Admissible Functions Research Articles

Pareto-optimal reinsurance under individual risk constraints

This paper studies the design of Pareto-optimal reinsurance contracts in a market where the insurer and reinsurer maximize their expected utilities of end-of-period wealth. In addition, we assume that the insurer and reinsurer wish to control their solvency risks, which are defined through distortion risk measures of their end-of-period risk exposures. To prevent ex post moral hazard, the no-sabotage condition is exogenously imposed on the set of ex ante admissible indemnity functions. By adopting piece-wise linear distortion functions for the risk measures, we partition the domain of the loss into disjoint pieces as per the features of distortion functions and then derive the parametric form of the optimal indemnity function over each piece, where the parameters are left for numerical optimizations. A concrete example where both the insurer and reinsurer apply Range Value-at-Risk is studied in detail.

Vibration Analysis of Rotating Combined Thin-Walled Shells With Multiple Conical Segments

Abstract In this paper, vibration analysis of rotating combined thin-walled shells with multiple conical segments has been carried out. Considering the centrifugal force, Coriolis force, and initial hoop tension due to rotation, the elastic strain energy and kinetic energy of a single rotating conical shell are expressed based on Love’s first approximation theory. The artificial springs are introduced to simulate the connections of adjacent conical shells and the boundaries of the rotating combined thin-walled shells. Taking characteristic orthogonal polynomial series as the admissible functions, the Rayleigh–Ritz method is employed to derive the frequency equations of the combined shell and corresponding vibration characteristics are then obtained. Given that the cylindrical shell and annular plates can be regarded as conical shells with semi-vertex angles of 0 deg and 90 deg, respectively, the solution given is also available for the vibration analysis of rotating combined thin-walled shells comprised of any segments of cylindrical, conical shell, and annular plate. As examples of rotating combined thin-walled shells with two and five segments, vibrations of rotating conical–conical joined shell and cylindrical–conical–cylindrical–conical–cylindrical joined shell are investigated in the paper. Traveling wave frequencies and corresponding mode shapes are shown, and the effects of rotating speed, circumferential wave number, spring stiffness, and semi-vertex angles on the vibration behavior are given in detail.

Development of an analytical model for the flexural vibration of fish bone active camber structures with truncated, variable thickness partitions

The need for smooth, gapless mechanisms that offer superior aerodynamic performance has been the prime mover for a wide range of studies on the morphing concepts from the early years of the twenty-first century. In light of the importance of novel analytic means for inspecting such structures, this article describes a comprehensive dynamic model for the flexural vibration of a special type of morphing structure known as fish bone active camber (FishBAC). In view of the shortcomings of previous models, the developed procedure considers the variable thickness of the central spine of FishBAC as well as the possibility of arbitrary truncations in its numerous partitions to offer more accurate results. A general idea is first proposed based on the assumptions of classical plate theory for such partitioned structures. The equations are derived using the energy method and the assumption of artificial springs to satisfy the continuity of shear force and bending moment along the connecting lines between partitions. A robust Rayleigh-Ritz method along with a set of fast-converging admissible functions is presented to solve the governing equations of motion. Combined with the power of Mathematica and validated by other analytic models and finite element codes, this technique can be used to deal with a plethora of similar systems while paving the path for the dynamic analysis of FishBAC built around various airfoils.

Higher differentiability of solutions for a class of obstacle problems with non standard growth conditions

We are going to prove a higher differentiability result for the solutions to a class of variational obstacle problems of the formmin⁡{∫ΩF(x,Dω)dx:ω∈Kψ(Ω)} where the function F satisfies non standard growth conditions of the type ν|z|p≤F(x,z)≤L(1+|z|q) with 1<p<q and 0<ν<L; in particular we will consider the subquadratic case: 1<p<q<2.Moreover Ω⊂Rn,n>2 is a bounded open domain, the function ψ:Ω→[−∞,+∞) is called obstacle and it belongs to the Sobolev class W1,p(Ω), p>1 and Kψ(Ω) is the set of admissible functions, i.e.Kψ(Ω)={ω∈u0+W01,p(Ω):ω≥ψa.e.inΩ} where u0 is a fixed boundary value. The main result consists in showing thatDψ∈Wloc1,r(Ω)⇒(1+|Du|2)p−24Du∈Wloc1,2(Ω) under the conditions:qp<1+1n−1r,1<p<q<2<n<r.

