 + 


                                  pow(a*fc*(-2 + 3*k) + (as1 + as2)*e0c*k*


                                        epsc1, 2)))))) + 


      8*pow(a, 2)*pow(fc, 2)*


        pow(k, 


          2)*(3*pow(as1, 2)*pow(e0c, 2)*(-2 + 3*k)*


              pow(epsc1, 


                2)*(10*fn*(-1 + k)*k*lp*


                    epsc1 + (-2 + 


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


                                2)*(-8*a*fc*(-1 + k)*k*(fn*lp - z3) + 


                                  pow(a*fc*(-2 + 3*k) + (as1 + as2)*e0c*k*


                                        epsc1, 2))) - 


                        sqrt(pow(epsc1, 


                                2)*(8*a*fc*(-1 + k)*k*z3 + 


                                  pow(a*fc*(-2 + 3*k) + (as1 + as2)*e0c*k*


                                        epsc1, 2))))) + 


            3*pow(as2, 2)*pow(e0c, 2)*(-2 + 3*k)*


              pow(epsc1, 


                2)*(10*fn*(-1 + k)*k*lp*


                    epsc1 + (-2 + 


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


                                2)*(-8*a*fc*(-1 + k)*k*(fn*lp - z3) + 


                                  pow(a*fc*(-2 + 3*k) + (as1 + as2)*e0c*k*


                                        epsc1, 2))) - 


                        sqrt(pow(epsc1, 


                                2)*(8*a*fc*(-1 + k)*k*z3 + 


                                  pow(a*fc*(-2 + 3*k) + (as1 + as2)*e0c*k*


                                        epsc1, 2))))) - 


            as2*e0c*(-1 + k)*


              epsc1*(45*pow(fn, 2)*(-1 + k)*k*pow(lp, 2)*epsc1 + 


                  fn*lp*(90*k*z3*epsc1 - 90*pow(k, 2)*z3*epsc1 - 


                        22*sqrt(pow(epsc1, 


                                2)*(-8*a*fc*(-1 + k)*k*(fn*lp - z3) + 


                                  pow(a*fc*(-2 + 3*k) + (as1 + as2)*e0c*k*


                                        epsc1, 2))) + 


                        33*k*sqrt(pow(epsc1, 


                                2)*(-8*a*fc*(-1 + k)*k*(fn*lp - z3) + 


                                  pow(a*fc*(-2 + 3*k) + (as1 + as2)*e0c*k*


                                        epsc1, 2)))) - 


                  11*(-2 + 3*k)*


                    z3*(sqrt(pow(epsc1, 


                                2)*(-8*a*fc*(-1 + k)*k*(fn*lp - z3) + 


                                  pow(a*fc*(-2 + 3*k) + (as1 + as2)*e0c*k*


                                        epsc1, 2))) - 


                        sqrt(pow(epsc1, 


                                2)*(8*a*fc*(-1 + k)*k*z3 + 


                                  pow(a*fc*(-2 + 3*k) + (as1 + as2)*e0c*k*


                                        epsc1, 2))))) + 


            12*pow(-1 + k, 


                2)*(pow(fn, 2)*pow(lp, 2)*


                    sqrt(pow(epsc1, 


                          2)*(-8*a*fc*(-1 + k)*k*(fn*lp - z3) + 


