Can any one please help me out in Nonlinear analysis of beams using Direct iteration method or Newton Raphson.
Here i am producing some of algorithms from the book of J.N.Reddy,"An_Introduction_to_Nonlinear_Finite_Element_Analysis__2004".
I have a doubt in the term DW, whether that is the difference between transverse dispalcements of Consecutive Nodes or the difference between transverse dispalcements of Node on Consecutive iterations.
please help me . Thanks in Advance.
ELF1(i) = ELF1(i) + FX ∗ SFL(i) ∗ CNST
ELF2(I) = ELF2(I) + QX ∗ SFH(I) ∗ CNST
ELK11(i, j) = ELK11(i, j)+ AXX ∗ GDSFL(i) ∗ GDSFL(j) ∗ CNST
ELK22(I, J) = ELK22(I, J)+ DXX ∗ GDDSFH(I) ∗ GDDSFH(J) ∗ CNST
in the full integration loop, and
ELK12(i, J) = ELK12(i, J) + 0.5 ∗ AXX ∗DW∗ GDSFL(i) ∗ GDSFH(J) ∗ CNST
ELK21(I, j) = ELK21(I, j) + AXX ∗DW∗ GDSFH(I) ∗ GDSFL(j) ∗ CNST
ELK22(I, J) = ELK22(I, J) + 0.5 ∗ AXX ∗DW ∗DW∗ GDSFH(I) ∗ GDSFH(J) ∗ CNST
in the reduced integration loop. Here,
SFL(i) = ψi, SFH(I) = φI ,GDSFH(I) = dφI/dx , GDDSFH(I) = d^2 φI/dx^2 , GDSFL(i) = dψi/dx
, and DW =(dw0/dx) for i, j = 1,2 and I, J = 1, 2, 3, 4.