Design of Trusses Under Uncertain Loads Using Convex Models

Interval static displacement analysis for structures with interval parameters

“…The ÿnite element model of the given structure consists of 88 nodes and 80 shell elements. The structural parameters are as follows: the thickness of the plate t c is 1cm; the Young's modulus of the element is E c =2:1×10 11 N=m 3 ; the mass density for elements is c = 7:8 × 10 3 kg=m 3 . If E and t are intervals, i.e.…”

Comparison of Fuzzy Set and Convex Model Theories in Structural Design

“…Pantelides and Tzan [24] and Tzan and Pantelides [25] used convex model theory in the seismic design of conventional and active structures. Pantelides and Ganzerli [26] investigated an ellipsoidal convex model to minimise either the structural volume or a selected displacement of a truss, subjected to uncertain loads in both magnitude and direction. The resulting optimal designs were compared to a &worst-case scenario' loading condition.…”

“…The maximised structural response is also called convex response and is identi"ed by the symbol F !-, . This response can be obtained by "nding the extremum of the quantity using Lagrange multipliers [26] or by using convex model superposition [27]. F !-, can be calculated by adding to the magnitude of the nominal response F, the magnitude of the response F, which is obtained by loading the structure with only P multiplied by the percent deviation of P , i.e.…”

“…The actual optimisation calculations for the two methods are not carried out in the present paper. The reader interested in the actual optimisation procedures is referred to related articles [16,26].…”

Static and Sensitivity Analysis of Nonlocal Nanobeams Subject to Load and Material Uncertainties by Convex Modeling

“…The problem analysis is conducted using convex modeling of uncertainties to determine the least favourable conditions to produce the highest deflection. Convex modeling has been used extensively in the past to deal with various engineering problems containing data uncertainties (see Adali et al, 1995a,b;Pantelidis and Ganzerli, 1998;Jiang et al, 2007;Kang and Luo, 2009;Hu and Qiu, 2010;Radebe and Adali, 2013). For further information, the reader is referred to the review articles by Wang et al (2001) and the book by Ben-Haim and Elishakoff (1990).…”