                            pow(a*fc*(-2 + 3*k) + (as1 + as2)*e0c*k*epsc1, 


                                2))) - 


                  2*fn*lp*z3*


                    sqrt(pow(epsc1, 


                          2)*(-8*a*fc*(-1 + k)*k*(fn*lp - z3) + 


                            pow(a*fc*(-2 + 3*k) + (as1 + as2)*e0c*k*epsc1, 


                                2))) + 


                  pow(z3, 


                      2)*(sqrt(pow(epsc1, 


                                2)*(-8*a*fc*(-1 + k)*k*(fn*lp - z3) + 


                                  pow(a*fc*(-2 + 3*k) + (as1 + as2)*e0c*k*


                                        epsc1, 2))) - 


                        sqrt(pow(epsc1, 


                                2)*(8*a*fc*(-1 + k)*k*z3 + 


                                  pow(a*fc*(-2 + 3*k) + (as1 + as2)*e0c*k*


                                        epsc1, 2))))) + 


            as1*e0c*epsc1*(-45*pow(fn, 2)*pow(-1 + k, 2)*k*pow(lp, 2)*


                    epsc1 + (-2 + 3*k)*(11*(-1 + k)*z3 + 


                        6*as2*e0c*(-2 + 3*k)*


                          epsc1)*(sqrt(pow(epsc1, 


                                2)*(-8*a*fc*(-1 + k)*k*(fn*lp - z3) + 


                                  pow(a*fc*(-2 + 3*k) + (as1 + as2)*e0c*k*


                                        epsc1, 2))) - 


                        sqrt(pow(epsc1, 


                                2)*(8*a*fc*(-1 + k)*k*z3 + 


                                  pow(a*fc*(-2 + 3*k) + (as1 + as2)*e0c*k*


                                        epsc1, 2)))) + 


                  fn*(-1 + k)*


                    lp*(90*pow(k, 2)*epsc1*(z3 + 2*as2*e0c*epsc1) + 


                        22*sqrt(pow(epsc1, 


                                2)*(-8*a*fc*(-1 + k)*k*(fn*lp - z3) + 


                                  pow(a*fc*(-2 + 3*k) + (as1 + as2)*e0c*k*


                                        epsc1, 2))) - 


                        3*k*(30*z3*epsc1 + 40*as2*e0c*pow(epsc1, 2) + 


                              11*sqrt(pow(epsc1, 


                                      2)*(-8*a*fc*(-1 + k)*k*(fn*lp - z3) + 


                                        pow(a*fc*(-2 + 3*k) + (as1 + as2)*


                                        e0c*k*epsc1, 2))))))));





  }





  else{





    in1=0.;





  }


  return in1;


 }


  


//prace na ocelove casti prurezu pro prubeh normalove sily (-z3 + fn x) pres element delky lp 


double normmat::compute_in2 (double lp)


{


	double in2;	


	


	


  if (fn == 0. && z3>= 0.0){





    in2=1/(16.*pow(a, 2)*pow(fc, 2)*pow(-1 + k, 2))*((as1 + as2)*e0c*lp*


      pow(a*fc*(-2 + 3*k)*epsc1 + (as1 + as2)*e0c*k*pow(epsc1, 2) - 


          sqrt(pow(epsc1, 


                  2)*(8*a*fc*(-1 + k)*k*z3 + 


                    pow(a*fc*(-2 + 3*k) + (as1 + as2)*e0c*k*epsc1, 2))), 2));





