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A Three-point Coupled Compact Integrated RBF Scheme for Second-order Differential Problems
Get PDFIn this paper, we propose a three-point coupled compact integrated radial basis function (CCIRBF) approximation scheme for the discretisation of second-order differential problems in one and two dimensions. The CCIRBF employs integrated radial basis functions (IRBFs) to construct the approximations for its first and second derivatives over a three-point stencil in each direction. Nodal values of the first and second derivatives (i.e. extra information), incorporated into approximations by means of the constants of integration, are simultaneously employed to compute the first and second derivatives. The essence of the CCIRBF scheme is to couple the extra information of the nodal first and second derivative values via their identity equations. Owing to its coupling of the information of the nodal first and second derivatives, the CCIRBF scheme becomes more accurate, stable and efficient than the normal compact integrated radial basis function (CIRBF) schemes proposed by [Thai-Quang, Mai-Duy, Tran, and Tran-Cong (2012)]. The main features of the CCIRBF scheme include: three-point, high-order accuracy, stability, efficiency and inclusion of boundary values. Several analytic problems are considered to verify the present scheme and to compare its accuracy, stability and efficiency with those of the CIRBF, higher-order compact finite difference (HOC) and some other high-order schemes. Numerical results show that highly accurate and stable results are obtained with the proposed scheme. Additionally, the present scheme also takes less time to achieve target accuracy in comparison with the CIRBF and HOC schemes
Variance-based Sensitivity Analyses of Piezoelectric Models
Get PDFIn the recent years many publications appeared putting emphasis on the simulation-based identification of piezoelectric material parameters from electrical or mechanical measurements and combinations of them. By experience, one is aware of the importance of a single input parameter. However, it is not yet fully understood and in particular quantified to which extend missing knowledge in the single parameters (parameter uncertainty) influences the quality of the model's prognosis. In this paper, we adapt and apply variance-based sensitivity measures to models describing the piezoelectric effect in the linear case and derive global information about the single input parameter's sensitivities
Improved Failure Mode Identification and Reliability Estimates for Electricity Transmission Towers
Get PDFStudies on the theory of structural system reliability includes identification of main the failure modes and calculation of inclusive failure probabilities for the structural system. The efficient and accurate identification of failure modes in structural systems is difficult and represents a key focus for research in system reliability. The fundamental theory of the branch and bound algorithm for stage critical strength is reviewed in this paper. Some deficiencies in this method are highlighted. Corresponding approaches to overcome these deficiencies are proposed. Calculated system reliability solutions to the classical model, a truss with 10 elements, indicate that the improvement measures proposed in this paper increase the efficiency of recognising the main failure modes of the structural system, and are readily validated. The outcomes of this type of benchmark analysis suggest that the proposed methodology may be capable of representing a suitable basis for the structural system reliability analysis of complex truss-like structures, including transmission towers. Using the proposed approach, the principal failure modes and system reliability of a transmission tower are calculated. Based on practical engineering considerations, effective methods to improve this structural system reliability are proposed
Numerical Investigation of a Hybrid Wave Absorption Method in 3D Numerical Wave Tank
No full textApplying an efficient numerical wave absorption method is very important for realization of an open sea condition especially for long time numerical fluid structure interaction simulation. This paper proposed a hybrid numerical wave absorption method for the fully nonlinear fluid structure simulation. A numerical code “QBEM” which is based on the quadratic boundary element method is applied to evaluate the efficiency of the wave absorption methods and damping schemes by checking the energy conservation and wave elevation in the computational domain. Specifically, we conduct a 3D numerical wave tank experiment to find the bestperforming damping scheme inside the damping zone and the associated optimal ramp shape. In addition, different damping coefficients, phase velocities and numerical domain sizes are introduced and compared by the numerical wave tank in order to evaluate their influences on the numerical wave absorption. At last, the most accurate and efficient hybrid numerical wave absorption method is introduced and validated by the comparison between the numerical results and physical wave tank experiments
