Michael Jäger

The calculation of moments of area is one of the most fundamental aspects of engineering mechanics for calculating the properties of beams or for the determination of invariants in different kind of geometries. While a variety of shapes, such as circles, rectangles, ellipses, or their combinations, can be described symbolically, such symbolic expressions are missing for freeform cross-sections. In particular, periodic B-spline cross-sections are suitable for an alternative beam cross-section, e.g., for the representation of topology optimization results. In this work, therefore, a symbolic description of the moments of area of various parametric representations of such B-splines is computed. The expressions found are then compared with alternative computational methods and checked for validity. The resulting equations show a simple method that can be used for the fast conceptual computation of such moments of area of periodic B-splines.

The calculation of moments of area is one of the most fundamental aspects of engineering mechanics for calculating the properties of beams or for the determination of invariants in different kind of geometries. While a variety of shapes such as circles, rectangles, ellipses or their combinations can be described symbolically, such symbolic expressions are missing for freeform cross-sections. In particular, periodic B-spline cross-sections are suitable for an alternative beam cross-section, e.g. for the representation of topology optimization results. In this work, therefore, a symbolic description of the moments of area of various parametric representations of such B-splines is computed. The expressions found are then compared with alternative computational methods and checked for validity. The resulting equations show a simple way for fast conceptual computation of such moments of area of periodic B-splines.

Truss structures are a stiff, economical, and efficient lightweight design, the limiting factor of these structures are usually the load transfer elements. This paper presents an analytical design method for optimized adhesive tubular lap joints between CFRP tubes and aluminium inserts. The analytically optimized design agrees very well with the numerical simulations and experimental results. Although the experiments show a highly non-linear behaviour, where a linear elastic correlation is expected, the total load capacity is only reached when the adhesive is fully plasticised.

Trusses represent an economical; rigid and effective lightweight construction method. However; the connecting parts (nodes) between the struts are a design challenge; especially in highly optimized trusses. Several struts with different geometries (diamet