Category Archives: Newton

The hole through the middle of the Earth – acceleration

Posted on 29/06/2010 by dougaj4

In my first go at modelling a ball falling through a hole through the middle of the Earth I assumed constant density, and hence the acceleration at any point was proportional to the distance from the centre.  That is of course … Continue reading →

Posted in Differential Equations, Newton | Tagged , , , | 2 Comments

More on buckling columns

Posted on 27/06/2010 by dougaj4

Coincidentally, at about the same time as I wrote about column buckling for a column with a point load on the end, Autar Kaw at The Numerical Methods Guy was writing about buckling of columns under self weight, using the theory of … Continue reading →

Posted in AlgLib, Beam Bending, Excel, Maths, Newton, UDFs, VBA | Tagged , , , , , , | 1 Comment

SplineBeam update

Posted on 20/06/2010 by dougaj4

Previous SplineBeam post I have modified the SplineBeam spreadsheet to allow input of a single span (simply supported or with end constraints), and to optionally allow input of the position of intermediate nodes, rather than dividing each span into equal segment lengths.  This … Continue reading →

Posted in Arrays, Beam Bending, Excel, Frame Analysis, Newton, UDFs, VBA | Tagged , , , , | 1 Comment

Elegant solutions, Column buckling, and the hole through the middle of the Earth

Posted on 19/06/2010 by dougaj4

The previous post presented some examples of solution of differential equations using an iterative process, including the simple harmonic motion problem of a ball falling through an evacuated hole through the middle of the Earth.  The final example was concerned … Continue reading →

Posted in Beam Bending, Differential Equations, Newton | Tagged , , | 5 Comments

Using the AlgLib ODE (Runge-Kutta) Solver with Excel

Posted on 18/06/2010 by dougaj4

Or to be more correct, the AlgLib Cash-Karp Solver, Cash-Karp being a refinement of the Runge-Kutta method of solving ordinary differential equations. Solution of differential equations is an iterative process requiring the repeated application of the solver routine followed by evaluation of … Continue reading →

Posted in AlgLib, Beam Bending, Differential Equations, Excel, Maths, Newton, UDFs, VBA | Tagged , , , , , , , , | 8 Comments