No abstract

The four series oo oo ^ sin(2A: + 1)a/(2A: + 1)2 , J^ cos(2A: + 1)a/{2k + 1)3, 0 0 oo oo YgAlk+Xl(2k + \)1, and ^A2k+i/(2k + ¡)3 0 0 are very slowly convergent for 0 < a < 71 and as A-» 1 ~. Direct summation involves thousands of terms to get the accuracy desired. Plana's summation formula along with Romberg's method of integration significantly and consistently improves the convergence and accuracy for the above series.

No abstract

BeamTool is a qualitatively powerful beam-analysis tool with significant educational value. The theory behind BeamTool, ideal for automation, is traditionally mentioned in textbooks but is not usually the approach taught in class because of the amount of work involved. In BeamTool, this classical beam theory is coupled via a graphical user interface to a symbolic solver. Each problem is solvable both symbolically and numerically, the former with the amount of detail that one finds in the classic design reference Roark's Formulas for Stress and Strain, and the latter with interactively requested shear, moment, slope, displacement, and stress plots. BeamTool is written in Microsoft Visual Cþþ and runs on Windows. The symbolic solutions are afforded by Maple, which has to be installed on the user's PC.

An axisymmetric floating plate of infinite extent is subjected to prescribed dynamics under the action of a point load. The problem of inverting the forcing is studied mathematically with a view to classifying its properties within the framework of integral equations. In the process, the floating plate problem is shown to be moderately ill-posed and the rate of change of the forcing is shown to initially be directly proportional to the acceleration of the plate. This latter result is incorporated into the numerical study that follows. Throughout the paper, a model problem is used as an analytical and numerical benchmark.