Global to Local for plates (and three node beams)

Posted on 02/03/2014 by dougaj4

The Glob_to_Loc function (see Converting from global to local coordinates (and vice versa) ) converts forces and deflections of a beam from the global coordinate system to the local system, defined by the longitudinal axis of the beam and a rotation angle from the horizontal plane.  The rotation angle is required because a beam defined by its two end nodes has no defined rotation, but an alternative is to define the beam orientation with three nodes; i.e. the two end nodes and a third node lying on the local x-y plane.  This approach is also used for plate-shell elements, where the plane of the element is defined by the coordinates of the corner nodes.

To work with elements defined by 3 nodes I have added two new user defined functions (UDFs) to the IP2 spreadsheet:  Glob_to_Loc3 and Loc_to_Glob3.  The new version of the spreadsheet may be downloaded from: IP2.ZIP – including full open source code.  The download zip file also includes a Python version of these functions.  Use of the Python versions requires the PyXll add-in.  See Installing Python, Scipy and Pyxll for more details. Details of usage are shown in the screen-shot below (also included in the download file).:

Glob_to_Loc3 and Loc_to_Glob3 functions

Glob_to_Loc3 and Loc_to_Glob3 functions

The example below shows input for a trapezoidal plate element, followed by results from the FEA program Strand7:

glob_loc3-0a

glob_loc3-1

For a 3 Node beam element, using the Strand7 definition of the beam principal axes, use the Axtype = 3 option as shown below.  In this case the beam orientation is defined by the 3 node coordinates, with an additional rotation of 30 degrees.
glob_loc3-0b

glob_loc3-2

Posted in Coordinate Geometry, Excel, Finite Element Analysis, Frame Analysis, Link to Python, Maths, Newton, Strand7, UDFs, VBA | Tagged , , , , , , , | 3 Comments

The angle between two vectors, Python version

Posted on 01/03/2014 by dougaj4

I posted a VBA function to return The angle between two vectors, in 2D or 3D last year, and have just discovered that Python and Numpy are lacking this function.  Since all the suggested code I found in a quick search used:

Cos θ = (a.b)/(|a||b|)

which gives inaccurate results for small angles, I have written my own, using the same procedure as the VBA version:

Tan θ = |(axb)|/ (a.b)

Here is the lengthy code:

import numpy as np
import numpy.linalg as la

@xl_func("numpy_row v1, numpy_row v2: float")
def py_ang(v1, v2):
    """ Returns the angle in radians between vectors 'v1' and 'v2'    """
    cosang = np.dot(v1, v2)
    sinang = la.norm(np.cross(v1, v2))
    return np.arctan2(sinang, cosang)

For details on how to link to Python functions from Excel, using Pyxll, see: Installing Python, Scipy and Pyxll ; also an updated Glob_to_Loc function, using the py_ang function, will appear within the next few days.

Posted in Coordinate Geometry, Excel, Link to Python, Maths, Newton, NumPy and SciPy | Tagged , , , | 10 Comments

Using Frame4Buckle with the Alglib solver

Posted on 01/03/2014 by dougaj4

The Frame4Buckle spreadsheet carries out a buckling analysis of a column or strut, which may be divided into any number of segments with varying cross section details, allowing the analysis of stepped or tapered members.  The spreadsheet includes a VBA solver which works well for up to about 20 segments, but becomes very slow for 50 or more segments.  Also included is the option to call a much faster external compiled solver, using the ALGLIB library, but this requires the installation of two additional interface files (ALMatrixLib.tlb and ALMatrixLib.dll), and the AlgLib dll file (Alglibnet2.dll).  These files are now included in the download zip file: Frame4Buckle.zip, and detailed step by step installation instructions are given at: Frame4; now with added Alglib.  The Alglib solver has been tested on systems with 32 bit and 64 bit windows, but not with 64 bit Excel.

Note that if you have already installed the Alglib files to run the Frame4 spreadsheet it is not necessary to change anything.  Also if the Alglib files are not installed, or are not working, the spreadsheet should automatically switch to the VBA solver.

Finally, for those with Python and Pyxll installed, I will soon be posting versions of the Frame4 and Frame4Buckle spreadsheets using Python solvers.

In case of any problems with installing the files or running the spreadsheet, please leave a comment here.

Posted in AlgLib, Computing - general, Finite Element Analysis, Frame Analysis, Link to dll, Newton, VBA | Tagged , , , , , | 5 Comments

Rabbits, Foxes, and Lorenz Attractors

Posted on 23/02/2014 by dougaj4

Following comments here and here I have added two examples to the ODE Solver spreadsheet showing use of the ODE function to solve systems of differential equations with two or more coupled equations. The new version (including full open source code) may be downloaded from ODESolver.zip.

The first new example is the system of equations for the Lorenz-Attractor.  As for the examples given previously, it is necessary to create a short VBA function to evaluate each of the differential equations for given values of the variables and coefficients.  This function is called by the Alglib ODE solver (included with the download file) to solve the system of equations for any specified series of steps:

Lorenz Attractor Solver

Results for coefficients as used by Lorenz:

ODE8-1

The second example is the classic predator-prey system, where increasing prey numbers are limited by increasing numbers of predators, until the prey animals go into a rapid decline, followed by decline in predators, until prey numbers start to increase again. This example was taken from the document on solution of differential equations at the XNumbers site: ODE Tutorial

Predator-Prey Solver

ODE8-2

Posted in AlgLib, Differential Equations, Excel, Maths, Newton, UDFs, VBA | Tagged , , , , , , , , | 2 Comments

Skydrive becomes Onedrive

Posted on 21/02/2014 by dougaj4

As noted in the previous post, the free on-line disc space provided by Microsoft is no longer called Skydrive, but is now known as Onedrive.  On this occasion the change is not due to a desperate bid by their marketing department to combat the dominance of Google and Apple  in the on-line world, but rather a law suit by another company who claim to own the word “Sky”, which claim a British court decided to be valid.

For now, links to Skydrive still work, and if you try to generate an embedded link for use on WordPress from the new Onedrive, it won’t work.  The links generated by Microsoft have to be modified to actually work with the WordPress software, so WordPress automatically edits them whenever you save.  Unfortunately this process looks for the word “skydrive”, which is no longer to be found, so the link is deleted.  The solution is simple: generate the link in Onedrive, copy and paste into the WordPress editor (in text view), then just change the “one” in onedrive to “sky”  (see update below).

How long the skydrive links will continue to work, I don’t know, but for now this seems to be the only simple way to get a Sky/Onedrive embedded link to work in WordPress.

WordPress Forum discussion on the topic:
Skydrive to Onedrive

Edit 23 Feb 2014:

The WordPress developers have now updated their link routines to recognise “onedrive”, so the automatic link generated by the Onedrive site should work without modification.

Posted in Computing - general | Tagged , , , | 1 Comment