Tuesday, February 25, 2014

Online Euler Buckling Solver for Multiple Segment Axial Members

The subject online axial Euler buckling solver can determine the Euler buckling load for an axial member with up to 5 segments each with its own elastic modulus and area moment of inertia.  Boundary conditions of free, simple support, fixed slope and or elastic spring can be applied at the start and end of each segment.  The output includes the buckling load, maximum compression stress using the smallest input area and a slenderness ratio using the full length and smallest EA value.  The later two output parameters can be used to determine if Euler buckling is an adequate representation of the simulation.  Compression stress values approaching the material yield and low slenderness ratios suggest nonlinear buckling maybe more appropriate.

The calculator matches the classic Euler buckling equation Pcr = EI(π/KL)2 for simple-simple (K=1), fixed-fixed (K=0.5), simple-fixed (K=0.7) and fixed-free (K=2) end conditions.

An extended version of this calculator which also includes a nonlinear option can be found at www.xl4sim.com.

Friday, February 14, 2014

Web Page Embedded Euler Beam Calculator

The Euler Beam Calculator shown below is a web page (this page) embedded active Excel spreadsheet.  It uses the Microsoft SkyDrive file sharing system and does not require the user to have Excel to use.

This calculator will solve a user defined multi-span beam.  Up to 5 beam segments can be input each with its own elastic modulus, bending area moment-of-inertia, and top and bottom section moduli. Concentrated loads and moments can be input along with slope and displacement boundary conditions.

The solution provides a deflection chart, moment and shear diagrams and stress plots.  The calculator updates immediately as cells are changed.

This calculator is active.  Change a cell and watch it update the solution.

Thursday, February 6, 2014

Rubber State-of-Cure vs Time and Position

Rubber state of cure generally depends on the temperature time history during the mold cycle.  It can be a complex thermal kinetics problem due to the transient nature of the cure and temperature in time and position.  The attached MS Excel Macro is a temperature and state-of-cure calculator that has 5 molding configurations:  1) planar with one heated side; 2) planar with two heated sides; 3) cylindrical with a heated inner surface; 4) heated outer surface and 5) both inner and outer surfaces heated.  For these configurations it is assumed that the molded shape has a high length-to-thickness ratio allowing the problem to be treated 2-dimensionally.

The dashboard looks like this with a worksheet tab for each configuration.

Rubber State-of-Cure Calculator Dashboard.
The calculator uses the user input cure curve information for the rubber and the calculator solves the time/position/temperatures and the resulting state-of-cure versus time and position.

This section was added on 2/22/2014:

The implicit finite difference formulation is used to solve the for the temperatures in time and position. The implicit method is unconditionally stable in time, although this does not preclude using a small time step for improved accuracy.  Progressively decreasing the time step until convergence is always good practice.  The same is true for the spatial size. In this case the number of nodes.  Any number of good references are available that describe the methodology including Fundamentals of Heat and Mass Transfer by Incropera and DeWitt, 4th Edition.

This module assumes that the thermal properties (conductivity and specific heat) do not change over the temperature range and state-of-cure.  It also assumes there is no significant additional heating from the curing kinetics.

The MS Excel Macro has been code signed with a 3rd party code signing certificate to allow higher macro security settings.

A version enabling a larger range of shapes is underway.