A problem about virtual work principle

athosanian · Sep 25, 2014

hello, I want to apply the virtual work principle to a continuous mechanical system to derive equilibrium equation, naemly, a long thin bar with one end fixed in the wall and other end applied with pressure P. but I can not derive the correct equilibrium equations. I hope some expert could give some advice.
my thhinking is shown below:

Typed page titled Virtual work principle applied to a continuous system, with section 1 introduction giving equilibrium equation dT/dx = 0, boundary condition T = P at the right end, constitutive law T = ES and strain S = du/dx.

Diagram of a long bar fixed at the left wall with pressure P applied at the right end, coordinate x along the bar, and an inset of a small element showing forces T and T + dT/dx dx and displacements δu and δu + dδu/dx dx.

Handwritten-style typed derivation using the virtual work principle: equations (5) to (7) integrate T du/dx and dT/dx terms by parts to give delta W = T delta u at the endpoints, with delta u = 0 at x=0, leading to T at x=L equal to 0.

voko · Sep 26, 2014

Obviously, if the two terms from (4) result in ## T \delta u |_0^L = 0 ##, which gives you no condition on ##T## because ## \delta u(0) = \delta u(L) = 0 ##, it is the neglected third term that you must take into account.

A problem about virtual work principle

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