Recieved:

04/08/2026

Accepted:

01/10/2026

Page: 

–

doi:

http://dx.doi.org/10.17515/resm2026-1812st0804rs

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16

Seismic performance optimization of reinforced concrete shells generated by the force density method: A nonlinear multilayered approach

Jesús Gerardo Pérez Vega1, Orlando Susarrey Huerta1, Héctor Aureliano Sánchez Sánchez2

1Graduate Studies and Research Section, Higher School of Mechanical and Electrical Engineering (Zacatenco Unit), National Polytechnic Institute (IPN), Mexico City, Mexico
2Graduate Studies and Research Section, Higher School of Engineering and Architecture (Zacatenco Unit), National Polytechnic Institute (IPN), Mexico City, Mexico

Abstract

The construction of concrete shell roofs in Mexico has declined owing to seismic vulnerability and slenderness effects. Traditional form-finding guarantees static equilibrium under self-weight alone and remains inadequate under seismic demand, where stiffness degradation and stress reversal govern the response. Three form-found anticlastic shells with four, six and eight supports were generated by the force density method, which yields compression-dominant configurations before reinforcement is defined. Reinforcement was first designed with the Eurocode 2 three-layer sandwich model, which neglects the compressive contribution of the reinforcement; a nonlinear multilayered formulation was then adopted to resolve the stress state through the shell thickness. Design actions followed NTC-2023; the analyses incorporated initial geometric imperfections, nonlinear buckling, the Takeda hysteretic model and synthetic accelerograms for Mexico City. The shells developed controlled, low-level nonlinear behavior, with compression governing the response and the reinforcement carrying a significant fraction of the compressive demand under stress reversal. Eigenmode-affine imperfections reduced the ultimate capacity by 45.2% to 22.1%, the reduction diminishing with the number of supports: more petals stiffen the shell and raise its capacity, at the cost of ductility. Since imperfections consume so large a share of that capacity, recovering design margin becomes decisive: accounting for the compressive contribution of the reinforcement reduces the required area by 10%, making the multilayered representation a design requirement rather than a refinement. The numerical cracking patterns coincide spatially with the damage documented after the 2017 earthquake in Félix Candela’s Los Manantiales restaurant, supporting a framework transferable to other earthquake-prone regions.

Keywords

Concrete shells; Geometric optimization; Non-linear analysis; Time-history analysis; Form-finding; Earthquake design; Buckling; Stiffness degradation; Force density method; Nonlinear multi-layered model; Geometric imperfections; Seismic reintroduction

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