A frequency-domain BIEM combining DBIEs and TBIEs for 3-D crack-inclusion interaction analysis

The influence of a spherical elastic inclusion on a penny-shaped crack embedded in an infinite elastic matrix subjected to a time-harmonic crack-face or incident wave loading is investigated. A boundary integral equation method (BIEM) combining displacement boundary integral equations (DBIEs) on the matrix-inclusion interface and traction boundary integral equations (TBIEs) on the crack-surface is developed and applied for the numerical solution of the corresponding 3-D elastodynamic problem in the frequency domain. The singularity subtraction and mapping techniques in conjunction with a collocation scheme are implemented for the regularization and the discretization of the BIEs by taking into account the local structure of the solution at the crack-front. As numerical examples, the interaction of an elastic inclusion and a neighboring penny-shaped crack subjected to a tensile crack-surface loading or an incident plane longitudinal wave loading is investigated. The effects of the inclusion are assessed by the analysis of mixed-mode dynamic stress intensity factors (DSIFs) in dependence on the wave number, the material combination of the matrix and the inclusion, and the crack-inclusion orientation, size and distance.     

Analysis of thin piezoelectric solids by the boundary element method

The piezoelectric boundary integral equation (BIE) formulation is applied to analyze thin piezoelectric solids, such as thin piezoelectric films and coatings, using the boundary element method (BEM). The nearly singular integrals existing in the piezoelectric BIE as applied to thin piezoelectric solids are addressed for the 2-D case. An efficient analytical method to deal with the nearly singular integrals in the piezoelectric BIE is developed to accurately compute these integrals in the piezoelectric BEM, no matter how close the source point is to the element of integration. Promising BEM results with only a small number of elements are obtained for thin films and coatings with the thickness-to-length ratio as small as 10⁻⁶, which is sufficient for modeling many thin piezoelectric films as used in smart materials and micro-electro-mechanical systems.     

A fast BEM for the analysis of damaged structures with bonded piezoelectric sensors

A fast boundary element method for the analysis of three-dimensional solids with cracks and adhesively bonded piezoelectric patches, used as strain sensors, is presented. The piezoelectric sensors, as well as the adhesive layer, are modeled using a 3D state-space finite element approach. The piezoelectric patch model is formulated taking into account the full electro-mechanical coupling and embodying the suitable boundary conditions and it is eventually expressed in terms of the interface variables, to allow a straightforward coupling with the underlying host structure, which is modeled through a 3D dual boundary element method, for accurate analysis of cracks. The technique is computationally enhanced, in terms of memory storage and solution time, using the hierarchical format in conjunction with a GMRES solver. An original strategy retaining the advantages of the fast hierarchical solution without increasing the implementation complexity to take into account the piezoelectric patches is proposed for the solution of the final system. The presented work is a step towards modeling of structural health monitoring systems.     

Realtime Two‐Way Coupling of Meshless Fluids and Nonlinear FEM

In this paper, we present a novel method to couple Smoothed Particle Hydrodynamics (SPH) and nonlinear FEM to animate the interaction of fluids and deformable solids in real time. To accurately model the coupling, we generate proxy particles over the boundary of deformable solids to facilitate the interaction with fluid particles, and develop an efficient method to distribute the coupling forces of proxy particles to FEM nodal points. Specifically, we employ the Total Lagrangian Explicit Dynamics (TLED) finite element algorithm for nonlinear FEM because of many of its attractive properties such as supporting massive parallelism, avoiding dynamic update of stiffness matrix computation, and efficient solver. Based on a predictor‐corrector scheme for both velocity and position, different normal and tangential conditions can be realized even for shell‐like thin solids. Our coupling method is entirely implemented on modern GPUs using CUDA. We demonstrate the advantage of our two‐way coupling method in computer animation via various virtual scenarios.     

A moving Kriging interpolation-based element-free Galerkin method for structural dynamic analysis

In this paper, a meshfree method based on the moving Kriging interpolation is further developed for free and forced vibration analyses of two-dimensional solids. The shape function and its derivatives are essentially established through the moving Kriging interpolation technique. Following this technique, by possessing the Kronecker delta property the method evidently makes it in a simple form and efficient in imposing the essential boundary conditions. The governing elastodynamic equations are transformed into a standard weak formulation. It is then discretized into a meshfree system of time-dependent equations, which are solved by the standard implicit Newmark time integration scheme. Numerical examples illustrating the applicability and effectiveness of the proposed method are presented and discussed in details. As a consequence, it is found that the method is very efficient and accurate for dynamic analysis compared with those of other conventional methods.     

