Stressed spline structures.
This thesis concerns stressed spline structures. A spline is defined as `an initially
straight member with identical second moment of area about any axis
perpendicular to its centroidal axis, bent into a spatial curve'. An analytical
proof is presented to show that the spline's torsional stiffness is of no importance
in its analysis (provided construction details do not introduce any torsional
moment). This paramount proof allows the formulation of a spline analysis that
relies solely on three translational degrees of freedom (3DOF) per node.
Applying this 3DOF analysis to unstrained curves and battened or hoop
supported membranes is approximate since the bending stiffness would
correspond to one direction only.
A series of four test cases validates the proposed 3DOF analysis. The
analysis is first applied to a laterally loaded spline ring, where solution
convergence and the effect of unequal length segment modelling are investigated.
Most significantly, this test case demonstrates that the spline ring has a greater
out-of-plane stiffness than a pre-bent ring. This feature lies at the basis of spline
stressed membranes - the spline has superior out-of-plane stiffness under the
action of forces applied by the membrane. The second and third test cases --
buckling of elastica and of a shallow sinusoidal arch -- clearly demonstrate that
the 3DOF analysis is much faster, more accurate, and produces results closer to
the analytical values compared with a 6DOF analysis. The fourth test case
proves the efficiency of the 3DOF analysis through investigating buckling
behaviour and loads of four circular arches under radial loading.
As the torsional stiffness does not enter the 3DOF analysis, the stiffness
of a spline constructed of spliced segments is identical to that of a continuous
spline. In order to demonstrate their feasibility, five medium span (161n-32m)
Glass Fibre Reinforced Plastic (GFRP) and one large span (57nt) steel tensegrity
stressed spline membranes are designed, form-found and analysed under realistic
loading conditions. These design studies show firstly that the spline and
membrane stresses occurring under loading are within acceptable material limits
and secondly that buckling occurs at values much higher than those encountered in reality. This thesis has demonstrated that engineered stressed spline structures,
for which the development of a 3DOF was essential, have great design potential.