Static Formulation Research Articles

Static and Kinematic Formulation of Planar Reciprocal Assemblies

Planar reciprocal frames are two dimensional structures formed by elements joined together according to the principle of structural reciprocity. In this paper a rigorous formulation of the static and kinematic problem is proposed and developed extending the theory of pin-jointed assemblies. This formulation is used to evaluate the static and kinematic determinacy of reciprocal assemblies from the properties of their equilibrium and kinematic matrices.

A simulation analysis for the re-solving issue of the network revenue management problem

The classic dynamic programming approach is not applicable to the airline network revenue management (RM) problem of a practical size due to the curse of dimensionality. Many heuristic methods, including the most popular bid-price control approach, generate the approximate control decisions based on various static formulations, which need to be re-solved to take into account the dynamic features of the problem. By a simulation experiment, this study examines the re-solving issue of the bid-price method and tests a new method, the parameterized function approach, in which no problem-resolving is required. Based on the results, the parameterized function approach is found to be a promising alternative. As for the bid-price control approach, a high re-solving frequency is needed for a good result.

Parallel solutions of static Hamilton-Jacobi equations for simulations of geological folds

Two new algorithms for numerical solution of static Hamilton-Jacobi equations are presented. These algorithms are designed to work efficiently on different parallel computing architectures, and numerical results for multicore CPU and GPU implementations are reported and discussed. The numerical experiments show that the proposed solution strategies scale well with the computational power of the hardware. The performance of the new methods are investigate for tow types of static Hamilton-Jacobi formulations are investigated, the isotropic eikonal equation and an anisotropic formulation used to simulate different types of geological folding. Simulations of geological folding is a key component in an industrial software used in oil and gas exploration. In particular, our experiments indicate that the new algorithms would be capable of accelerating an existing industrial simulator substantially. Direct comparison with the current industry code shows that computing times can be reduced from several minutes to a few seconds. The new methods are now being migrated to the industrial software.

Project Team Social Capital, Safety Behaviors, and Performance: A Multi-level Conceptual Framework

The current Hong Kong construction industry safety state of affairs are undesirable. While a myriad of safety approaches have been adopted in the industry through normative compliance, error prevention, and climate intervention, the situations remain dismal. One of the reasons for the ineffectiveness of these approaches to ensure construction projects’ safety performance is the mismatch between the approaches’ rigid and static formulations of construction operations that are put to use in the operations that are emergent and dynamic. We propose that the deficiency can be rectified through the project team adaptive inputs and interactions that are grounded in the project team social capital. We (1) explore such possibility by establishing the theoretical underpinning through extant literature and (2) propose a conceptual framework befitting a relational approach to ensuring project safety outcomes. To accomplish the objectives set forth above, we conduct literature search and review in the domains of social capital, construction safety, social psychology, and small team research. Through the process of convergent and refinement of the literary domains, we put forth a conceptual framework that can be put into empirical test. The framework reveals that project team social capital can be modeled as a multi-level phenomenon emanating from individual level network structure. These structural features, together with the relational and cognitive features at the group level, influence the individual safety behaviors, and in turn, their safety outcomes. The analysis through literature review and modeling have shown that project team members’ safety behaviors are influenced by the interaction of both the individual and group level relational phenomena. This study enriches current safety research agenda by highlighting the effects of team dynamics in safety performance. In this respect, we also provide methodological suggestions to empirically test the framework.

A contact dynamics approach to the Granular Element Method

We present a contact dynamics (CD) approach to the Granular Element Method (GEM) Andrade et al. (2012) [1], abbreviated here as CD–GEM. By combining particle shape flexibility through Non-Uniform Rational Basis Splines, properties of implicit time-integration discretization (e.g., larger time steps) and non-penetrating constraints, as well as a reduction to a static formulation in the limit of an infinite time step, CD–GEM targets system properties and deformation regimes in which the classical discrete element method either performs poorly or simply fails; namely, in granular systems comprising of rigid or highly stiff angular particles and subjected to quasi-static or intense dynamic flow conditions. The integration of CD and GEM is made possible while significantly simplifying implementation and maintaining comparable performance with existing CD approaches.

Nonlinear forced vibrations of rotating anisotropic beams

This work deals with forced vibration of nonlinear rotating anisotropic beams with uniform cross sections. Coupling the Galerkin method with the balance harmonic method, the nonlinear intrinsic and geometrically exact equations of motion for anisotropic beams subjected to large displacements, are converted into a static formulation. This latter is treated with two continuation methods. The first one is the asymptotic-numerical method, where power series expansions and Pade approximants are used to represent the generalized vector of displacement and the frequency. The second one is the pseudo-arclength continuation method. Numerical tests dealing with isotropic and anisotropic beams are considered. The natural frequencies obtained for prismatic beams are compared with the literature. Response curves are obtained and the nonlinearity is investigated for various geometrical conditions, excitation amplitudes and kinematical conditions. The nonlinearity related to the angular speed for prismatic isotropic beam is thus identified. The stability of the solution branch is examined, in the frequency domain using the Floquet theory.

