Semi-analytical Procedure Research Articles

Energy analysis of the critical force of slender RC columns

A semi-analytical procedure for the determination of the critical force of a pin-ended column loaded by axial force and bending moment is proposed. It is based on the principle of minimum potential energy of internal and external forces. The equations for strain energy have been derived for the first- and the second-order displacements per section, including compressed and tensile concrete and reinforcement. The energy of the external forces with axial and flexural displacement effects has been derived on the assumed sinusoidal deflection curve. The trapezoid rule is applied to integrate the segment internal energy. The proposed method uses a non-linear stress–strain curve for concrete; bilinear elastic–plastic relationship for reinforcement; equilibrium conditions at a sectional level to generate the strain energies along the member. The effects of shear deformations are neglected. The effect of lateral confining by the stirrups to strength is also analysed. The results obtained with the proposed model have been verified and compared with experimental results from the literature.

Simplified modeling of beam vibrations induced by a moving mass by regression analysis

In this paper, we propose a fast computation of beam-type dynamic response to a moving mass. Dynamics of a single-span beam is first accurately computed with a semi-analytical procedure based on characteristic orthogonal polynomials (COPs), in the case of a force or a mass traveling across. A regression analysis is then adopted to automatically define the effects of the moving mass once the effects of the moving force are known. Best-fitting multivariable correlation splines, with strictly given coefficients, are obtained. The provided correlation splines conveniently interpolate the maximum design parameters of the base beam over a wide range of load inertia and velocity. Results provided are valid for any geometry and elastic stiffness of the beam, thanks to a properly set normalization factor here defined. Hence, practitioners are provided with an effortless and highly simplified direct prediction of design parameters when inertial interactions are taken into consideration.

Asymptotic analysis of first passage time problems inspired by ecology.

A hybrid asymptotic-numerical method is formulated and implemented to accurately calculate the mean first passage time (MFPT) for the expected time needed for a predator to locate small patches of prey in a 2-D landscape. In our analysis, the movement of the predator can have both a random and a directed component, where the diffusivity of the predator is isotropic but possibly spatially heterogeneous. Our singular perturbation methodology, which is based on the assumption that the ratio [Formula: see text] of the radius of a typical prey patch to that of the overall landscape is asymptotically small, leads to the derivation of an algebraic system that determines the MFPT in terms of parameters characterizing the shapes of the small prey patches together with a certain Green's function, which in general must be computed numerically. The expected error in approximating the MFPT by our semi-analytical procedure is smaller than any power of [Formula: see text], so that our approximation of the MFPT is still rather accurate at only moderately small prey patch radii. Overall, our hybrid approach has the advantage of eliminating the difficulty with resolving small spatial scales in a full numerical treatment of the partial differential equation (PDE). Similar semi-analytical methods are also developed and implemented to accurately calculate related quantities such as the variance of the mean first passage time (VMFPT) and the splitting probability. Results for the MFPT, the VMFPT, and splitting probability obtained from our hybrid methodology are validated with corresponding results computed from full numerical simulations of the underlying PDEs.

Semi-analytical buckling analysis of reinforced concrete columns exposed to fire

A new semi-analytical procedure is derived for the determination of buckling of the reinforced concrete column exposed to fire. The fire analysis is performed in three separate steps, of which the time development of temperatures in the fire compartment is performed first, followed by the coupled heat and moisture transfer analysis and, finally, by the mechanical analysis. A particular emphasis has been given to the critical buckling time and the remaining critical buckling load at a selected time. For this purpose, a parametric study has been performed by which the influence of different geometric parameters on the buckling load capacity of reinforced concrete columns has been assessed. The results of this study show that the load-carrying capacity of the column reduces significantly with the increasing time of fire exposure and the column slenderness. Moreover, the initial mechanical load has a small, although not negligible effect on the buckling load capacity.