Random vibration study of functionally graded porous curved beams with elastically restrained ends

Firstly, the random vibration characteristics of functionally graded porous (FGP) curved beams with elastically restrained ends are studied. An efficient model is presented by the Timoshenko beam theory and spectral-Chebyshev method. In this paper, three different types of porous distribution are considered, and the relationship between porosity coefficient and material parameters is determined according to the typical mechanical properties of open cell foam metal. Four types of curved beams with different curvatures are selected for the study, which are elliptical beam, parabolic beam, hyperbolic beam and circular beam. The one-dimensional admissible displacement functions of the FGP curved beam are constructed by Chebyshev polynomials of the first kind with Gauss-Lobatto sampling points discretization. Three artificial boundary springs are used to impose elastic boundary constraints at the ends of the curved beam. The pseudo excitation method is used to apply stationary and non-stationary random excitations, including point excitation and base acceleration excitation. The stationary random vibration responses of the FGP curved beam with different boundary conditions, involving the power spectral density (PSD) and root mean square (RMS) values of displacement, velocity and acceleration, are calculated and agreed well with the finite element method (FEM). At last, the RMS values of the non-stationary random vibration response of the FGP curved beam are given.

On the properties of the set of trajectories of nonlinear control systems with integral constraints on the control functions

MSC: 93C10, 93B03, 93B35 DOI: 10.21538/0134-4889-2022-28-3-274-284 The control systems described by nonlinear differential equations and integral constraints on the control functions are studied. Admissible control functions are chosen from a closed ball of the space $L_p,$ $p\in (1,\infty]$, with radius $r$ and centered at the origin. It is proved that the set of trajectories

Large amplitude free vibration of sandwich beams with flexible core and FG Graphene Platelet Reinforced Composite (FG-GPLRC) face sheets based on extended higher-order sandwich panel theory

The present article deals with the nonlinear free vibration analysis of sandwich beams with flexible core integrated with face sheets which are reinforced with graphene platelets (GPLs). Each layer of the composite media may have a different amount of graphene platelets which leads to a functionally graded (FG) distribution. The elastic modulus of the reinforced composite (RC) is calculated via the Halpin–Tsai model. Following the extended higher order sandwich panel theory (EHSAPT) which captures the core thickness compressibility effect and the axial stress of the core, the complete set of governing equations is obtained using the Lagrangian formulation. To analyze the effect of the inclusion of nonlinear terms in the core, hitherto not reported in the literature, results are computed considering the von Kármán type of geometrical nonlinearity assumptions for the core and face sheets. With the aid of the Ritz-based method, Chebyshev functions are implemented as admissible functions of the displacement fields. Furthermore, the nonlinear governing equations are solved using a direct displacement control technique. As the EHSAPT can be applied with any combination of the core and face sheets and not only the soft cores that the other theories demand, the results for the sandwich beam with stiff core and consist of functionally graded carbon nanotube-reinforced composite face sheets provided for validation. Since this study is the first in the open literature to develop nonlinear vibration of the sandwich beam based on EHSAPT, Timoshenko beam theory (TBT) is also applied to investigate the problem and to extract nonlinear frequencies with various stiffness of the core, meanwhile, the results are compared with those obtained by the EHSAPT. Parametric studies are conducted in detail to examine the influences of weight fraction and distribution pattern of graphene platelets, core to face sheet thickness ratio, boundary conditions, length to thickness ratio, and amplitude of vibrations. It is found that by increasing the stiffness of the core, the inclusion of nonlinear effects in the core as well as the face sheet strain nonlinearity is more significant. Finally, the nonlinear vibration analysis of sandwich beams can change the variation trend of frequency predicted in the linear analysis, and the different trends are observed depending on the vibration amplitude.

Moving load response of ring-stiffened sandwich truncated conical shells with GPLRC face sheets and porous core

As a first attempt, the dynamic responses of sandwich truncated conical shells with graphene platelets reinforced composite (GPLRC) face sheets, porous core and circumferential stiffeners under asymmetric internal ring-shaped moving load are analyzed. The face sheets and porous core are reinforced by uniformly distributed and randomly oriented graphene platelets (GPLs). The spatially discretized equations of motion subjected to different boundary conditions are derived based on the first-order shear deformation theory (FSDT) using the Chebyshev–Ritz method. The admissible functions of the field variables are constructed using the trigonometric functions in the circumferential direction and the one-dimensional Chebyshev polynomials in conjunction with the suitable boundary functions in the meridional direction. The Newmark’s time integration scheme is employed to solve the resulting ordinary differential equations of motion. The robustness and accuracy of the method are demonstrated through the different examples. After that, the influences of core porosity, face sheets, GPLs parameters, shell geometric parameters, boundary conditions, and the arrangement, number and size of stiffeners on the results are explored. The results show that porosity, face sheets, the location, size and number of stiffeners play important roles on the dynamical response of the shells under investigation. Also, it is found that the critical load velocity decreases by increasing the porosity coefficients and increases by increasing the number of ring-stiffeners.