Reflexión sobre enfoques y métodos utilizados en la ciencia de los transportes

Se presenta un análisis crítico sobre las metodologías y enfoques de modelación utilizados actualmente en la ciencia de los transportes. Se señalan inconsistencias que surgen de la confrontación entre la práctica, las herramientas de modelaje utilizadas y los desarrollos teóricos en varias disciplinas. Se plantean cuatro ejes de análisis: la modelación del comportamiento del individuo según la perspectiva de sicología social y en micro-sicología; el enfoque clásico de análisis del comportamiento propuesto en economía; la formulación determinista vis-à-vis en contraste con la formulación estocástica, tomando partido por esta última, y la formulación estática versus la dinámica, optando por esta última.

Gauge theory of the liquid-glass transition in static and dynamical approaches

We propose static and dynamical formulations of the liquid-glass transition theory based on the glass gauge theory and the fluctuation theory of phase transitions. In accordance with the proposed theory, the liquid-glass transition is an unattainable second-order phase transition blocked by a premature critical slowing of the gauge field relaxation caused by the system frustration. We show that the proposed theory qualitatively agrees well with experimental data.

Foundation impedance and tower transfer functions for offshore wind turbines

This article investigates the dynamic interaction between a horizontal-axis wind turbine, modelled as a discrete Euler–Lagrangian system, and the soil–foundation system, modelled in a finite element framework. The model comprises a rotor blade system, a nacelle and a flexible tower connected to the soil–foundation system using a substructuring approach. The aerodynamic loading on the rotor blades is modelled using blade element momentum theory. The offshore wind turbine is founded on a monopod suction caisson foundation. The soil–foundation system is modelled using a finite element method (Plaxis 3D dynamics) and a 1D strength of materials based on wave propagation approach (cone method) for comparison. A dynamic-stiffness matrix and a static stiffness matrix formulation are used to represent the soil–foundation behaviour at the mudline. Tower displacement response transfer functions are generated using each soil–foundation model at various soil stiffness. The effects of the soil stiffness on the displacement transfer functions and the wind turbine dynamics are discussed. Results from a static stiffness formulation (with coupling) are seen to match those given by frequency-dependent models, indicating that such simplified models maybe used for analysis under certain conditions.

Computation of static and frequency-dependent line parameters of multilayer CPW using static SDA and single layer reduction method

We reformulate the quasi-static SDA applicable to a lossy multilayer CPW that also incorporates two-layer model of a conductor thickness and the concept of effective permeability due to magnetic field penetration in an imperfect conductor. The present static SDA formulation accounts for the effect of conductor thickness and low frequency dispersion on computation of quasi-static effective relative permittivity and characteristic impedance. The paper also presents the single layer reduction (SLR) formulation and circuit model to compute frequency dependent line parameters of a lossy multilayer CPW. The accuracy of formulation is comparable to that of HFSS and CST, without using complex and time consuming full-wave methods. The results of CST for εeff, Z0, αd, αc of multilayer CPW, in the frequency range 1–100 GHz, deviate from results of HFSS up to 1.26%, 2.78%, 11.75%, and 18.7%, respectively; whereas corresponding deviations of present formulation are up to 1.56%, 2.4%, 3.04%, and 7%. The results of the present formulation and HFSS are also compared against the available experimental results. © 2013 Wiley Periodicals, Inc. Int J RF and Microwave CAE 24:18–29, 2014.

Energy Efficiency Studies of A Morphing Unmanned Aircraft

In this paper an analytical model is used for the development of the controls for the optimal longitudinal performances of two small UAV aircraft which differ exclusively on the wing: an optimum Fixed Wing (FWA) and a telescopic and camber varying Morphing Wing (MWA). The aerodynamic data of the two wings is based on previous coupled FEM-CFD work. Both static and dynamic formulations for the longitudinal control are presented and applied to the two aircrafts. The static results show that the MWA has an extended operational range when compared to the FWA with the exception of the rate of climb which is slightly penalized. The dynamic results include the analysis of 128 different missions which include climb-cruise missions and descent missions. The dynamic formulation shows very satisfactory results in optimal control calculation for trajectory tracking. Energy actuation estimates based on the optimal control obtained for the missions are calculated and total mission energy consumption estimates comparisons are presented. The actuation energy estimates show that actuation energy is two orders of magnitude inferior to the engine output.

