@Christian Wolinski Many thanks for your reply. so is it ok to solve it by using polar coordinate? 

restart; r1 := .3*10^(-3); r2 := .3*10^(-3); U := 5*10^(-3); L := 3*10^(-3); T := .5*10^(-3); hz := (1/12)*T*U^3; hy := (1/12)*U*T^3; E := 69*10^9; v := .33; G := E/(2*(1+v)); d := .5*10^(-3); l := 14*10^(-3); h := 3.14*d^4*(1/64); `ΔZ` := 12.5*10^(-3); `ΔY` := 12.5*10^(-3); t := proc (x) options operator, arrow; piecewise(0 <= x and x < r1, T+2*r1-2*sqrt(-x^2+2*x*r1), r1 <= x and x < L-r2, T, L-r2 <= x and x <= L, T+2*r2-2*sqrt((L-x)*(2*r2-L+x))) end proc; / x -> piecewise\0 <= x and x < r1, / 2 \ T + 2 r1 - 2 sqrt\-x + 2 x r1/, r1 <= x and x < L - r2, T, L - r2 <= x and x <= L, \ T + 2 r2 - 2 sqrt((L - x) (2 r2 - L + x))/ C11 := (int(1/t(x), x = 0 .. L))/(E*U); -8 1.678752227 10 f := proc (z) options operator, arrow; int(1/t(x), x = 0 .. z) end proc; / 1 \ z -> int|----, x = 0 .. z| \t(x) / C26 := 12*(int(f(z), z = 0 .. L))/(E*U^3);