Frequency-dependent impedance of a strip foundation group and its representation in time domain

A semi-analytical procedure is presented to study the dynamic cross-interference among a group of long strip foundations on an elastic half-space, which is simplified as a two-dimensional problem. In addition to analytical solutions in terms of Green functions, a discretization method is applied to determine the lateral/rocking dynamic impedances of a foundation group. To determine the unknown contact stresses between the foundations and the supporting medium, the soil-foundation interfaces are discretized into a series of strip elements which are only subjected to constant lateral and vertical tractions. Multiple foundations with different widths and separation distances are considered in the formulations. For the time history analysis of those strongly frequency-dependent impedances of a foundation group through a substructure approach, complex Chebyshev polynomials are used to fit the lumped-parameter (L-P) model in the domain-transformation. Numerical results over a wide range of vibration frequencies for impedance calculation are verified with the existing methods. The effects of cross-interference on contact stress distributions and impedances for a group of two and three rigid foundations are discussed in detail. Finally, the accuracy and the validity of the L-P model are rigorously studied by simulating adjacent foundations on an elastic half-space within a close distance.

Search optimization for minimum load under detection performance constraints in multi-function phased array radars

This paper presents a solution procedure of surveillance parameter optimization to achieve minimum radar load while ensuring desired one-off and cumulative probabilities of detection in a multi-function phased array radar. The key approach is to convert the nonlinear optimization on four search parameters – beam width, beam spacing ratio, dwell time, and frame time – into a scalar optimization on signal-to-noise ratio by a semi-analytic procedure based on subproblem decomposition, which improves computational efficiency of the optimization process as well as facilitates physical interpretation of the optimized parameters. The efficacy of the proposed solution approach is verified with theoretical analysis and numerical case study on an airborne phased array radar.

A Low-Dispersive Symplectic Partitioned Runge-Kutta Method for Solving Seismic-Wave Equations: I. Scheme and Theoretical Analysis

Abstract In this article, a series of nearly analytic symplectic partitioned Runge–Kutta (NSPRK) methods for the 3D seismic‐wave equation are developed. First, the Hamiltonian formulations for acoustic and elastic‐wave equations are presented, and then the spatial derivatives are discretized by a nearly analytic discrete operator to obtain a semidiscrete Hamiltonian system. The second‐, third‐, and fourth‐order symplectic partitioned Runge–Kutta schemes are then applied as the time integrator. A semianalytic procedure to facilitate the analysis of stability conditions and numerical dispersion relations is presented, and subsequent theoretical analysis shows that the NSPRK schemes preserve the wave velocity better than conventional symplectic schemes, especially on coarser grids. The numerical solutions computed by NSPRK schemes are compared with analytic solutions for the 3D acoustic and elastic cases. We implemented the NSPRK and some conventional schemes for a 3D acoustic wave propagation simulation in a parallel computer and compared their computational efficiencies. To generate comparable results, the NSPRK schemes require much less computer memory, central processing unit time, and communication time, which substantially accelerates the computation speed. The final simulation in the two‐layer acoustic model shows that the NSPRK schemes can suppress numerical dispersion and preserve the waveforms better than conventional symplectic schemes.

A dynamical model of tumour immunotherapy

A coupled ordinary differential equation model of tumour-immune dynamics is presented and analysed. The model accounts for biological and clinical factors which regulate the interaction rates of cytotoxic T lymphocytes on the surface of the tumour mass. A phase plane analysis demonstrates that competition between tumour cells and lymphocytes can result in tumour eradication, perpetual oscillations, or unbounded solutions. To investigate the dependence of the dynamic behaviour on model parameters, the equations are solved analytically and conditions for unbounded versus bounded solutions are discussed. An analytic characterisation of the basin of attraction for oscillatory orbits is given. It is also shown that the tumour shape, characterised by a surface area to volume scaling factor, influences the size of the basin, with significant consequences for therapy design. The findings reveal that the tumour volume must surpass a threshold size that depends on lymphocyte parameters for the cancer to be completely eliminated. A semi-analytic procedure to calculate oscillation periods and determine their sensitivity to model parameters is also presented. Numerical results show that the period of oscillations exhibits notable nonlinear dependence on biologically relevant conditions.

