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Mathematics
Differential Equations
How to make the deflection equation at any point along a snow ski profile?
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[QUOTE="erobz, post: 6638583, member: 700856"] I suspect you are going to have to use the following: $$ \frac{ \frac{d^2y}{dx^2} }{ \left[ 1 + \left( \frac{dy}{dx} \right)^2 \right]^{(3/2)} } = \frac{M(x)}{E I(x)} $$ When we encounter this equation in engineering, we typically can neglect ## \frac{dy}{dx}## for structural beams. However, a ski, with a 300 N ( 70 lbf ) load... I have wonder if the simplifying assumptions are no more? Have you checked the bending stresses don't exceed the allowable stress for the desired loading? As for the changing modulus of rigidity, unless you can write ##I(x) = \frac{1}{12} B(x) h(x)^3## , you are going to have to discretize it as you planned. I would try to write the shape functions, and solve the single resulting equation numerically, but maybe the FEA analysis isn't too bad? Its something I haven't personally performed. [/QUOTE]
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Mathematics
Differential Equations
How to make the deflection equation at any point along a snow ski profile?
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