A new trajectory control of a flexible-link robot based on a distributed-parameter dynamic model

The objective of this study is to develop a new trajectory-tracking control method, free from the so-called spillover instability, for a flexible-link robot. Based on a distributed-parameter dynamic model (a partial differential equation), a new moment-feedback trajectory-tracking control scheme is designed for a one-link flexible robot having a payload at the free end, in which zero geometric boundary conditions at the hub end and non-zero dynamic boundary conditions at the free end are taken into account. The proposed control is then extended to an adaptive scheme to cope with parametric uncertainties. The proposed control is stable for trajectory-tracking control and asymptotically stable at desired goal positions, which is proven by using the Lyapunov stability theorem. In addition, the proposed trajectory-tracking control, based on a distributed-parameter dynamic model, does not have the spillover problem. Furthermore, the control performance is guaranteed regardless of the magnitude of desired angle of rotation, which does not require any additional actuators such as piezoelectric actuators on the link and boundary force or moment actuators at the free end. The effectiveness of the proposed control has been shown by experiments.     

Multi-scale boundary element modelling of material degradation and fracture

In the present paper a multi-scale boundary element method for modelling damage is proposed. The constitutive behaviour of a polycrystalline macro-continuum is described by micromechanics simulations using averaging theorems. An integral non-local approach is employed to avoid the pathological localization of micro-damage at the macro-scale. At the micro-scale, multiple intergranular crack initiation and propagation under mixed mode failure conditions is considered. Moreover, a non-linear frictional contact analysis is employed for modelling the cohesive-frictional grain boundary interfaces. Both micro- and macro-scales are being modelled with the boundary element method. Additionally, a scheme for coupling the micro-BEM with a macro-FEM is also proposed. To demonstrate the accuracy of the proposed method, the mesh independency is investigated and comparisons with two macro-FEM models are made to validate the different modelling approaches. Finally, microstructural variability of the macro-continuum is considered to investigate possible applications to heterogeneous materials.     

Numerical study of partial slip on the MHD flow of an Oldroyd 8-constant fluid

The steady flow of an Oldroyd 8-constant magnetohydrodynamic (MHD) fluid is considered for a cylindrical geometry when the no-slip condition between the cylinders and the fluid is no longer valid. The inclusion of the partial slip at boundaries modifies the governing boundary conditions, changing from a linear to a non-linear situation. The non-linear differential equation along with non-linear boundary conditions governing the flow has been solved numerically using a finite-difference scheme in combination with an iterative technique. The solution for the no-slip condition is a special case of the presented analysis. A critical assessment is made for the cases of partial slip and no-slip conditions.     

Assessment of a non-traditional operator split algorithm for simulation of reactive transport

A non-traditional operator split (OS) scheme for the solution of the advection-diffusion-reaction (ADR) equation is proposed. The scheme is implemented with the recently published central scheme [A. Kurganov, E. Tadmor, New high-resolution central schemes for non-linear conservation laws and convection-diffusion equations, J. Comput. Phys. 160 (2000) 241–282] to accurately simulate advection-reaction processes. The governing partial differential equation (PDE) is split into two PDEs, which are solved sequentially within each time step. Unlike traditional methods, the proposed scheme provides a very efficient method to solve the ADR equation for any value of the grid-Péclet number. An analytical mass balance error analysis shows that the proposed non-traditional scheme incurs a splitting error, which behaves differently to the splitting error incurred in traditional OS schemes. Numerical results are presented to illustrate the robustness of the proposed scheme.     

A Newton-like finite element scheme for compressible gas flows

Semi-implicit and Newton-like finite element methods are developed for the stationary compressible Euler equations. The Galerkin discretization of the inviscid fluxes is potentially oscillatory and unstable. To suppress numerical oscillations, the spatial discretization is performed by a high-resolution finite element scheme based on algebraic flux correction. A multidimensional limiter of TVD type is employed. An important goal is the efficient computation of stationary solutions in a wide range of Mach numbers, which is a challenging task due to oscillatory correction factors associated with TVD-type flux limiters. A semi-implicit scheme is derived by a time-lagged linearization of the nonlinear residual, and a Newton-like method is obtained in the limit of infinite CFL numbers. Special emphasis is laid on the numerical treatment of weakly imposed characteristic boundary conditions. Numerical evidence for unconditional stability is presented. It is shown that the proposed approach offers higher accuracy and better convergence behavior than algorithms in which the boundary conditions are implemented in a strong sense.     