Dynamical scalarization of neutron stars in scalar-tensor gravity theories

We present a framework to study generic neutron-star binaries in scalar-tensor theories of gravity. Our formalism achieves this goal by suitably interfacing a post-Newtonian orbital evolution (described by a set of ordinary differential equations) with a set of nonlinear algebraic equations, which provide a description of the scalar charge of each binary's component along the evolution in terms of isolated-star data. We validate this semianalytical procedure by comparing its results to those of fully general-relativistic simulations, and use it to investigate the behavior of binary systems in large portions of the parameter space of scalar-tensor theories. This allows us to shed further light on the phenomena of ``dynamical scalarization,'' which we uncovered in [E. Barausse et al., Phys. Rev. D 87, 081506(R) (2013)] and which takes place in tight binaries, even for stars that have exactly zero scalar charge in isolation. We also employ our formalism to study representative binary systems, obtain their gravitational-wave signals and discuss the extent to which deviations from general relativity can be detected. The insights gained by this framework allow us to additionally show that eccentric binaries can undergo scalarization/descalarization phenomena.

Dynamic analysis of composite laminated and sandwich hollow bodies of revolution based on three-dimensional elasticity theory

This paper presents a semi-analytical procedure for solving linear vibration problems of composite laminated and sandwich hollow bodies of revolution with arbitrary combinations of boundary constraints in the framework of the three-dimensional theory of elasticity. Multilevel partitioning hierarchy, viz., multilayered body of revolution, individual layer and layer segment, is adopted in the theoretical analysis. The appropriate continuity constraints on common interfaces are imposed by means of a modified variational principle combined with the least-squares weighted residual method. The displacement field of each layer segment is characterized by a mixed series of basis functions, i.e., Fourier series and orthogonal polynomials. Numerical examples concerning the free vibrations of composite laminated and sandwich hollow cylinders, cones, and spheres, are presented to show the performance of the method, and comparisons of the present results are made with solutions available in the literature and those obtained from finite element analyses. With regard to the forced vibration problems, steady-state vibration responses of a sandwich hollow cylinder under a uniformly distributed normal harmonic pressure are analyzed, and time-domain solutions of composite laminated and sandwich hollow spheres subjected to various impulsive loads, including a rectangular pulse, a triangular pulse, a half-sine pulse and an exponential pulse, are also examined. Numerical experiments show that the present method is accurate, efficient and reliable for predicting the full spectrum of vibration behaviors of multilayered hollow bodies of revolution.

Dynamical scalarization of neutron stars in scalar-tensor gravity theories

We present a framework to study generic neutron-star binaries in scalar-tensor theories of gravity. Our formalism achieves this goal by suitably interfacing a post-Newtonian orbital evolution (described by a set of ordinary differential equations) with a set of nonlinear algebraic equations, which provide a description of the scalar charge of each binary's component along the evolution in terms of isolated-star data. We validate this semianalytical procedure by comparing its results to those of fully general-relativistic simulations, and use it to investigate the behavior of binary systems in large portions of the parameter space of scalar-tensor theories. This allows us to shed further light on the phenomena of ``dynamical scalarization,'' which we uncovered in [E. Barausse et al., Phys. Rev. D 87, 081506(R) (2013)] and which takes place in tight binaries, even for stars that have exactly zero scalar charge in isolation. We also employ our formalism to study representative binary systems, obtain their gravitational-wave signals and discuss the extent to which deviations from general relativity can be detected. The insights gained by this framework allow us to additionally show that eccentric binaries can undergo scalarization/descalarization phenomena.

A general method for analyzing moderately large deflections of a non-uniform beam: an infinite Bernoulli–Euler–von Kármán beam on a nonlinear elastic foundation

The present paper concerns a semi-analytical procedure for moderately large deflections of an infinite non-uniform static beam resting on a nonlinear elastic foundation. To construct the procedure, we first derive a nonlinear differential equation of a Bernoulli–Euler–von Karman “non-uniform” beam on a “nonlinear” elastic foundation, where geometrical nonlinearities due to moderately large deflection and beam non-uniformity are effectively taken into account. The nonlinear differential equation is transformed into an equivalent system of nonlinear integral equations by a canonical representation. Based on the equivalent system, we propose a method for the moderately large deflection analysis as a general approach to an infinite non-uniform beam having a variable flexural rigidity and a variable axial rigidity. The method proposed here is a functional iterative procedure, not only fairly simple but straightforward to apply. Here, a parameter, called a base point of the method, is also newly introduced, which controls its convergence rate. An illustrative example is presented to investigate the validity of the method, which shows that just a few iterations are only demanded for a reasonable solution.

