I have a problem defining the boundary conditions to this system. I have done the virtual work functional equation but got struck in the boundary conditions. Please help me.
Right side:
1) essential, w(L) = 0;
2) natural, M(L) = EI*w"(L) = 0.
Left side:
1) essential, w(0) = w'(0)*L;
2) natural, M(0) = V(0)*L, or EI*w"(0) = EI*w"'(0)*L.
I have changed the notations, so that it fits yours. We have the same left side essential BC. But I do not think the moment is zero for the left of the flexible beam. It should be V(0)*L.
@NaijiaXiao thank you for the reply. But i really didn't understand the notation.
As of my knowledge ECB for the flexible beam are w(L)=0 (right side of flexible beam) and w(0) -Lw'(0)=0 (left side of flexible beam). are these correct. I took the second condition because there is a rigid member to the left of the flexible beam. so moments will be zero. Here w meas displacement. Please can you help me now?
@NaijiaXiao But there is a concentrated P load acting at the same cut. How should I manifest that? Also if I take a cubic polynomial approximation. for finding the base functions the w(x)= a0 + a1 x + a2 x^2 +a3 x^3. Is this fine or should I take x/L instead of x? The next step would be to just differentiate the displacement equation and put the boundary conditions and find the base functions and calculate the K and F matrices. is this process correct?
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