A subdivision algorithm for generalized Bernstein–Bézier curves

In this article we present a computationally efficient subdivision algorithm for the evaluation of generalized Bernstein–Bézier curves. As particular cases we have subdivision algorithms for classical as well as trigonometric Bernstein–Bézier curves.     

A priori and a posteriori analysis for a locking-free low order quadrilateral hybrid finite element for Reissner–Mindlin plates

This paper proposes a quadrilateral finite element method of the lowest order for Reissner–Mindlin (R–M) plates on the basis of Hellinger–Reissner variational principle, which includes variables of displacements, shear stresses and bending moments. This method uses continuous piecewise isoparametric bilinear interpolation for the approximation of transverse displacement and rotation. The piecewise-independent shear stress/bending moment approximation is constructed by following a self-equilibrium criterion and a shear-stress-enhanced condition. A priori and reliable a posteriori error estimates are derived and shown to be uniform with respect to the plate thickness t. Numerical experiments confirm the theoretical results.     

Assembly variation analysis of flexible curved surfaces based on Bézier curves

Assembly variation analysis of parts that have flexible curved surfaces is much more difficult than that of solid bodies, because of structural deformations in the assembly process. Most of the current variation analysis methods either neglect the relationships among feature points on part surfaces or regard the distribution of all feature points as the same. In this study, the problem of flexible curved surface assembly is simplified to the matching of side lines. A methodology based on Bézier curves is proposed to represent the side lines of surfaces. It solves the variation analysis problem of flexible curved surface assembly when considering surface continuity through the relations between control points and data points. The deviations of feature points on side lines are obtained through control point distribution and are then regarded as inputs in commercial finite element analysis software to calculate the final product deformations. Finally, the proposed method is illustrated in two cases of antenna surface assembly.     

A direct hybrid finite element – Wave based modelling technique for efficient coupled vibro-acoustic analysis

This paper presents a newly developed hybrid simulation technique for coupled structural–acoustic analysis, which applies a wave based model for the acoustic cavity and a direct or modally reduced Finite Element model for the structural part. The resulting hybrid model benefits from the computational efficiency of the wave based method, while retaining the Finite Element Method’s ability to model the structural part of the problem in great detail. Application of this approach to the analysis of three fully coupled vibro-acoustic problems with an increasing modelling complexity shows the improved computational efficiency as compared to classical Finite Element procedures and illustrates the potential of the hybrid method as a powerful tool for the analysis of coupled structural–acoustic systems in the low- and mid-frequency range.     

A note on degenerate triangular Bézier patches

In (Neamtu and Pfluger, 1994) degenerate Bézier patches were used to interpolate irregularly structured spatial data. This very interesting approach is based on the observation that singular parametrizations are no fundamental obstacle to modeling smooth spline surfaces. However, the smoothness conditions on degenerate Bézier patches provided in (Neamtu and Pfluger, 1994) are inaccurate. Moreover, proving tangent plane continuity is not sufficient to guarantee smoothness in the sense of differential geometry. What has to be shown is regularity, i.e. the existence of a regular smooth re-parametrization representing a degenerate patch locally near the singular point. Both correct sufficient smoothness conditions and the proof of regularity are presented in this paper.     

Analysis and optimal design of plates and shells under dynamic loads – I: finite element and sensitivity analysis

In this paper we consider the development, integration, and application of reliable and efficient computational tools for the geometry modeling, mesh generation, structural analysis, and sensitivity analysis of variable-thickness plates and free-form shells under dynamic loads. A flexible shape-definition tool for surface modeling using Coons patches is considered to represent the shape and the thickness distribution of the structure, followed by an automatic mesh generator for structured meshes on the shell surface. Nine-node quadrilateral Mindlin–Reissner shell elements degenerated from 3D elements and with an assumed strain field, the so-called Huang–Hinton elements, are used for the FE discretization of the structure. The Newmark direct integration algorithm is used for the time discretization of the dynamic equilibrium equations for both the structural analysis and the semi-analytical (SA) sensitivity analysis. Alternatively, the sensitivities are computed by using the global finite difference (FD) method. Several examples are considered. In a companion paper, the tools presented here are combined with mathematical programming algorithms to form a robust and reliable structural optimization process to achieve better dynamic performance on the shell designs.     

