3D Frame with zero stiffness hinges

Posted on 09/04/2019 by dougaj4

The previous version of 3DFrame allowed for spring releases at beam ends, but if the release stiffness was entered as zero it was treated as a rigid connection for that freedom.  Effectively zero stiffness releases could be modelled by entering a very low stiffness value, but this sometimes caused arithmetic problems, resulting in enormous deflections being reported for the released freedoms.  To avoid this problem the code has been modified so that any freedom entered as zero stiffness is treated as fully released.  The new version (Rev. 2.08) may be downloaded from:

3DFrame.zip

The solver links to two dll files that need to be installed as described here:

Installing C# dll files, reminder

The download zip file also includes a VBA only version, that should work without any further installation, other than extracting from the zip file.

Typical input showing both spring and zero stiffness releases is shown in the screen shot below:

Further details of the program 3Daxis system and the related stiffness matrices can be found at:

3D Frames, axes and stiffness matrices

Posted in Beam Bending, Excel, Finite Element Analysis, Frame Analysis, Newton | Tagged , , , , , | 11 Comments

Rubick’s Cube Solves Itself

Posted on 29/03/2019 by dougaj4

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Bett’s Dance

Posted on 24/03/2019 by dougaj4

I have posted a link to Bert Jansch playing Bett’s Dance here before:
Jansch and Renbourn live

Here is another live version:

… and (probably) a studio version, included on the album  “Living in the Shadows, Part 1”, which is available on vinyl or CD from the link below:

Bett’s Dance at Earth Recordings

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Numerical Integration; Tanh-Sinh Quadrature v. 4.42

Posted on 17/03/2019 by dougaj4

Back to Newton and Excel.

I recently received a new update to the Tanh-Sinh Quadrature spreadsheet from Graeme Dennes, which may be downloaded from:

Tanh_Sinh Quadrature.

From the Readme:

The Tanh-Sinh quadrature workbook has been enhanced as follows:

  1. The Tanh-Sinh integrator in the workbook may be the fastest finite-interval integrator on the planet!!
  2. The speed of the DE programs has been doubled.
  3. A fast finite interval program TINT has been added. It runs at over twice the speed of the Gauss-Kronrod program.
  4. The speed of the Gauss-Kronrod program has been improved through modifications developed by Berntsen, Espelid and Sorevik.
  5. The Romberg integrator, written by the author, may be the fastest and most accurate Romberg integrator on the planet!!
  6. Now includes over 1200 test integrals with true results. This may be the largest set of diverse test integrals available at no cost. It includes several of the “standard” sets of test integrals in wide use.
  7. The Plotter worksheet now shows two plots: the plot of the selected function over the finite interval (a,b), and the plot of the selected function after being transformed by the Tanh-Sinh function.
  8. Minor change to allow compatibility with Excel 2007.
  9. Minor correction.

Graeme Dennes

Posted in Charts, Excel, Maths, Newton, Numerical integration, UDFs, VBA | Tagged , , , , , , , , | 10 Comments

Mini-tours of India 9

Posted on 15/03/2019 by dougaj4

To Jaipur. The capital and largest city of Rasjasthan, also known as the Pink City:

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… and finally, we follow a monkey on a moped back to New Delhi, the airport, and home.

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