I have attached a figure with this, to help in understanding the problem. A ring whose circumference is attached to its center by infinite springs. Center is fixed. thickness of ring is h, width is b, Young's modulus E and moment of area I. Now a radial force is applied(shown in the figure by an arrow) at theta= - pi/2. How to find the static deflection. i have derived the equation(6th order in w)(w is radial displacement). i am able to find out the characteristic equation, by which homogeneous solution can be found. but how to find the particular solution. What will be the boundary conditions? in beams, end boundary conditions are specified either in terms of displacements or forces or moments. Using them the solutions can be found. i first thought that, w and all derivatives of w are continuous at theta=3*pi/2 and -pi/2? but this doesn't help. please help..