## 754 Reputation

11 years, 152 days

## tnx everyone,...

@Alejandro Jakubi tnx everyone,i thought it is just for me since i have some browsers problem,really thanks for your answers. good luck

## oh sorry then...

@sarra   please have a good break,and take care,sorry .

## at first it returns an error !...

@mehdi jafari at first it returns an error !

executing this line :
int(convert(F,exp), z = 0 .. infinity,numeric, epsilon = 0.1e-1); # which returns 2.259350091#

but execute F again and it will return #2.259350091# !!!!
what's wrong with maple !!!

## make sure of two things !...

first be sure of your TC is correct and second your t2 is exactly what you want ,

restart:
TC := (p*A*((lambda-sigma)*(exp(lambda*t2)-1)+lambda*(exp((lambda-sigma)*T)-exp((lambda-sigma)*t2)))/(lambda*(lambda-sigma))-Ca-A*exp(lambda*t1)*((beta*a2+b2)*(exp(beta*t1)-1)/beta^2-(lambda*a2-b2)*(1-exp(-lambda*t1))/lambda^2)/(beta+lambda)+A*exp(lambda*t1)*b2*t1/(lambda*beta)-W*((alpha*a1+b1)*(1-exp(-alpha*t1))-alpha*b1*t1*exp(-alpha*t1))/alpha^2+A*(exp(lambda*t2)*((a1+b1*t2)*lambda*alpha+b1*(lambda-alpha))-exp(lambda*t1)*(b1*(alpha^2-lambda^2*exp((lambda+alpha)*(t2-t1)))-(a1+b1*t1)*lambda*alpha*(alpha+lambda*exp((lambda+alpha)*(t2-t1))))/(lambda+alpha))/(lambda^2*alpha^2)+Cs*A*exp((lambda-sigma)*t2)*((T-t2)*(lambda-sigma)-exp((T-t2)*(lambda-sigma))+1)/(lambda-sigma)^2-L*A*((exp(lambda*T)-exp(lambda*t2))/lambda-(exp((lambda-sigma)*T)-exp((lambda-sigma)*t2))/(lambda-sigma))-C*(A*(exp((beta+lambda)*t1)-1)/(beta+lambda)+W+A*(exp((lambda-sigma)*T)-exp((lambda-sigma)*t2))/(lambda-sigma)))/(T);

# and make sure of this #

t2 = (ln(W*(lambda+alpha)/A)+(lambda+alpha)*t1)/(lambda+alpha);

# if these two are correct,thus your answers are surely correct ! #

## too interesting !...

it is too interesting that you appreciate the answer , but you do not vote it up ! :)

@italopersechino your are very welcome,and a very good and modest guy.

u have repeated your answers so much !   but i could not find out what is going to be solved ?! i can not undertand what do u mean unless you explain in algebric expreesions that what are your knowns,what are your unknowns ,what are your equataions, and what is going to be solved. please delet your reapetitive replies. tnx

## too easy...

@italopersechino just put # in the lines which define x1 and PZc , that's all !

 > restart: with(linalg): with(plots): Digits:=15:
 > #E:=214000: sig_Y:=853: n:=0.0595: eps_f:=1.1005: #R:=0.1: dK_th:=4.2: c:=-0.679: nu:=0.3: dK:=100:
 > P_str_fact:=1/(1-2*nu):
 > #pi:=3.141592654:
 >
 > #Size of plastic zone at dK #PZc:=(1/((4*pi*P_str_fact^2)*(1+n)))*(dK/sig_Y)^2; #[m]
 > #Size of plastic zone at dK=dK_th #x1:=(1/((4*pi*P_str_fact^2)*(1+n)))*(dK_th/sig_Y)^2; #[m]
 > #Strain plastic amplitude along crack ligament (r) deps:=(2*sig_Y/E)*(PZc/(r+x1))^(1/(1+n));
 (1)
 > deps_tip:=subs(r=0,deps);
 (2)
 > deps_PZc:=subs(r=PZc-x1,deps);
 (3)
 >
 >
 > #LCF depsLCF:=2*eps_f*(2*Nf)^c;
 (4)
 > Nf:=1/Dam;
 (5)
 >
 > appo:=depsLCF=deps;
 (6)
 > Damage:=solve(appo,Dam);
 (7)
 > eval(%,{PZc=(1/((4*pi*P_str_fact^2)*(1+n)))*(dK/sig_Y)^2,x1=(1/((4*pi*P_str_fact^2)*(1+n)))*(dK_th/sig_Y)^2});
 (8)
 >
 >

