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A Sliding Mode Control Algorithm for Solving an Ill-posed Positive Linear System
Get PDFFor the numerical solution of an ill-posed positive linear system we combine the methods from invariant manifold theory and sliding mode control theory, developing an affine nonlinear dynamical system with a positive control force and with the residual vector as being a gain vector. This system is proven asymptotically stable to the zero residual vector by using an argument from the Lyapunov stability theory. We find that the system fast tends to the sliding surface and then moves with a sliding mode, such that the resultant sliding mode control algorithm (SMCA) is robust against large noise and stable to find the numerical solution of an ill-posed linear system. It is interesting that even under a random noise with an intensity 10-5 we can obtain a quite accurate solution of the linear Hilbert problem with dimension n = 500. For this highly ill-conditioned problem the number of iterations is still smaller than 100. Numerical tests, including the inverse problems of backward heat conduction problem and Cauchy problems, confirm that the present SMCA has superior computational efficiency and accuracy even for a highly ill-conditioned linear equations system under a large noise
A Real-time Monitoring Technique for Local Plasticity in Metals Based on Lamb Waves and a Directional Actuator/Sensor Set
Get PDFA real-time monitoring technique for local plasticity using Lamb waves was developed. Tensile test of a thin aluminum plate with a circular hole where high stress concentration was induced was conducted to verify this technique. During the tensile test, a series of wave signals passing through the local plastic region were collected using a directional actuator/sensor set to monitor plasticity evolution. A pulse compression technique was used to process the wave signals. With the increase of tensile stress in the specimen, the amplitude changes of S0 and A0 modes were obtained and the difference of Lamb wave signals was further evaluated using a proposed signal index I calculated by wavelet analysis. Combined with the numerical stress analysis of the tensile specimen, the influence of the plasticity on the amplitudes of S0 and A0 wave modes was analyzed. As the plastic zone grows gradually, the wave amplitudes and I of S0 and A0 wave modes show their different change tendencies compared with those in elastic stage. The amplitude change is more sensitive to mild plasticity than that of I, while the change of I caused by severe plasticity is more obvious than the amplitude change
On the Homogenization Analysis of Electromagnetic Properties for Irregular Honeycombs
Get PDFHoneycombs are widely used in aerospace structures due to their low density and high specific strength. In this paper, effective electromagnetic properties of irregular honeycombs are investigated, by using the three dimensional homogenization theory and corresponding computational procedure. This homogenization method, being the extension of two-scale asymptotic approach, is employed to determine the expressions of the effective dielectric permittivity, magnetic permeability and electrical conductivity. To verify and validate the proposed model and procedure, effective permittivities of a typical irregular honeycomb are studied and compared with those of semi-empirical formulae. Moreover, the effect of geometry of honeycomb's unit cell on effective permittivities is also examined. Compared to semi-empirical estimations, the two-scale asymptotic homogenization method can be used to achieve more accurate results of effective electromagnetic properties for honeycombs in the scope of numerical modeling, and it can be also extended for estimation of effective electromagnetic tensors for various periodic composites
Analysis of Elastic-PlasticWaves in a Thin-Walled Tube By a Novel Lie-Group Differential Algebraic Equations Method
Get PDFIn this paper, we adopt the viewpoint of a nonlinear complementarity problem (NCP) to derive an index-one differential algebraic equations (DAEs) system for the problem of elastic-plastic wave propagation in an elastic-plastic solid undergoing small deformations. This is achieved by recasting the pointwise complementary trio in the elastic-plastic constitutive equations into an algebraic equation through the Fischer-Burmeister NCP-function. Then, for an isotropicallyhardening/ softening material under prescribed impulse loadings on a thin-walled tube with combined axial-torsional stresses, we can develop a novel algorithm based on the Lie-group differential algebraic equations (LGDAE) method to iteratively solve the resultant DAEs at each time marching step, which converges very fast. The one-dimensional axial-torsional wave propagation problems under different imposed dynamical loading conditions and initial conditions are solved, to assess the performance of the LGDAE
ANN Model to Predict Fracture Characteristics of High Strength and Ultra High Strength Concrete Beams
Get PDFThis paper presents fracture mechanics based Artificial Neural Network (ANN) model to predict the fracture characteristics of high strength and ultra high strength concrete beams. Fracture characteristics include fracture energy (Gf), critical stress intensity factor (KIC) and critical crack tip opening displacement (CTODc). Failure load of the beam (Pmax) is also predicated by using ANN model. Characterization of mix and testing of beams of high strength and ultra strength concrete have been described. Methodologies for evaluation of fracture energy, critical stress intensity factor and critical crack tip opening displacement have been outlined. Back-propagation training technique has been employed for updating the weights of each layer based on the error in the network output. Levenberg- Marquardt algorithm has been used for feed-forward back-propagation. Four ANN models have been developed by using MATLAB software for training and prediction of fracture parameters and failure load. ANN has been trained with about 70% of the total 87 data sets and tested with about 30% of the total data sets. It is observed from the studies that the predicted values of Pmax, Gf, failure load, KIc and CTODc are in good agreement with those of the experimental values
