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ANSYS varification manual 9

# Ansys release 90 002114 sas ip inc index node to node

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Unformatted text preview: ile 2 Density = 1.0 lb-s /in Volume = 1 in3 (1 in x 1 in x 1 in) 2 Modulus of Elasticity = 1.0 lb/in Poisson's Ratio = 0.30 Air Resistance (Viscous Damping) Alpha Damping Used, Alpha = 1.0 Loading The acceleration due to gravity is ay = 386.4 in/s2 in the y-direction. The initial velocity in the x-direction is Vxi = 100 in/s2, and the initial velocity in the y-direction is Vyi = 500 in/s2. Analysis Assumptions and Modeling Notes The acceleration due to gravity is ay = 386.4 in/s2 in the y-direction. The initial velocity in the x-direction is Vxi = 100 in/s2, and the initial velocity in the y-direction is Vyi = 500 in/s2. The material properties have no effect on the results of interest, so they are selected arbitrarily. As outlined in J. B. Marion, S. T. Thornton, Classical Dynamics of Particles & Systems, the force due to the air resistance is assumed to be proportional to the mass, m, and the velocity, v, according to: f air = − k m v where k is a constant of proportionality. If the initial projectile velocity in the x-direction is U, the initial projectile velocity in the y-direction (vertical) is V, and the acceleration due to gravity is g, then the x and y-direction projectile displacements are given by: x= gt kV + g U (1 − exp ( − kt )) ; y = − + ( 1 − exp( − kt ) ) k k k2 For a projectile fired from the ground, the total travel time, T, before returning to the ground, is given by the transcendental equation: T= kV + g ( 1 − exp ( − kT ) ) gk In thi...
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