Exact solutions of sequential limit analysis of pressurized cylinders with combined hardening based on a generalized Hölder inequality: Formulation and validation

The paper aims to investigate nonlinear combined isotropic/kinematic hardening cylinders under internal proportional pressure by sequential limit analysis. The Armstrong–Frederick kinematic hardening model is adopted and the Voce hardening law is incorporated for isotropic hardening behavior. In particular, we establish the kinematic formulation of sequential limit analysis from the corresponding static formulation by a generalized Hölder inequality. Especially, it is found that the derived kinematic formulation involving combined isotropic/kinematic hardening is equivalent to that by the bipotential concept. Further, exact solutions of plastic limit pressure were developed analytically by performing both static and kinematic limit analysis. Finally, the problem formulation and the solution derivations presented here are validated by a very good agreement between the numerical result of exact solutions of the present work and the upper bounds from the kinematic formulation available in literature.

The Nonlinear Static Formulation of Variable Cross-Section Beam Element Based on Positional Description

Based on positional FEM (finite element method), the nonlinear static formulation to treat large deflection of variable cross-section beam element is created by using the lowest potential energy theory. Adopting linear constitutive relation for hyper-elastic materials, the formulation and the solution procedure by Newton-Raphson iteration method are very simple.

Stability of a rectangular plate axially compressed on its two opposite free edges

AbstractThe stability of a rectangular plate under two different compressive loading scenarios applied to the free edges of the plate has been investigated. It is assumed that under the applied load the edges have translational and rotational degrees of freedom. In the first case, a conservative external force, that is assumed to have a fixed direction with respect to the deforming body, is applied while in the second case the load is directed to be tangential to the deflected middle surface, the follower force. It is found that for a sufficiently narrow plate the buckling is localized in the neighborhood of free edges as the conservative load is applied. A similar phenomenon is known for the case when a plate is uniformly compressed along hinged edges. In the case of a follower force, the static formulation of the problem leads to the conclusion that localized buckling does not exist. However, depending on the parameters of the problem, the usual (global) buckling is predicted.

Granular contact dynamics using mathematical programming methods

A class of variational formulations for discrete element analysis of granular media is presented. These formulations lead naturally to convex mathematical programs that can be solved using standard and readily available tools. In contrast to traditional discrete element analysis, the present granular contact dynamics formulation uses an implicit time discretization, thus allowing for large time steps. Moreover, in the limit of an infinite time step, the general dynamic formulation reduces to a static formulation that is useful in simulating common quasi-static problems such as triaxial tests and similar laboratory experiments. A significant portion of the paper is dedicated to exploring the consequences of the associated frictional sliding rule implied by the variational formulation adopted. In this connection, a new interior-point algorithm for general linear complementarity problems is developed and it is concluded that the associated sliding rule, in the context of granular contact dynamics, may be viewed as an artifact of the time discretization and that the use of an associated flow rule at the particle scale level generally is physically acceptable.

THE ANALYSIS OF GEOMETRICALLY NONLINEAR ELASTIC-PLASTIC SPACE FRAMES / TAMPRIAI PLASTINIŲ GEOMETRIŠKAI NETIESINIŲ ERDVINIŲ RĖMŲ ANALIZĖ

The establishment of the real stress-strain state of the structure is one of the most important problems for designing and undertaking the reconstruction of building constructions as well as making calculations for the purpose of optimizing cross-sections of various structural elements. This task can be achieved by analysing the structure as a geometrically nonlinear system (refusing an assumption of small displacements) and taking into consideration plastic deformations. Modern computer technologies and mathematical tools enable us to perform strength analysis of space structures and to increase the accuracy of stress-strain state analysis. The present paper develops a technique for constructing a finite element tangent matrix for the nonlinear analysis of the space frame structure aimed at determining plastic deformations. The mathematical models of the problems based on static and kinematic formulations using the dual theory of mathematical programming were created for analysis. Strength conditions presented in construction codes and specifications AISCLRFD and suggested by other researchers (e.g. Orbison's strength conditions) are used in the formulations of the analysed problems. The mathematical models of the considered problems are tested by calculating a two-storied space frame. The results of the performed analysis are compared with data obtained within the studies conducted by other researchers. Santrauka Projektuojant ar rekonstruojant konstrukcijas, atliekant jos elementų skerspjūvių optimizavimo skaičiavimus, vienas iš svarbiausių uždavinių – konstrukcijos tikrojo įtempto deformuoto būvio (ĮDB) nustatymas. Tai galima pasiekti atliekant konstrukcijos kaip geometriškai netiesinės sistemos (atsisakant mažų poslinkių prielaidos) analizę, įvertinant plastines deformacijas. Taikant šiuolaikines kompiuterines technologijas ir matematinį aparatą, tapo įmanoma vykdyti erdvinės konstrukcijos stiprumo analizę ir padidinti konstrukcijos ĮDB analizės tikslumą. Tuo tikslu šiame darbe toliau plėtojama tangentinės standumo matricos sudarymo metodika erdvinės rėminės konstrukcijos netiesinei analizei, įvertinant plastines deformacijas. Naudojant matematinio programavimo dualumo teoriją sudaryti analizės statinės ir kinematinės formuluočių uždavinių matematiniai modeliai. Naudojamos AISC-LRFD normatyviniuose dokumentuose pateiktos ir kitų autorių (pavyzdžiui, Orbison) pasiūlytos stiprumo sąlygos. Suformuluoti analizės uždavinių matematiniai modeliai buvo aprobuoti skaičiuojant dviejų aukštų erdvinį rėmą. Gauti analizės rezultatai palyginti su eksperimentiniais ir kitų autorių analitiniais rezultatais.