Thermo-elastic Stresses in a Functional Graded Material Under Thermal Loading, Pure Bending and Thermo-mechanical Coupling
Get PDFAnalytical expressions have been derived for the through thickness stresses of a Functional graded materials (FGMs) thin plate subjected to thermal loading, pure bending and thermo-mechanical coupling, respectively. The structure is comprised of a metallic layer, a ceramic layer and a functional graded layer. Continuous gradation of the volume fraction in the FGM layer is modeled in the form of an "m" power polynomial of the coordinate axis in thickness direction of the plate. Numerical scheme of discretizing the continuous FGM layer with different graded distributions such as linear (m=1), quadratic (m=2) and square root (m=0.5) has been developed by the averaging technique of composites. Solutions for the stress distributions have been derived for the system under thermal loading, pure bending and thermo-mechanical coupling, respectively
Dynamic Analysis of a Layered Cylinder Reinforced by Functionally Graded Carbon Nanotubes Distributions Subjected to Shock Loading using MLPG Method
Get PDFIn this paper, the meshless local Petrov-Galerkin (MLPG) method is exploited for dynamic analysis of functionally graded nanocomposite cylindrical layered structure reinforced by carbon nanotube subjected to mechanical shock loading. The carbon nanotubes (CNTs) are distributed across radial direction on thickness of cylinder, which can be simulated by linear and nonlinear volume fraction. Free vibration and elastic wave propagation are studied for various value of volume fraction exponent at various time intervals. The layered cylinder is assumed to be under axisymmetric and plane strain conditions. Four types of CNTs distributions including uniform and three kinds of functionally graded distributions along the radial of cylinder are considered. Material properties are simulated by a micro mechanical model. In the MLPG analysis, radial basis function (RBF) is used for approximation of displacement field in the weak form of governing equations and Heaviside function is used as test Function. For time domain analysis, the Newmark finite difference method is used. Effects of various distributions of carbon nanotubes on the propagation of elastic wave are illustrated and studied in details. The results obtained by the present analysis are compared and validated with those obtained by FEM, which were reported in previous published literatures
A Meshless Method for Solving the 2D Brusselator Reaction-Diffusion System
Get PDFIn this paper, the two-dimensional (2D) Brusselator reaction-diffusion system is simulated numerically by the method of lines. The proposed method is implemented as a meshless method based on spatial trial functions in the reproducing kernel Hilbert spaces. For efficiency and stability reasons, we use the Newton basis introduced recently by Müller and Schaback. The method is shown to work in all interesting situations described by Hopf bifurcations and Turing patterns
Dynamic Response of Borehole in Poroelastic Medium with Disturbed Zone
Get PDFDynamic response of an infinite cylindrical borehole in a poroelastic medium with an excavation disturbed zone is investigated in this paper. The borehole is subjected to axisymmetric time-harmonic loads and fluid sources applied to its surface, which is either fully permeable or impermeable. The governing equations based on Biot’s poroelastodynamics theory are solved by using two scalar potentials and two vector potentials. The general solutions are then derived through the application of Fourier integral transform with respect to the vertical coordinate. An exact stiffness matrix scheme is established from the derived general solutions to include the excavation disturbed zone. Boundary value problems corresponding to a borehole with the disturbed zone subjected to axisymmetric loads and fluid sources are formulated, and selected numerical results are presented to portray dynamic response of a borehole in a poroelastic medium with consideration of excavation disturbed zone
A Boundary Element - Response Matrix Method for 3D Neutron Diffusion and Transport Problems
Get PDFAn application of a 3D Boundary Element Method (BEM), coupled with the Response Matrix (RM) technique, to solve the neutron diffusion and transport equations for multi-region domains is presented. The discussion is here limited to steady state problems, in which the neutrons have a wide energy spectrum, which leads to systems of several diffusion or transport equations. Moreover, the number of regions with different physical constants can be very large. The boundary integral equations concerning each region are solved via a polynomial moment expansion and, taking advantage of suitable recurrence formulas, the multi-fold integrals there involved are reduced to single or double integrals. The usual unknowns (the boundary particle density and its normal derivative) are here replaced by the partial currents entering or leaving each computational cell. The intuitive physical meaning of such quantities facilitates the application of the response matrix technique. Only eigenvalue (criticality) problems will be here considered. As it regards the transport equation, the use of the so called Simplified Spherical Harmonics method (SPN) allows, through suitable approximations, to cast the problem into a system of differential elliptic equations of the diffusion type, which can still be solved by BEM