  }


  else if (fn != 0. && z3>= 0.0){





    in2=1/(96.*pow(a, 3)*pow(fc, 3)*fn*pow(-1 + k, 3)*k)*((as1 + as2)*e0c*


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


            pow(epsc1, 


              3)*(sqrt(pow(epsc1, 


                        2)*(-8*a*fc*(-1 + k)*k*(fn*lp - z3) + 


                          pow(a*fc*(-2 + 3*k) + (as1 + as2)*e0c*k*epsc1, 


                              2))) - 


                sqrt(pow(epsc1, 


                        2)*(8*a*fc*(-1 + k)*k*z3 + 


                          pow(a*fc*(-2 + 3*k) + (as1 + as2)*e0c*k*epsc1, 


                              2)))) + 


          pow(a, 3)*pow(fc, 3)*


            pow(2 - 3*k, 


              2)*(12*fn*(-1 + k)*k*lp*


                  epsc1 + (-2 + 


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


                              2)*(-8*a*fc*(-1 + k)*k*(fn*lp - z3) + 


                                pow(a*fc*(-2 + 3*k) + (as1 + as2)*e0c*k*


                                        epsc1, 2))) - 


                      sqrt(pow(epsc1, 


                              2)*(8*a*fc*(-1 + k)*k*z3 + 


                                pow(a*fc*(-2 + 3*k) + (as1 + as2)*e0c*k*


                                        epsc1, 2))))) + 


          pow(a, 2)*pow(fc, 2)*


            k*(-24*pow(fn, 2)*pow(-1 + k, 2)*k*pow(lp, 2)*


                  epsc1 + (-2 + 3*k)*(8*(-1 + k)*z3 + 


                      3*(as1 + as2)*e0c*(-2 + 3*k)*


                        epsc1)*(sqrt(pow(epsc1, 


                              2)*(-8*a*fc*(-1 + k)*k*(fn*lp - z3) + 


                                pow(a*fc*(-2 + 3*k) + (as1 + as2)*e0c*k*


                                        epsc1, 2))) - 


                      sqrt(pow(epsc1, 


                              2)*(8*a*fc*(-1 + k)*k*z3 + 


                                pow(a*fc*(-2 + 3*k) + (as1 + as2)*e0c*k*


                                        epsc1, 2)))) + 


                8*fn*(-1 + k)*


                  lp*(3*pow(k, 2)*epsc1*(2*z3 + 3*(as1 + as2)*e0c*epsc1) + 


                      2*sqrt(pow(epsc1, 


                              2)*(-8*a*fc*(-1 + k)*k*(fn*lp - z3) + 


                                pow(a*fc*(-2 + 3*k) + (as1 + as2)*e0c*k*


                                        epsc1, 2))) - 


                      3*k*(2*z3*epsc1 + 2*as1*e0c*pow(epsc1, 2) + 


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


                            sqrt(pow(epsc1, 


                                    2)*(-8*a*fc*(-1 + k)*k*(fn*lp - z3) + 


                                      pow(a*fc*(-2 + 3*k) + (as1 + as2)*e0c*


                                        k*epsc1, 2)))))) + 


          a*(as1 + as2)*e0c*fc*pow(k, 2)*


            epsc1*(3*as1*e0c*


                  epsc1*(4*fn*(-1 + k)*k*lp*


                        epsc1 + (-2 + 


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


                                    2)*(-8*a*fc*(-1 + k)*k*(fn*lp - z3) + 


                                      pow(a*fc*(-2 + 3*k) + (as1 + as2)*e0c*


                                        k*epsc1, 2))) - 


                            sqrt(pow(epsc1, 


                                    2)*(8*a*fc*(-1 + k)*k*z3 + 


                                      pow(a*fc*(-2 + 3*k) + (as1 + as2)*e0c*


                                        k*epsc1, 2))))) + 


                3*as2*e0c*


                  epsc1*(4*fn*(-1 + k)*k*lp*


                        epsc1 + (-2 + 


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


                                    2)*(-8*a*fc*(-1 + k)*k*(fn*lp - z3) + 


                                      pow(a*fc*(-2 + 3*k) + (as1 + as2)*e0c*


                                        k*epsc1, 2))) - 


                            sqrt(pow(epsc1, 


                                    2)*(8*a*fc*(-1 + k)*k*z3 + 


                                      pow(a*fc*(-2 + 3*k) + (as1 + as2)*e0c*


                                        k*epsc1, 2))))) - 


                8*(-1 + 


                      k)*(fn*lp*


                        sqrt(pow(epsc1, 


                              2)*(-8*a*fc*(-1 + k)*k*(fn*lp - z3) + 


                                pow(a*fc*(-2 + 3*k) + (as1 + as2)*e0c*k*


                                        epsc1, 2))) + 


                      z3*(-sqrt(pow(epsc1, 


                                    2)*(-8*a*fc*(-1 + k)*k*(fn*lp - z3) + 


                                      pow(a*fc*(-2 + 3*k) + (as1 + as2)*e0c*


                                        k*epsc1, 2))) + 


                            sqrt(pow(epsc1, 


                                    2)*(8*a*fc*(-1 + k)*k*z3 + 


                                      pow(a*fc*(-2 + 3*k) + (as1 + as2)*e0c*


                                        k*epsc1, 2))))))));





  }





  else{