Boundary Handling at Cloth–Fluid Contact

We present a robust and efficient method for the two‐way coupling between particle‐based fluid simulations and infinitesimally thin solids represented by triangular meshes. Our approach is based on a hybrid method that combines a repulsion force approach with a continuous intersection handling to guarantee that no penetration occurs. Moreover, boundary conditions for the tangential component of the fluid's velocity are implemented to model the different slip conditions. The proposed method is particularly useful for dynamic surfaces, like cloth and thin shells. In addition, we demonstrate how standard fluid surface reconstruction algorithms can be modified to prevent the calculated surface from intersecting close objects. For both the two‐way coupling and the surface reconstruction, we take into account that the fluid can wet the cloth. We have implemented our approach for the bidirectional interaction between liquid simulations based on Smoothed Particle Hydrodynamics (SPH) and standard mesh‐based cloth simulation systems.     

Non-linear position-force control of objects grasped by multifingered mechanical hands

This paper presents a new non-linear position-force control scheme for control of interaction of objects, grasped by multifingered mechanical hands, with the environment. Using the theory of input-output linearization, the hand-object dynamics in joint space is first projected along the position and force control directions, input-output linearized and decoupled. Along the position control direction(s), a state feedback controller (SFC) is used for trajectory tracking. A new dynamic SFC, which programs a variable compliance, is used along the force control direction(s). The variable compliance is appropriately modulated on the basis of the force feedback information to maintain a desired interaction force level. An optimal grasp force decomposition scheme is also developed for the control of grasping forces. The proposed scheme ensures grasp stability under dynamic conditions. The efficacy of the overall control scheme is demonstrated through numerical simulation.     

Solidification and control of a liquid metal column

In this paper, two different 1D mechanistic models for the solidification of a pure substance are presented. The first model is based on the two-domain approach, resulting in 2 partial differential equations (PDEs) and one ordinary differential equation (ODE) with 2 boundary conditions, 2 interface conditions, and one initial condition: the Stefan problem.In the second model, the metal column is considered as one-domain, and one PDE is valid for the whole domain. The result is one PDE with two boundary conditions.The models are implemented in MATLAB, and the ODE solver ode23s is used for solving the systems of equations. The models are developed in order to simulate and control the dynamic response of the solidification rate. The control scheme is based on a linear PI controller.     

An energy conserving non-linear dynamic finite element formulation for flexible composite laminates

Finite element formulation for non-linear dynamic analysis of flexible composite laminates is presented. A first-order shear-deformation theory, capable of modelling finite deformations and finite rotations in geometrically exact manner, is developed. A model allows simulation of a general elastic material with varied mass density, degree of orthotropy and elastic material parameters and is suitable for non-linear elasto-dynamic analysis of relatively thin and flexible laminates composed of fibre-reinforced composites. Coupling of mid-surface and shell-director fields is exactly taken into account, so that the kinetic energy is not of simple quadratic form. An implicit, one-step, second-order accurate numerical time-integration scheme is applied. In particular, the energy and momentum conserving algorithm, which exactly preserves the fundamental constants of the shell-like body motion, is accomodated for composite laminates. Spatial finite element discretization is based on the four noded multilayered shell finite element with isoparametric interpolations. Fully discrete weak form of the initial boundary value problem is consistently linearized in order to achieve a quadratic rate of asymptotic convergence typical for the Newton–Raphson based solution procedures. Numerical examples are presented.     

Cylindrical bending of piezoelectric laminates with a higher order shear and normal deformation theory

An analytical solution, based on a higher order shear and normal deformation theory, is presented for the cylindrical flexure of piezoelectric plates. The primary displacement terms are expanded in thickness coordinate and an exact nature of electric potential is obtained in actuator and sensing layers. The electric potential function is evaluated by solving a second order ordinary differential equation satisfying electric boundary conditions along thickness direction of piezoelectric layer. A unidirectional composite plate attached with distributed actuator and sensor layers is analyzed under electrical and mechanical loading conditions and comparison of results with exact solution is presented. Results for non-piezoelectric plates are also compared with elasticity and other solutions of cylindrical bending.     