Ducted Propeller Flow Analysis by Means of a Generalized Actuator Disk Model

The paper presents a generalized semi-analytical actuator disk model as applied to the analysis of the flow around ducted propellers at different operating conditions. The model strongly couples the non-linear actuator disk method of Conway[1] (J. Fluid Mech. 1998; 365: 235-267) and the vortex element method of Martensen[2] (Arch. Rat. Mech. 1959; 3: 235-270) and it returns the exact solution, although in an implicit formulation, for incompressible, axisymmetric and inviscid flows. The solution is made explicit through a semi-analytical procedure developed and validated by Bontempo and Manna[3] (J. Fluid Mech. 2013;728:163-195). Moreover the method duly accounts for non-uniform load radial distribution, slipstream contraction, mutual non-linear interaction between duct and propeller, wake rotation, and ducts of general shape. Thanks to its extremely reduced computational cost it can easily be integrated into design systems based on the repeated analysis scheme of hierarchical type. A comparison between open and ducted rotors is carried out in order to quantify the effects of the duct on the overall performance of the device. Emphasis is given to the appropriate matching between the duct geometry and the propeller load to exploit the benefits that could arise ducting the propeller.

A micromechanical approach for semi-analytical low-velocity impact analysis of a bidirectional functionally graded circular plate resting on an elastic foundation

All the rare investigations made on low velocity impact analysis of the functionally graded plates have employed the simple rule of mixture that may lead to inconsistent results in some circumstances, e.g., when the Poisson ratios of the constituent materials are quite different. On the other hand, these researches have been performed either by purely using a commercial finite element software or employing the conventional Hertz-type contact laws that are valid only if the overall plate flexibility is ignored. In the present paper, it is mainly focused on four novelties: (i) description of the apparent stiffness of the contact region of the plate based on the micromechanical Mori-Tanaka model for two-directional variations of the material properties of the functionally graded plates, (ii) employing an enhanced contact model, considering the micromechanics-based material model and plate and foundation compliances, (iii) evaluation effects of the foundation stiffness on the apparent impact stiffness and the plate responses, and (iv) using a weighted residual semi-analytical solution procedure and an iterative updating scheme to solve the nonlinear governing equations. Presence of the elastic foundation has caused very interesting, unexpected but reasonable behaviors to be observed.

Hydroelastic vibration of circular plates immersed in a liquid-filled container with free surface

In the present study, a theoretical method is developed to investigate free vibrations of circular plates immersed in fluids and a series of experimental tests are presented to validate the model. The coupled governing equations of both hydroelastic vibration of the plate and liquid sloshing are solved by a semi-analytical procedure, simultaneously. The effect of the plate, used as a baffle, on suppression free surface waves is also considered. Plates with two different boundary conditions, free-edge and clamped edge, are studied. The fluid domain is non-convex because of the presence of the plate, which introduces a singularity in the formulation of the fluid velocity potential. Both the least square and Galerkin methods are applied to determine the unknown coefficients in the velocity potential. Natural frequencies and mode shapes are obtained using the Rayleigh–Ritz method, taking fluid–structure interaction into account. The present approach is validated by comparison to results of modal test on two different steel plates with the free edge and submerged in water, as well as comparison to those of a commercial finite element code. The results obtained from the present method agree with those obtained from modal test and the finite element analysis.

A spectral element approach for the stability analysis of time-periodic delay equations with multiple delays

This paper describes a general spectral element approach to study the stability of multiple time delay systems (MTDS). We show, for the first time, how this approach can be applied to periodic MTDS where the delays and the period are incommensurate. In contrast to prior works on MTDS, the spectral element approach is applicable to both autonomous as well as non-autonomous MTDS. Both MTDS of first order or higher can be obtained and systems with or without damping can be investigated. Since the spectral element approach uses efficient interpolation and a set of well-distributed interpolation points, the size of the matrices necessary for convergence is kept small. Further, since the spectral element approach is a semi-analytical procedure, it avoids the need to use tedious time marching algorithms to explore the stability behavior of the system.

