A form-finding method for membrane shells with radial basis functions
نویسندگان
چکیده
The equilibrium of a membrane shell is governed by Pucher’s equation that described in terms the relations among external load, shape shell, and Airy stress function. Most existing funicular form-finding algorithms take discretized network as input find shape. When resulting does not meet user’s expectation, there no direct clue on how to revise input. paper utilizes method radial basis functions, which typically used smoothly approximate arbitrary scalar represent C ∞ smooth shapes functions shells. Thus, boundary value problem solving can be converted into least-squares regression problem, without need discretizing governing equation. provided or function admits solution, algorithm recommends users tweak order an solution. load this easily incorporate vertical horizontal components. latter part might always negligible, especially for seismic hazard zones. This identifies peripheral walls are preferable allow shells carry loads various directions deviating from their original shapes. sufficient supports, also suggest potential eccentricities, could inform design reinforcing beams. • process starts either provisional represented functions. Horizontal compatible with method. Boundary conditions switched increasing weight least squares. restrains important subjected multiple cases.
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Article history: Received 13 April 2012 Received in revised form 10 October 2012 Accepted 27 October 2012 Available online 8 December 2012
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ژورنال
عنوان ژورنال: Engineering Structures
سال: 2022
ISSN: ['0141-0296', '1873-7323']
DOI: https://doi.org/10.1016/j.engstruct.2021.113514