Masonry and monolithic circular arches strengthened with composite materials – A finite element model

A finite element model for the stress analysis of circular arches strengthened with composite materials is developed. The formulation uses the principle of virtual work, the Bernoulli–Euler curved beam theory for the arch and the composite reinforcement, and a high-order kinematic assumption that satisfies the compatibility and (with the constitutive laws) the tangential equilibrium conditions of the adhesive. The character of the masonry arch is introduced through the constitutive equations with a distinction between the masonry units and the mortar joints. Convergence and numerical studies that support using high-order shape functions and examine the capabilities of the model are presented.     

A Subdivision Scheme for Rational Triangular Bézier Surfaces

An explicit formula is developed to decompose a rational triangular Bezier patch into three non-degenerate rational rectangular Bezier patches of the same degree.This formula yields a stable algorithm to compute the control vertices of those three rectangular subpatches.Some properties of the subdivision are discussed and the formula is illustrated with an example.     

A Subdivision Scheme for Rational Triangular Bézier Surfaces

1IntroductionSubdivisionalgorithmsforB6ziersurfacesareimportantinCADandcomputergraPhics.ThiangularB6ziersurfaceshavebeenstudiedextensivelyI1'3],andsomesubdivisionschemeshavebeendevelopedtosplittheoriginaltriangularpatchintoanumberofsmalltriangularpatchesI3-5].Asstatedby[7],itisusuaJlyavoidedtoincludetriangularpatchesinexistingornewCADsystems,whichuserectangularpatches.ItiswelLknownthattrian-gularpatcheshaveafundamentallydifferentgeometricstructurefromrectangularpatchesl1].Tliereforetheyr…     

CASQUS: A new simulation tool for coupled 3D finite element modeling of tectonic and surface processes based on ABAQUS™ and CASCADE

CASQUS is a numerical simulation tool to model the feedback mechanism between surface and tectonic processes. It includes the surface processes model CASCADE into the finite element solver ABAQUS/Standard?. The finite element method allows for geomechanical simulations of the subsurface with geometrically complex structures in 3D. Additionally, in the commercial software ABAQUS? various types of rheological behavior are already implemented. CASCADE simulates erosion and sedimentation as the combination of fluvial transport and hillslope processes. For the integration of CASCADE into ABAQUS/Standard? an Arbitrary Lagrangian–Eulerian modeling technique is used, which makes a coupled and automated simulation possible. Two benchmark models that are easy to reproduce demonstrate the functionality of CASQUS. Our tool aims at a better understanding of the feedback between mass redistribution at the Earth's surface and processes within a heterogenous subsurface, and at a quantification of the involved processes.     

A finite volume method on NURBS geometries and its application in isogeometric fluid–structure interaction

A finite volume method for geometries parameterized by Non-Uniform Rational B-Splines (NURBS) is proposed. Since the computational grid is inherently defined by the knot vectors of the NURBS parameterization, the mesh generation step simplifies here greatly and furthermore curved boundaries are resolved exactly. Based on the incompressible Navier–Stokes equations, the main steps of the discretization are presented, with emphasis on the preservation of geometrical and physical properties. Moreover, the method is combined with a structural solver based on isogeometric finite elements in a partitioned fluid–structure interaction coupling algorithm that features a gap-free and non-overlapping interface even in the case of non-matching grids.     

A new gear fault feature extraction method based on hybrid time–frequency analysis

Gear is one of the popular and important components in the rotary machinery transmission. Vibration monitoring is the common way to take gear feature extraction and fault diagnosis. The gear vibration signal collected in the running time often reflects the characteristics such as non-Gaussian and nonlinear, which is difficult in time domain or frequency domain analysis. This paper proposed a novel gear fault feature extraction method based on hybrid time–frequency analysis. This method combined the Mexican hat wavelet filter de-noise method and the auto term window method at the first time. This method can not only de-noise noise jamming in raw vibration signal, but also extract gear fault features effectively. The final experimental analysis proved the feasibility and the availability of this new method.     

