The validity of assumptions (i) and (iii) run quite parallel. Stability is only considered inside a rigid multi-body model and according to the first assumption (i).Ī high span or great depth of the mortar between voussoirs would make the first assumption impossible, (i) Assumption (ii) can be checked a posteriori. Friction between the voussoirs is sufficient to prevent failure due to sliding between them (iii). The assumptions inside this frame are: (i) Constitutive equations are rigid-plastic, with no tensile strength but infinite compressive strength, (ii). The first application of Limit Analysis theory ( Kooharian, 1952) for the analysis and design of masonry structures has being notably expanded and consolidated ( Heyman, 1966, 1969). This paper will describe a wire frame model, either linked with linear elements or representing membrane discretization, with special focus on the case where there is only tension or internal compression force although some procedures are valid for both tension and compression if proper constraints are considered. cable structures, but could also be applied to surface elements, e.g. The funicular concept is not restricted to linear elements, e.g. Additional assumptions would also make it a design tool, as in the case of masonry structures Limit Analysis. 1.2 Funicular analysis versus masonry structuresįunicular analysis refers to the use of a 2D or 3D funicular as an analytical tool at any stage of the analytical process. The Force Density Method, FDM ( Linkwitz & Schek, 1971 Schek, 1974) was developed in the 1970s as a form-finding procedure for cable tensile structures ( Grundig, Moncrieff, Singer, & Ströbel, 2000).įDM was selected for this research due to four main considerations: (1) It manages equilibrium equations in a totally direct way, and is therefore especially suited for a funicular solution (2) equilibrium equations are linearized, which simplifies the numerical process, even though an iterative analysis is usually needed (3) no pre-sizing is required for this method this is a crucial question for many approaches and particularly for the two new applications addressed and (4) the three equilibrium equations are uncoupled, an important property that will be exploited here. The link between form-finding methods and funicular analysis is therefore straightforward. This is also the case for masonry structures when a Limit Analysis approach is used, as the problem here is also based on the funicular concept. The search for an initial shape compatible with a set of loads and constraints is termed form-finding.Ī tensile structure can be seen as a materialization of a 3D funicular. the position of the nodes, is a priori unknown. As a result, their final equilibrium configuration geometry, i.e. Most unstressed 2D and 3D tensile bar structures are kinematically indeterminate. See more Open Accessġ Introduction 1.1 Form-finding versus the Force Density Method Measurement devices (pressure, temperature, flow, voltage, frequency etc.), precision engineering, medical devices, instrumentation for education (devices and software), sensor technology, mechatronics and robotics.
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