CENN: Conservative energy method based on neural networks with subdomains for solving variational problems involving heterogeneous and complex geometries

We propose a conservative energy method based on neural networks with subdomains for solving variational problems (CENN), where the admissible function satisfying the essential boundary condition without boundary penalty is constructed by the radial basis function (RBF), particular solution neural network, and general neural network. Loss term is the potential energy, optimized based on the principle of minimum potential energy. The loss term at the interfaces has the lower order derivative compared to the strong form PINN with subdomains. The advantage of the proposed method is higher efficiency, more accurate, and less hyperparameters than the strong form PINN with subdomains. Another advantage of the proposed method is that it can apply to complex geometries based on the special construction of the admissible function. To analyze its performance, the proposed method CENN is used to model representative PDEs, the examples include strong discontinuity, singularity, complex boundary, non-linear, and heterogeneous problems. Furthermore, it outperforms other methods when dealing with heterogeneous problems.

Acoustic field characteristic analysis of the rotary acoustic cavity coupled system

The rotary acoustic cavity coupled system can be generated in working conditions of aviation, aerospace, ship, machinery, and other fields. The rotary acoustic cavity includes cylindrical, spherical, and conical acoustic cavities, which integrates into the unified analysis model by iso-parametric transformation in finite element method. To study the acoustic field characteristic of rotary acoustic cavity coupled system, a unified analysis model of rotary acoustic cavity coupled system is established: First, the acoustic field characteristic of the coupled system is researched by improved Fourier series method, and the admissible sound pressure function is constructed by three-dimensional modified Fourier series. Then, the acoustic field domain energy functional is established, and the coupled domain energy functional including the coupled potential energy between the sound cavities is introduced to acquire the total energy functional of the coupled system. Finally, the energy equation is solved by Rayleigh–Ritz method, and the natural frequency and corresponding mode of the coupled system are obtained. The unified analysis model demonstrates excellent convergence and accuracy, which is verified by the results of finite element method. Sound pressure responses of the coupled system are obtained by introducing the internal point sound source excitation. The effect of relevant parameters of the coupled system on natural frequency and sound pressure response is investigated, which can provide theoretical guidance for vibration and noise reduction.

Characteristic functions and functional models on noncommutative varieties

In this paper we develop a Sz.-Nagy-Foiaş type theory of characteristic functions and functional models on noncommutative domains and varieties in \(B(\mathcal{H})^n\), where \(B(\mathcal{H})\) is the algebra of all bounded linear operators on a Hilbert space \(\mathcal{H}\), associated with admissible free holomorphic functions for operator model theory. This includes, in particular, a large class of commutative domains in \(B(\mathcal{H})^n\). In the commutative case, the characteristic functions are multipliers of reproducing kernel Hilbert spaces on domains in \(\mathbb{C}^n\). We also show that the universal operator model associated with any admissible noncommutative variety has the quasi-wandering property.

A 2D-graph model-based heuristic approach to visual backtracking security vulnerabilities in physical protection systems

The paper presents a heuristic backward path tracing algorithm in combination with optimization EASI model for effective estimation of time delay remaining after detection TTR. The heuristic backward search algorithm is implemented based on a graph-based model representation of a hypothetical facility for visual path tracing and planning. A comparative analysis between the implementation of non-heuristic and heuristic search for the most vulnerable adversary paths identification in terms of the shortest distance (d), probability of detection (PD), and probability of interruption (PI) on different intrusion detection fields is carried out and in detail discussed. The comparison results show that the global optimal solutions can be obtained using the heuristic backward path tracing algorithm with high search efficiency and accuracy. The knotty problem encountered in unknown path generation under uncertainties for calculating TTR and PI is effectively solved for admissible and consistent heuristic function design.