Energy modelling for the national economy — generalized model based on a physical systems theory approach

This paper presents an approach to the study of the energy related issues of the national economy using physical systems theory concepts for economic and real life systems. The main issues are: the efficiency of various energy conversion and utilization processes in terms of the macro-level technological coefficients; the direct and indirect energy wastes as calculated on the basis of technological coefficients; the effect of energy wastes on the unit cost of energy available to the consumers; the consumption of natural resources based on the final and intermediate demands of various sectors; and the amount of environmental pollution due to energy wastes disposed of to nature. A model is developed for a simplified two-sector national economy which is later extended to a generalized multi-sector model in a branchchord framework. This generalization is a step forward in simplifying the solution methodology for the multi-sector models through substitution, thus avoiding the necessity of drawing a complex system graph or solving large matrices required in the solution methodology.     

High-Performance Computation of Bézier Surfaces on Parallel and Heterogeneous Platforms

Bézier surfaces are mathematical tools employed in a wide variety of applications. Some works in the literature propose parallelization strategies to improve performance for the computation of Bézier surfaces. These approaches, however, are mainly focused on graphics applications and often are not directly applicable to other domains. In this work, we propose a new method for the computation of Bézier surfaces, together with approaches to efficiently map the method onto different platforms (CPUs, discrete and integrated GPUs). Additionally, we explore CPU–GPU cooperation mechanisms for computing Bézier surfaces using two integrated heterogeneous systems with different characteristics. An exhaustive performance evaluation—including different data-types, rendering and several hardware platforms—is performed. The results show that our method achieves speedups as high as 3.12x (double-precision) and 2.47x (single-precision) on CPU, and 3.69x (double-precision) and 13.14x (single-precision) on GPU compared to other methods in the literature. In heterogeneous platforms, the CPU–GPU cooperation increases the performance up to 2.09x with respect to the GPU-only version. Our method and the associated parallelization approaches can be easily employed in domains other than computer-graphics (e.g., image registration, bio-mechanical modeling and flow simulation), and extended to other Bézier formulations and Bézier constructions of higher order than surfaces.     

An analysis of the time integration algorithms for the finite element solutions of incompressible Navier–Stokes equations based on a stabilised formulation

This work is concerned with the analysis of time integration procedures for the stabilised finite element formulation of unsteady incompressible fluid flows governed by the Navier–Stokes equations. The stabilisation technique is combined with several different implicit time integration procedures including both finite difference and finite element schemes. Particular attention is given to the generalised-α method and the linear discontinuous in time finite element scheme. The time integration schemes are first applied to two model problems, represented by a first order differential equation in time and the one dimensional advection–diffusion equation, and subjected to a detailed mathematical analysis based on the Fourier series expansion. In order to establish the accuracy and efficiency of the time integration schemes for the Navier–Stokes equations, a detailed computational study is performed of two standard numerical examples: unsteady flow around a cylinder and flow across a backward facing step. It is concluded that the semi-discrete generalised-α method provides a viable alternative to the more sophisticated and expensive space–time methods for simulations of unsteady flows of incompressible fluids governed by the Navier–Stokes equations.     

Application of nonlocal strain–stress gradient theory and GDQEM for thermo-vibration responses of a laminated composite nanoshell

In this article, thermal buckling and frequency analysis of a size-dependent laminated composite cylindrical nanoshell in thermal environment using nonlocal strain–stress gradient theory are presented. The thermodynamic equations of the laminated cylindrical nanoshell are based on first-order shear deformation theory, and generalized differential quadrature element method is implemented to solve these equations and obtain natural frequency and critical temperature of the presented model. The results show that by considering C–F boundary conditions and every even layers’ number, in lower value of length scale parameter, by increasing the length scale parameter, the frequency of the structure decreases but in higher value of length scale parameter this matter is inverse. Finally, influences of temperature difference, ply angle, length scale and nonlocal parameters on the critical temperature and frequency of the laminated composite nanostructure are investigated.