Geometrically nonlinear finite element analysis of a glulam timber dome
A finite element modeling and geometrically nonlinear static analysis of glued-laminated timber domes is presented. The modeling and analysis guidelines include: the generation of the geometry, the selection of finite elements to model the components of a dome (beams, purlins, connections, and tension ring), the specification of boundary conditions, the specification of material properties, the determination of a sufficiently accurate mesh, the determination of design loads and the specification of load combinations, the application of analysis procedures to trace the complete response of the structure, and the evaluation of the response. The modeling assumptions and analysis procedures are applied to a dome model whose geometry is based on an existing glulam timber dome of 133 ft span and 18 ft rise above the tension ring. This dome consists of triangulated networks of curved southern pine glulam members connected by steel hubs. The members lie on great circles of a spherical surface of 133.3 ft radius. The dome is covered with a tongue-and-groove wood decking, which is not considered in this study. Therefore, the surface pressures are converted into member loads and then discretized into nodal concentrated loads.
A geometrically nonlinear, 3-d, 3-node, isoparametric beam element for glulam beams is formulated, and a program is developed for the analysis of rigid-jointed space frames that can trace the response of the structure by the modified Newton-Ralphson and the modified Risk-Wempner methods. The material is assumed to be continuous, homogeneous, and transversely isotropic. The material properties are assumed to be constant through the volume of the element. The transverse isotropy assumption is validated for southern pine by testing small samples in torsion. The accuracy of the modeling assumptions for southern pine glulam beams is experimentally verified by testing full-size, curved and straight, glulam beams under combined loads. The results show that the isobeam element can accurately represent the overall linear response of the beams. However, to analyze glulam domes with the program, connector elements to model the joints and a truss element to model the tension ring must be added. Therefore, the finite element program ABAQUS is used for the analysis of the dome model.
Three dead-load/snow-load combinations are considered in the analysis of the dome model. The space frame joints and the purlin-to-beam connections are modeled with 2-node isobeam elements. A 3-d, 2-node, truss element is used to model the tension ring. Three distinct analyses are considered for rigid and flexible joints: a linear analysis to check the design adequacy of the members. A linearized eigenvalue buckling prediction analysis to estimate the buckling load, which provided accurate estimates of the critical loads when rigid joints were specified. Finally, an incremental, iterative, geometrically nonlinear analysis to trace the complete response of the structure up to failure. It is shown that elastic instability, which is governed by geometric nonlinearities, is the dominant failure mode of the test dome. At the critical load, the induced element stresses remained below the proportional limit of the material. A discussion of the results is presented, and recommendations for future extensions are included.