StructuralDynamicsODESolvers.jl

This package contains pure Julia implementations of ordinary differential equations (ODE) solvers for structural dynamics problems.

Features

The following solvers for linear dynamic equations are available:

• Bathe (equal size sub-steps) [BAT07]
• Central difference
• Houbolt [HOU50]
• Newmark [NEW509]
• Backward Euler (for first order systems)

Example

The following example is explained in this notebook.

For further examples see the Examples section of the documentation.

using StructuralDynamicsODESolvers

k  = 2 ; m  = .5 ;  c = .1 
u0 = 1 ; v0 = 0 

alg = Bathe(Δt = 0.1)

M = m*ones(1, 1)
C = c*ones(1, 1)
K = k*ones(1, 1)
R = zeros(1)

sys = SecondOrderAffineContinuousSystem(M, C, K, R)

U₀ = u0 * ones(1)
V₀ = v0 * ones(1)

prob = InitialValueProblem(sys, (U₀, V₀))

sol = solve(prob, alg, NSTEPS=300);

using Plots

plot(sol, vars=(0, 1), xlab="time", ylab="displacement")

Related libraries

This package has been created for research purposes. If you are new to numerically solving differential equations in Julia, we suggest that you use the DifferentialEquations.jl suite.

References

• [BAT07] Bathe, Klaus-Jürgen. "Conserving energy and momentum in nonlinear dynamics: a simple implicit time integration scheme." Computers & structures 85.7-8 (2007): 437-445.
• [NEW59] Newmark, Nathan M. "A method of computation for structural dynamics." Journal of the engineering mechanics division 85.3 (1959): 67-94.
• [HOU50] Houbolt, John C. "A recurrence matrix solution for the dynamic response of elastic aircraft." Journal of the Aeronautical Sciences 17.9 (1950): 540-550.