State estimation and multi-sensor data fusion using data-based neurofuzzy local linearisation process models

Modelling unknown non-linear dynamic processes is an essential prerequisite for model-based state estimation and fusion. Fuzzy local linearisation (FLL) is a useful divide-and-conquer method for coping with complex problems such as data-based non-linear process modelling. In this paper, a hybrid learning scheme which combines a modified adaptive spline modelling (MASMOD) algorithm and the expectation-maximisation (EM) algorithm is developed for FLL modelling, based on which Kalman filter type algorithms for state estimation and multi-sensor data fusion are investigated. Two commonly used measurement fusion methods are analytically compared. A hierarchical multi-sensor data fusion architecture is proposed, with an example of non-linear trajectory estimation to validate the proposed method, which integrates the techniques for FLL modelling, neurofuzzy state estimation and multi-sensor data fusion. Whilst this paper mainly focuses on state estimation and data fusion for unknown non-linear dynamic processes, maneuvering targets are also briefly considered.     

Forced vibrations of fluid-conveyed double piezoelectric functionally graded micropipes subjected to moving load

This article is aimed to study the forced vibrations of double piezoelectric functionally graded material micropipes conveying fluid carrying a moving load based on the flexoelectricity theory and modified couple stress theory. The two micropipes are identical and are connected with each other continuously by visco-Pasternak medium. The top micropipe is traversed by a load and is labeled as the primary micropipe. The bottom micropipe is labeled as the secondary micropipe. Non-classical governing equations together with corresponding boundary conditions based on the Hamilton’s principle are obtained and then solved by differential quadrature and Runge–Kutta methods. The influences of the material gradient index, length scale parameter, potential electrical, visco-Pasternak foundation, fluid velocity, various boundary conditions, velocity of the moving load and flexoelectric effect on the dimensionless dynamic deflections of system are discussed. The results show that the flexoelectric and piezoelectric effects tend to increase/decrease the dimensionless dynamic deflections of the primary/secondary pipe, respectively. In addition, the effects of spring constant, shear constant and damping coefficient of the visco-Pasternak medium on the dynamic displacement of the primary and secondary micropipes are vice versa.     

Solution schemes for the system equations of flexible robots

In this work, a method for generating the dynamic equations of flexible robots with open-chain linkage mechanisms is developed. A general transformation matrix associated with the elastic deformation is introduced. In determining the elastic response, a method of separation of variables and the Galerkin's approach are suggested for the boundary-value problem with time-dependent boundary conditions. Besides the formulation scheme, the present work also studies the difficulty of dealing with the inverse kinematic problem, in which the unknowns involve the rigid-body displacements and the elastic deflections. Finally, the ideas presented here have been implemented in a computer simulation, and the formulation of the boundary-value problem has been employed to obtain the equations of motion of a flexible robot. Simulation results are presented.     

Local absorbent boundary condition for non-linear hyperbolic problems with unknown Riemann invariants

Generally, in problems where the Riemann invariants (RI) are known (e.g. the flow in a shallow rectangular channel, the isentropic gas flow equations), the imposition of non-reflective boundary conditions is straightforward. In problems where Riemann invariants are unknown (e.g. the flow in non-rectangular channels, the stratified 2D shallow water flows) it is possible to impose that kind of conditions analyzing the projection of the Jacobians of advective flux functions onto normal directions of fictitious surfaces or boundaries. In this paper a general methodology for developing absorbing boundary conditions for non-linear hyperbolic advective–diffusive equations with unknown Riemann invariants is presented. The advantage of the method is that it is very easy to implement in a finite element code and is based on computing the advective flux functions (and their Jacobian projections), and then, imposing non-linear constraints via Lagrange multipliers. The application of the dynamic absorbing boundary conditions to typical wave propagation problems with unknown Riemann invariants, like non-linear Saint-Venant system of conservation laws for non-rectangular and non-prismatic 1D channels and stratified 1D/2D shallow water equations, is presented. Also, the new absorbent/dynamic condition can handle automatically the change of Jacobians structure when the flow regime changes from subcritical to supercritical and viceversa, or when recirculating zones are present in regions near fictitious walls.