Free Vibration Analysis of Circular Cylindrical Shells: Comparison of Different Shell Theories

In order to study the free vibration of simply supported circular cylindrical shells, a semi-analytical procedure is discussed in detail. In this technique, beam function is used as an approximation for simply supported boundary conditions. A literature review reveals that beam functions are used extensively in predicting natural frequencies of shells. Since this method does not involve with boundary condition equations, there is no need to deal with intense calculations. Hence, it is important to check the accuracy of this approximate technique. So this method was applied to ten different shell theories: 1) Donnell-Mushtari, 2) Love-Timoshenko, 3) Arnold-Warburton, 4) Houghton-Johns, 5) Flugge-Byrne-Lur’ye, 6) Reissner-Naghdi-Berry, 7) Sanders, 8) Vlasov, 9) Kennard-Simplified and 10) Soedel. The approximate procedure was compared favorably with experimental results. Finally, variations and influences of length, radius and thickness were studied on amplitude ratios.

Acrosswind aeroelastic response of square tall buildings: a semi-analytical approach based of wind tunnel tests on rigid models

The present paper is focused on the prediction of the acrosswind aeroelastic response of square tall buildings. In particular, a semi-analytical procedure is proposed based on the assumption that square tall buildings, for reduced velocities corresponding to operational conditions, do not experience vortex shedding resonance or galloping and fall in the range of positive aerodynamic damping. Under these conditions, aeroelastic wind tunnel tests can be unnecessary and the response can be correctly evaluated using wind tunnel tests on rigid models and analytical modeling of the aerodynamic damping. The proposed procedure consists of two phases. First, simultaneous measurements of the pressure time histories are carried out in the wind tunnel on rigid models, in order to obtain the aerodynamic forces. Then, aeroelastic forces are analytically evaluated and the structural response is computed through direct integration of the equations of motion considering the contribution of both the aerodynamic and aeroelastic forces. The procedure, which gives a conservative estimate of the aeroelastic response, has the advantage that aeroelastic tests are avoided, at least in the preliminary design phase.

Coulomb Green’s function and image potential near a planar diffuse interface, revisited

In this work, we revisit the problem of calculating the Coulomb Green’s function and the image potential near a planar diffuse interface in which the dielectric constant changes continuously in a transition layer between two dielectrics. In particular, we extend previous work in two ways. Firstly, a new diffuse interface model, termed the quasi-harmonic interface model, is constructed, for which analytical calculation of Green’s function and the image potential is easy to achieve and need not use any special function. Secondly and also more importantly, a robust semi-analytical numerical procedure to build Green’s functions for general diffuse interface models is developed in analogy to the analysis of transmission lines, thus opening the way to treat in principle any well-behaving and physically plausible dielectric permittivity profile for the transition layer. Numerical experiments are given to illustrate the quasi-harmonic diffuse interface model, and to validate the semi-analytical numerical method particularly by demonstrating its convergence as the number of the sublayers used to partition the transition layer goes to infinity.

Heat conduction in one-dimensional functionally graded media based on the dual-phase-lag theory

In this article, heat conduction in one-dimensional functionally graded media is investigated based on the dual-phase-lag theory to consider the microstructural interactions in the fast transient process of heat conduction. All material properties of the media are assumed to vary continuously according to a power-law formulation with arbitrary non-homogeneity indices except the phase lags which are taken constant for simplicity. The one-dimensional heat conduction equations based on the dual-phase-lag theory are derived in a unified form which can be used for Cartesian, cylindrical, and spherical coordinates. A semi-analytical solution for temperature and heat flux is presented using the Laplace transform to eliminate the time dependency of the problem. The results in the time domain are then given by employing a numerical Laplace inversion technique. The semi-analytical solution procedure leads to exact expressions for the thermal wave speed in one-dimensional functionally graded media with different geometries based on the dual-phase-lag and hyperbolic heat conduction theories. The transient temperature distributions have been found for various types of dynamic thermal loading. The numerical results are shown to reveal the effects of phase lags, non-homogeneity indices, and thermal boundary conditions on the thermal responses for different temporal disturbances. The results are verified with those reported in the literature for hyperbolic heat conduction in cylindrical and spherical coordinates.