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A study of the elastic lateral-torsional buckling behaviour of hot-rolled steel beams with flange upstands
Published in Alphose Zingoni, Insights and Innovations in Structural Engineering, Mechanics and Computation, 2016
The commercially available software ABAQUS is used to model and carry out the eigenvalue buckling analysis of the beams. The linear perturbation function was employed for this. This produced eigenvalue modes with values that are multiples of the applied unit load. The general-purpose shell element S4R was used in the models. This element is a 4-node element with reduced integration and hourglass control having 6 degrees of freedom at each node. It is recommended for most applications where shell elements are employed. The ABAQUS benchmarks guide, in a calibration check, indicates that the S4R element produces reasonable buckling load-predictions when compared to the most accurate but computationally more expensive S9R5 element. Equal seeding of the mesh in both vertical and horizontal faces was used in order to keep the element aspect ratio close or equal to one.
Generalized Additive Weighted Multifactorial Function and its Applications to Fuzzy Inference and Neural Networks
Published in Hongxing Li, C.L. Philip Chen, Han-Pang Huang, Fuzzy Neural Intelligent Systems, 2018
Hongxing Li, C.L. Philip Chen, Han-Pang Huang
Chapter 6 has detailed definitions and properties of multifactorial functions. Mulitfactorial functions, which can be used to compose the “states”, are very effective methods in multi-criteria fuzzy decision-making [1]. In addition, the multifactorial function is used to define fuzzy perturbation function [2]. In [3, 4], by means of multifactorial functions, multifactorial fuzzy sets and the multifactorial degree of nearness are given and they are used to deal with multifactorial pattern recognition and clustering analysis with fuzzy characteristics.
Stability of Freight Car Wheelset
Published in A.H. Wickens, The Dynamics of Vehicles on roads and on tracks, 2018
and L is the largest wave length of the frequency spectrum of the track perturbation function. Then, () y¨+a11y+a13y˙+a15ψ˙−a14ψ = −a12(y3−3y2Γ(θ)+3yΓ2(θ)−Γ3(θ))+a11Γ(θ)+Γ˙(θ)a13 () ψ+a21ψ˙+a22ψ−a23y˙+a24y = −a25(y3−3y2Γ(θ)+3yΓ2(θ)−Γ3(θ))−Γ˙(θ)a23+a24Γ(θ)
Duality for composite optimization problem within the framework of abstract convexity
Published in Optimization, 2023
Several efforts have been made for the last twenty years to investigate dualities for optimization problems within the framework of abstract convexity. In [16] strong duality is proved for the infimal convolution of Fenchel's duality. In [17], zero duality gap and exact multiplier of augmented Lagrangian are investigated by using the framework of abstract convexity. While in [18,19] necessary and sufficient conditions are given to achieve minimax equality from a general Lagrangian using the definition of abstract convexity. In the works of Dolgopolik [20], Gorokhovik and Tykoun [21,22], the authors applied abstract convexity to approximate the class of nonsmooth functions and formulate necessary optimal conditions for the global nonsmooth nonconvex problem. The authors in [23] investigated the problem of minimizing the finite sum of arbitrary functions and provided conditions for zero duality gap through infimal convolution dual. On the other hand, in [24], the problem of zero duality gap is studied with the help of the perturbation function.
Characterization of duality for a generalized quasi-equilibrium problem
Published in Applicable Analysis, 2018
Moreover, the ISA is an impactful technique to study duality theory. There have been some duality results about constrained extremum problems at present (see [17–21]). Giannessi has derived nonbinding Lagrangian weak duality theorem from a separation scheme in the image space for constrained extremum problems in [17]. After that, Giannessi et al. have also focused on Wolf duality and shown that the existence of a regular linear separation guarantees the equivalence between Wolfe and Mond–Weir duality under suitable generalized convexity assumptions in [18]. Furthermore, Mastroeni [19] has defined the perturbation function and analyzed the relationship between the subdifferentiability of the perturbation function and the existence of a regular linear separation, the analysis of properties of the perturbation function has led to a characterization of zero duality gap in the image space. Later in [20,21], Zhu and Li have proposed a unified duality scheme for constrained extremum problems by virtue of the class of regular weak separation functions which includes Lagrange-type duality, Wolfe duality and Mond–Weir duality as special duality schemes, and zero duality property has been obtained under some appropriate assumptions.
Equivariant perturbation in Gomory and Johnson's infinite group problem (V). Software for the continuous and discontinuous 1-row case
Published in Optimization Methods and Software, 2018
Chun Yu Hong, Matthias Köppe, Yuan Zhou
Let π be a minimal valid function that is piecewise linear over . Let F be a face of and let . If , then for any effective perturbation function .