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pendulumGeomExactBeam2Dsimple.rst

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pendulumGeomExactBeam2Dsimple.py

You can view and download this file on Github: pendulumGeomExactBeam2Dsimple.py

#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
# This is an EXUDYN example
#
# Details:  Example for GeometricallyExactBeam2D, connected with 2D revolute joint; uses GenerateStraightBeam
#
# Model:    Planar model of a highly flexible pendulum of length 0.5m with h=0.002m, b=0.01m, E=1e8 and density rho=1000kg/m^3;
#           The pendulum is released from the horizontal position under gravity acting in -y direction;
#
# Author:   Johannes Gerstmayr
# Date:     2021-03-25
#
# Copyright:This file is part of Exudyn. Exudyn is free software. You can redistribute it and/or modify it under the terms of the Exudyn license. See 'LICENSE.txt' for more details.
#
# *clean example*
#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

## import libaries
import exudyn as exu
from exudyn.utilities import *

import numpy as np
# from math import sin, cos, pi

## setup system container and mbs
SC = exu.SystemContainer()
mbs = SC.AddSystem()

## define parameters for beams
L = 0.5                # length of pendulum 
E=1e8                  # very soft elastomer
rho=1000               # elastomer
h=0.002                # height of rectangular beam element in m
b=0.01                 # width of rectangular beam element in m
A=b*h                  # cross sectional area of beam element in m^2
I=b*h**3/12            # second moment of area of beam element in m^4
nu = 0.3               # Poisson's ratio
ks = 10*(1+nu)/(12+11*nu) # shear correction factor
G = E/(2*(1+nu))          # shear modulus

## create beam template with beam parameters
beamTemplate = ObjectBeamGeometricallyExact2D(physicsMassPerLength=rho*A,
                                              physicsCrossSectionInertia=rho*I,
                                              physicsBendingStiffness=E*I,
                                              physicsAxialStiffness=E*A,
                                              physicsShearStiffness=ks*G*A,
                                              visualization=VObjectBeamGeometricallyExact2D(drawHeight = h), )

## create straight beam with 10 elements, apply gravity and fix (x,y) position of node 0 (rotation left free)
beamInfo = GenerateStraightBeam(mbs, positionOfNode0=[0,0,0], positionOfNode1=[L,0,0], 
                                numberOfElements=10, beamTemplate=beamTemplate,
                                gravity=[0,-9.81,0], fixedConstraintsNode0=[1,1,0],)
#beamInfo contains [nodeList, beamList, ...]

## assemble system and define simulation settings
mbs.Assemble()

simulationSettings = exu.SimulationSettings()

tEnd = 1
stepSize = 0.0025
simulationSettings.timeIntegration.numberOfSteps = int(tEnd/stepSize)
simulationSettings.timeIntegration.endTime = tEnd
simulationSettings.timeIntegration.verboseMode = 1
simulationSettings.solutionSettings.solutionWritePeriod = 0.005
simulationSettings.solutionSettings.writeSolutionToFile = True

simulationSettings.linearSolverType = exu.LinearSolverType.EigenSparse
simulationSettings.timeIntegration.newton.useModifiedNewton = True #for faster simulation


## add some visualization settings
SC.visualizationSettings.nodes.defaultSize = 0.01
SC.visualizationSettings.nodes.drawNodesAsPoint = False
SC.visualizationSettings.bodies.beams.crossSectionFilled = True

## run dynamic simulation
mbs.SolveDynamic(simulationSettings)

## visualize computed solution:
mbs.SolutionViewer()