@Kinkilla please insert your full code here so that we can completly understand what u are talking about !

@Hb i think u can easily do what u want,but please insert your code here so that we can help. good luck! what do u mean by specifying nodes on x axis ?  u can insert a sequence of numbers like this :
[seq](x,x=0..1,0.01);

u can also plot your list with listplot command. for more help please insert your code fully here. tnx

## hmm...

@Preben Alsholm thus what's wrong with this problem?

## i replaced but it does not change the an...

 >
 > TC := (p*A*((lambda-sigma)*(exp(1)^(lambda*t2)-1)+lambda*(exp(1)^((lambda-sigma)*T)-exp(1)^((lambda-sigma)*t2)))/(lambda*(lambda-sigma))-Ca-A*exp(1)^(lambda*t1)*((beta*a2+b2)*(exp(1)^(beta*t1)-1)/beta^2-(lambda*a2-b2)*(1-exp(1)^(-lambda*t1))/lambda^2)/(beta+lambda)+A*exp(1)^(lambda*t1)*b2*t1/(lambda*beta)-W*((alpha*a1+b1)*(1-exp(1)^(-alpha*t1))-alpha*b1*t1*exp(1)^(-alpha*t1))/alpha^2+A*(exp(1)^(lambda*t2)*((a1+b1*t2)*lambda*alpha+b1*(lambda-alpha))-exp(1)^(lambda*t1)*(b1*(alpha^2-lambda^2*exp(1)^((lambda+alpha)*(t2-t1)))-(a1+b1*t1)*lambda*alpha*(alpha+lambda*exp(1)^((lambda+alpha)*(t2-t1))))/(lambda+alpha))/(lambda^2*alpha^2)+Cs*A*exp(1)^((lambda-sigma)*t2)*((T-t2)*(lambda-sigma)-exp(1)^((T-t2)*(lambda-sigma))+1)/(lambda-sigma)^2-L*A*((exp(1)^(lambda*T)-exp(1)^(lambda*t2))/lambda-(exp(1)^((lambda-sigma)*T)-exp(1)^((lambda-sigma)*t2))/(lambda-sigma))-C*(A*(exp(1)^((beta+lambda)*t1)-1)/(beta+lambda)+W+A*(exp(1)^((lambda-sigma)*T)-exp(1)^((lambda-sigma)*t2))/(lambda-sigma)))/T:
 > TC2 := subs(t2 = (ln(W*(lambda+alpha)/A)+(lambda+alpha)*t1)/(lambda+alpha), TC):
 > x1 := diff(TC2, t1) = 0:
 > x2 := diff(TC2, T) = 0:
 > x3 := evalf(simplify(lhs(eval(x1,{A = 290, lambda = 4, a1 = .9, a2 = 2.4, b2 = 0.1e-1, b1 = 0.1e-2, alpha = 0.2e-1, beta = 0.4e-1, W = 90, Ca = 100, L = 11, C = 9, p = 12, Cs = 4, sigma = 0.2e-2}))));
 (1)
 > x4 := evalf(simplify(lhs(eval(x2,{A = 290, lambda = 4, a1 = .9, a2 = 2.4, b2 = 0.1e-1, b1 = 0.1e-2, alpha = 0.2e-1, beta = 0.4e-1, W = 90, Ca = 100, L = 11, C = 9, p = 12, Cs = 4, sigma = 0.2e-2}))));
 (2)
 > x5 := solve({x3, x4}, {T, t1});
 >
 (3)
 >