An analytical method for vibration analysis of arbitrarily shaped non-homogeneous orthotropic plates of variable thickness resting on Winkler-Pasternak foundation

A highly applicable analytical approach is proposed for the dynamic analysis of composite plate structures with complex variation of geometric characteristics (shape/boundary and thickness) and material characteristics (Young's modulus, shear modulus and density) resting on Winkler-Pasternak foundation with general elastic boundary conditions. Boundary conditions of the plates are treated by the penalty method, so that the admissible functions can use any complete set of orthogonal polynomials, which is obtained by Gram-Schmidt orthogonalization process. The interval where the in-plane coordinate variables of the plate domain are located can be selected as the orthogonalization intervals, so as to avoid the normalization procedure of coordinates and simplify the operation process. In order to calculate the energy integral of the arbitrarily shaped plate, the plate domain segmentation strategy is introduced. To verify the effectiveness and accuracy of the proposed method, convergence study and numerical verifications for different orthogonalization intervals, weight functions, penalty spring stiffness and the truncation number of orthogonal polynomials are carried out. Taking regular hexagonal plates as examples, the effects of the parameters of thickness, nonhomogeneity and foundations on the vibration characteristics of the plates are studied. These results can be used as reference data for future research.

On the thermal buckling and postbuckling responses of temperature-dependent graphene platelets reinforced porous nanocomposite beams

In this work, thermal buckling and postbuckling behaviors of graphene platelet (GPL) reinforced porous nanocomposite beams are studied with inclusion of temperature-dependent material properties for the first time. The Halpin-Tsai micromechanics model and extended rule of mixture as well as open-cell metal foam model are applied to determine the effective properties of nanocomposites. A high order shear deformation theory with the aid of von Kármán nonlinearity is implemented to yield governing equations corresponding to thermal buckling and postbuckling problems. The numerically stable admissible functions constructed through Gram-Schmidt procedure are developed to describe end restraints of beams. An eigenvalue equation without geometric nonlinearity is solved to obtain critical buckling temperatures, while an iterative methodology is implemented to find the temperature-dependent thermal postbuckling paths of beams. An extensive numerical study is performed to check the influences of internal pores and GPL reinforcements on the thermal buckling and postbuckling responses of GPL-reinforced metal foam beams. It is found that the temperature-dependency of material properties plays important roles on thermal buckling/postbuckling behaviors of GPL-reinforced porous beams, and dispersing more GPLs on the upper and lower surfaces and fabricating more internal pores near central portion of beams can improve thermal instability-resistance capability of composite structures.

Efficient Computation and Informative Estimation of h+ by Integer and Linear Programming

We investigate modeling cost optimal delete-free STRIPS Planning by Integer/Linear Programming (IP/LP). We introduce two IP models and their LP relaxations based on a recently formulated representation of relaxed plans, named causal relaxed plan representation. The new models are produced by enforcing acyclicity in so-called causal relation graphs using vertex elimination and time labeling methods. We empirically show that while the vertex elimination based method outperforms the time labeling based method and all previously introduced domain independent methods for computing the exact values of h+, the time labeling based LP model is faster to solve compared to its vertex elimination based alternative, making it more suitable for using as heuristic function for optimal planning. We also theoretically analyze the admissible heuristic functions obtained by solving our LP models, and prove that the vertex elimination based heuristic is at least as informative as the time labeling based heuristic. Moreover, our empirical analysis shows that our vertex elimination based heuristic, which is a novel admissible estimation of h+, often has information complementary to that of the LM-cut heuristic.

Unified series solution for thermal vibration analysis of composite laminated joined conical-cylindrical shell with general boundary conditions

We establish a unified series solution for the free, steady-state, and transient vibration analysis of composite laminated joined conical–cylindrical shells under thermal environment. Additionally, artificial spring technology was used to deal with the general boundary conditions and continuity conditions for the common edge of the joined conical–cylindrical shell. The spectro-geometric method (SGM) and the first-order shear deformation theory (FSDT) were employed to derive the dynamic equation of motion. Subsequently, the displacement admissible functions were expressed in a general form comprising the Fourier sine and cosine terms to manipulate the arbitrary boundary conditions without pre-satisfying them. Moreover, the convergence and solution efficiency of the proposed approach was demonstrated by comparison with the finite element method solution. Furthermore, the influence of critical factors on the vibration behaviors of the coupled shells was investigated, with findings that would aid in their structural design.

