Buckling design of submerged arches via shape parameterization

Abstract

Several of the geometric solutions obtained from the funicular design of submerged plane arches reach their critical buckling loads under service conditions. Consequently, the arch geometry must be modified, and then the bending moment increases considerably. Previous works have shown that the funicular shape of a submerged arch is close to either a parabolic or an elliptical form (depending on the water depth, the axial compressive force, and the arch height). In this work, such funicular shape is approximated using a parametric function of these two conical forms. Following this parameterization, the arch shape is optimized via an evolutionary algorithm taking into account its geometrically nonlinear behavior. As a result, the optimized shape shows a significative reduction in the second‐order bending stresses, due to a redistribution of the internal forces along the arch length. These results may find interesting applications in the optimal structural design of, among others, recreational underwater installations.

A Class of Efficient Sixth-Order Iterative Methods for Solving the Nonlinear Shear Model of a Reinforced Concrete Beam

“…where Equation ( 14) represents the strain compatibility, being ∆ε p and ε p the strain by imposition of the prestressing system and the strain of the prestressing strand, respectively, and Equation ( 15) represents the stress-strain relation for the prestressing steel, being f yp and E p its yield stress and elastic modulus, respectively. In summary, for a given value of tensile principal strain in concrete, ε 1 , where such strain works as an input parameter, the shear model for the prediction of the load-deformation behavior of a prestressed concrete beam is based on the nonlinear system of Equations (3)(4)(5)(6)(7)(8)(9)(10)(11), with to 10 equations (notice that Equation ( 13) is actually two equations in turn) in the 10 unknowns (θ, ε x , ε t , ν, ε 2 , σ 2 , σ s,x , σ s,t , ε p and σ p ).…”

“…The implementation of these models usually requires the application of numerical methods for solving the corresponding nonlinear equations, such as, for example, Newton-type methods [3]. In fact, the correct solver for solving a nonlinear problem is often a choice between computational cost and accuracy [4][5][6][7]. Moreover, in this work the previous determination of a solvability region using algebraic procedures is also necessary in order to improve the efficiency of the numerical solver, as indicated at Section 2.…”

Submerged Arches Optimal Design With a Multi-Method Ensemble Meta-Heuristic Approach

“…This restriction is not usually included in the design of submerged arches. However, it is important to estimate it prior to the construction of the structure, since deflections imply non-linearity behaviour [35] and in some cases it may entail an irreversible damage in the structure. Every arch shape is then evaluated and its maximum bending moment is calculated.…”

Parametric Iterative Method for Addressing an Embedded-Steel Constitutive Model with Multiple Roots

“…Nonlinearity usually arises in structural models [1,2]. In particular, materials such as reinforced concrete involve nonlinear stress-strain relationships in the mechanical model.…”