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The time interval limitation is driven by the period of the highest natural frequency mode of the discret system model. The time interval limitation for an explicit solver would be the same.
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The resulting sets of equations would be equivalent, assuming the same number and sizes of spring-mass combinations. An alternative which I think is what you are suggesting would be to model the system as alternating mass-less springs and point masses, which would also work. It probably depends in part of whether the line ever will become straight enough that the tension in the line depends significantly on the elastic stretch of the line.Ĭlick to expand.I'm considering a single element to to have both a spring and a mass, draw a box around one spring and one mass in your illustration and that's what I was considering to be an element. A question when modeling such a system is whether the elasticity of the lines needs to be considered, or whether they can be treated as suspended catenary. More and smaller elements improve accuracy but at computational cost.Ĥ) Back to the mooring lines for the buoy. This could be considered as the natural period of the element if it was a pendulum even though the elements are not pendulums.ģ) The question should be asked as to how many elements and how small elements are needed to obtain a solution with the desired accuracy. My guess it would be proportional to the square root of the (acceleration of gravity divided by the length) of the smallest element. If an explicit solver is used there will still be a limit to how long the time increments can be. In this case modeling the cable as rigid elements with mass is probably appropriate since elastic stretch of the cable will have only a second (or higher) order effect on the solution. If an implicit solver is used the time increment can be much longer, and this is the reason implicit solvers are generally prefered for complicated problems.Ģ) Consider the catenary problem of a suspended thin cable, tensioned only by gravity, being buffeted by wind gusts. It is not related to the natural period of the guitar string. That can be considered as the natural period of the element. If an explicit solver is used then the time step will need to be proportional to the square root of the (stiffness divided by the mass) of the smallest element. These elements can be assembled in a string and the equations of motion in the time domain derived.Įither an explicit or an implicit solver can be used to solve the equations of motion. Each element has a spring in one direction which exerts a force proportional to the elongation in the axial direction, and a mass lumped at one point. Probably the simpliest way to model a guitar string is using simple spring-mass elements. If a guitar string is modeled a string of rigid elements, then the string can't vibrate. Apparently his experience is that the implicit solver ran much faster for his problem.Ĭlick to expand.The approriate type of elements depend on the physics of the problem and what information is sought.ġ) Consider a guitar string and the time history of the guitar strong is desired. As floating noted in a previous message in this thread, OrcaFlex has both explicit and implicit solvers and the user can select which one to use. The choice of an explicit or implicit solver depends on the problem to be solved. Wrong selection of the parameters can either cause longer run times or, in some cases, the solution can be incorrect. The tradeoffs of implicit schemes is they are more computationally intense per time step, and they have parameters which need to selected. Implicit solvers allow much longer time steps, and frequently will automatically adjust the time increment to run as fast as possible. In this case the relevant time scale can be considered as the natural period of the element. The maximum size of the time increment is related to the size of the elements and the time scales inherent in the equations for the elements. The tradeoff is the increment has to be small.
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They are also generally robust provided the increment is small enough. Explicit solvers are very simple and efficient for an individual increment. Click to expand.The very short time step needed comes from the use of the simple explicit solver.