The Accuracy of Mathematical Models in Simulator Distributed Computing
Get PDFThe issue of simulation of decentralized mathematical models is discussed in the paper. The authors’ knowledge is based on a theory of design of decentralized computer control systems. Their knowledge is gained in the process of designing mathematical models that are simulated. A decomposed control system is required to meet the conditions of observation and control. The methodology of a multi-model design is based on main principles of object orientation such as abstraction, hierarchy, and modularity. Modelling on a parallel architecture has an impact on a simulator system. The system is defined by the equations shown below. An important part is the way of analyzing the simulation method, an analytical approach, and corresponding software implementation tools
Meshless Local Petrov-Galerkin Method for Rotating Timoshenko Beam: a Locking-Free Shape Function Formulation
Get PDFA rotating Timoshenko beam free vibration problem is solved using the meshless local Petrov-Galerkin method. A locking-free shape function formulation is introduced with an improved radial basis function interpolation and the governing differential equations of the Timoshenko beam are used instead of the alternative formulation used by Cho and Atluri (2001). The locking-free approximation overcomes the problem of ill conditioning associated with the normal approximation. The radial basis functions satisfy the Kronercker delta property and make it easier to apply the essential boundary conditions. The mass matrix and the stiffness matrix are derived for the meshless local Petrov-Galerkin method. Results are validated for the fixed-free boundary condition with published literature
Mathematical Programming Approaches for Interval Structural Behaviour and Stability Analysis
Get PDFTwo novel mathematical programming approaches are proposed to separately assess non-deterministic behaviour and stability of engineering structures against disparate uncertainties. Within the proposed computational schemes, uncertainties attributed by the material properties, loading regimes, as well as environmental influences are simultaneously incorporated and modelled by the interval approach. The proposed mathematical programming approaches proficiently transform the uncertain structural analyses into deterministic mathematical programs. Two essential aspects of structural analysis, namely linear structural behaviour and bifurcation buckling, have been explicitly investigated. Diverse verifications have been implemented to justify the accuracy and computational efficiency of the proposed approaches through practically motivated numerical examples
Parametric Study of Bubble Kinematic Behaviour in a Centrifugal Vacuum Separator
Get PDFThe dynamics of dispersed bubbles in a centrifugal separator are investigated with the aim to improve the efficiency of the system. The prototype separator consists of a rotor, a base, a diverting disc, a shaft, an oil trapping impeller, a central pipe, an inlet section for contaminated oil, an outlet section for purified oil and an air outlet. A hydrodynamic model is developed to predict the complex influence of parameters such as the centrifugal force and vacuum pressure. In particular, three different force models are selected to analyze the effect of the added mass and Basset forces (also including inertia, and the buoyancy and drag forces). The bubble kinematic behaviour is simulated in detail by using a discretephase numerical method. Results show that gas concentration and vacuum pressure can significantly influence the removal of bubbles
A New Theory of Strain Hardening and its Consequences for Yield Stress and Failure Stress
Get PDFA new theory of strain hardening is developed. Important in its own right, the strain hardening solution is also of decisive use in rigorously defining the historically broad concepts of yield stress and failure stress. Under ideal conditions yield stress is found to represent a 3rd order transition. Failure stress is an explicit "failure of function" criterion rather than just being the primitive notion of breaking into pieces. Computational extensions and opportunities are discussed
The Lie-group Shooting Method for Radial Symmetric Solutions of the Yamabe Equation
Get PDFWe transform the Yamabe equation on a ball of arbitrary dimension greater than two into a nonlinear singularly boundary value problem on the unit interval [0,1]. Then we apply Lie-group shooting method (LGSM) to search a missing initial condition of slope through a weighting factor r ∈ (0,1). The best r is determined by matching the right-end boundary condition. When the initial slope is available we can apply the group preserving scheme (GPS) to calculate the solution, which is highly accurate. By LGSM we obtain precise radial symmetric solutions of the Yamabe equation. These results are useful in demonstrating the utility of Lie-group based numerical approaches to solving nonlinear differential equations