Financial Deepening, Capital Inflows and Economic Growth Nexus in Tanzania: A Multivariate Model

In this study the dynamic causal relationship between financial deepening and economic growth is examined using a multivariate model. Unlike the majority of the previous studies, the current study includes foreign capital inflows as an intermittent variable between financial deepening and economic growth, thereby creating a simple trivariate model. Using the newly introduced ARDL-bounds testing procedure, the study finds a distinct unidirectional causal flow from economic growth to financial depth in Tanzania. This applies irrespective of whether the causality is estimated in the short run or in the long run. Other results show that there is a bi-directional causality between financial development and foreign capital inflows, and a prima-facie unidirectional causality from foreign capital inflows to economic growth. The study, therefore, concludes that financial development in Tanzania follows growth, irrespective of whether the causality is estimated in a static or dynamic formulation.

Modèles géographiques pour l’étude de l’incidence de la sclérose latérale amyotrophique (SLA) et de ses interactions spatiales avec les expositions environnementales collectives de quelques facteurs environnementaux d’intérêts étiologiques, Limousin, France

This work deals with damped nonlinear forced vibrations of thin elastic rectangular plates subjected to harmonic excitation by an asymptotic numerical method. Using the harmonic balance method and Hamilton’s principle, the governing equation is converted into a static formulation. A mixed formulation is used to transform the problem from cubic nonlinearity to quadratic one sequence. Displacement, stress and frequency are represented by power series with respect to a path parameter. Equating the like powers of this parameter, the nonlinear governing equation is transformed into a sequence of linear problems with the same stiffness matrix. Through a single matrix inversion, a considerable number of terms of the perturbation series can easily be computed with a limited computation time. The starting point, corresponding to a regular solution, is obtained by the Newton–Raphson method. In order to increase the step length, Padé approximants are used. Numerical tests are presented and compared with numerical and analytical results in the literature, for different boundary conditions, excitations and damping coefficients.

Dynamic liquidation under market impact

The optimal liquidation problem with transaction costs, which includes a positive fixed cost, and market impact costs, is studied in this paper as a constrained stochastic optimal control problem. We assume that trading is instantaneous and the dynamics of the stock to be liquidated follows a geometric Brownian motion. The solution to the impulse control problem is computed at each time step by solving a linear partial differential equation and a maximization problem. In contrast to results obtained from the static formulation of Almgren and Chriss [J. Risk, 2000, 3, 5–39], when risk is not considered, the optimal liquidation strategy from our stochastic control formulation depends on temporary market impact cost and permanent market impact cost parameters. In addition, our computational results indicate the following properties of the optimal execution strategy from the stochastic control formulation. Due to the existence of a no-transaction region, it may not be optimal for some individuals to sell their assets on some trading dates. As the value of the permanent market impact parameter increases, the expected optimal amount liquidated at the terminal time increases. As the value of the quadratic temporary impact cost parameter increases, the expected optimal amount liquidated at trading times tends to be uniform, and the no-transaction region shrinks. In the presence of quadratic temporary market impact costs, in contrast to optimal strategies that result from fixed and/or proportional transaction costs alone, portfolios in the selling region are neither re-balanced into the no-transaction region nor into the sell and no-transaction interface.

Finite Adaptability in Multistage Linear Optimization

In multistage problems, decisions are implemented sequentially, and thus may depend on past realizations of the uncertainty. Examples of such problems abound in applications of stochastic control and operations research; yet, where robust optimization has made great progress in providing a tractable formulation for a broad class of single-stage optimization problems with uncertainty, multistage problems present significant tractability challenges. In this paper we consider an adaptability model designed with discrete second stage variables in mind. We propose a hierarchy of increasing adaptability that bridges the gap between the static robust formulation, and the fully adaptable formulation. We study the geometry, complexity, formulations, algorithms, examples and computational results for finite adaptability. In contrast to the model of affine adaptability proposed in, our proposed framework can accommodate discrete variables. In terms of performance for continuous linear optimization, the two frameworks are complementary, in the sense that we provide examples that the proposed framework provides stronger solutions and vice versa. We prove a positive tractability result in the regime where we expect finite adaptability to perform well, and illustrate this claim with an application to Air Traffic Control.