Rotation-Induced Geometrical Stiffening of a Tapered, Pretwisted Blade

A linear geometrical stiffening model is developed for a rotating beam with an asymmetric cross section undergoing coupled stretch–bending–torsion motion. The model is verified for a twisted and tapered Timoshenko beam mounted on a rotating hub with a presetting angle. The floating frame of reference formulation is adopted where the configuration of the deformable beam is described by using different coordinate systems. Three coordinate systems, viz., inertial reference frame attached to the center of the rigid hub, local reference frame attached to an arbitrary point on the elastic axis of the undeformed beam, and body reference frame attached to the point on the elastic axis of the deformed beam, are defined. The global position vector of an arbitrary point on the beam is specified using a coupled set of reference and elastic coordinates. Reference coordinates define the location and orientation of a body reference frame, and elastic coordinates describe the beam deformation about the body reference frame. For a rotating beam problem, reference and elastic coordinates give the angular displacements of the hub and elastic deformations of the beam, respectively. The expressions for the kinetic and strain energy of the deformable beam are derived. The inertial coupling between the reference and elastic coordinates in the kinetic energy expression is identified as a gyroscopic coupling term. Further, the inertial mass matrix, spin softening matrix, and centrifugal stiffening matrix are obtained from kinetic energy expression. The elastic stiffness matrices, which are independent of elastic coordinates, are derived from strain energy expression. According to the Rayleigh–Ritz method, the elastic coordinates are expressed using a series of admissible functions that satisfy the geometric boundary conditions of a fixed-free beam. The ordinary differential equations of motion are then derived using Lagrange’s equations. A set of dimensionless parameters is identified after the nondimensionalization of the equations of motion. Due to the skew-symmetric nature of the gyroscopic coupling matrix, the eigenvalue problem is not amenable to classical modal analysis. Therefore, a complex modal analysis method is used to determine the modal characteristics. The results from the present model are verified with those available in the literature. The results are also compared with those obtained from the three-dimensional finite element method using ANSYS. The effect of these dimensionless parameters on the modal characteristics of a rotating blade is studied.

Adaptive algorithms for blind channel equalization in impulsive noise

The unsupervised adaptive mitigation of intersymbol interference in an additive impulsive noise environment, modeled as generalized Gaussian, is dealt in this work. The theory of statistical invariance, Wijsman’s theorem, is used to develop a maximal-invariant test to discriminate equally-likely pulsed signals against impulsive disturbance leading to an admissible cost function for blind equalization. The cost function is optimized to realize two adaptive equalizers capable of not only mitigating intersymbol interference but also robust to impulsive disturbance. Numerical simulations, obtained on a baseband digital microwave radio system for amplitude-phase shift keying signaling in an additive (generalized Gaussian and symmetric-alpha stable) impulsive environment, confirm the admissibility of the proposed equalizers in terms of robustness and steady convergence.

Fixed Points of Proinov Type Multivalued Mappings on Quasimetric Spaces

In this paper, we obtain new results which have not been encountered before in the literature, in multivalued quasimetric spaces, inspired by Proinov type contractions. We use admissible function as proving theorems. We also give an example that supports our theorems.

Petri-Net-Based Scheduling of Flexible Manufacturing Systems Using an Estimate Function

In this paper, a novel admissible estimate function is proposed to schedule flexible manufacturing systems (FMSs) by using heuristic search. The FMSs to be scheduled are modeled by P-timed Petri nets. The problem is to make the system evolve from the initial marking to a given final marking by firing a sequence of transitions. The structure of jobs in an FMS is always symmetrical to utilize the shared resources, but the processing time of each job is asymmetrical to reduce the global process time. By utilizing the structural symmetry of a Petri net model of an FMS, a partial reachability graph is generated such that the notorious state explosion problem is mitigated. For each generated marking, the proposed estimate function is used to provide an estimated cost for firing the transition sequence. Then, we can select the marking with the smallest cost from the generated markings and compute its successors. This process is continued until the system reaches the final marking. With the proposed method, the performance is evaluated in terms of the cost of the obtained transition firing sequence and the number of the expanded markings. The cost provided by the proposed estimate function is closer to the optimal cost than the previous work, i.e., the proposed method can find a transition firing sequence with less expanded markings and minimal process time from a marking to the final marking. Experimental results are used to demonstrate and evaluate the proposed approach.