Search

Purpose: Realistic composite vehicles with 2, 3, 5 and 9 axles, consisting of a truck with one or two trailers, are addressed in this paper by computational models for vehicle–bridge interaction analysis. Design/methodology/approach: The vehicle–bridge interaction (VBI) models are formed by sets of 2-D rigid blocks interconnected by mass, damping and stiffness elements to simulate their suspension system. The passage of the vehicles is performed at different speeds. Several rolling surface profiles are admitted, considering the maintenance grade of the pavement. The spectral density functions are generated from an experimental database to form the longitudinal surface irregularity profiles. A computational code written in Phyton based on the finite element method was developed considering the Euler–Bernoulli beam model. Findings: Several models of composite heavy vehicles are presented as manufactured and currently travel on major roads. Dynamic amplification factors are presented for each type of composite vehicle. Research limitations/implications: The VBI models for compound heavy vehicles are 2-D. Social implications: This work contributes to improving the safety and lifetime of the bridges, as well as the stability and comfort of the vehicles when passing over a bridge. Originality/value: The structural response of the bridge is affected by the type and size of the compound vehicles, their speed and the conservative grade of the pavement. Moreover, one axle produces vibrations that can be superposed by the vibrations of the other axles. This effect can generate not usual dynamic responses. [ABSTRACT FROM AUTHOR]

Purpose – The purpose of this paper is devoted to present an accurate assessment for determine natural frequencies for uniform and non-uniform Euler-Bernoulli beams and frames by an adaptive generalized finite element method (GFEM). The present paper concentrates on developing the C1 element of the adaptive GFEM for vibration analysis of Euler-Bernoulli beams and frames. Design/methodology/approach – The variational problem of free vibration is formulated and the main aspects of the adaptive GFEM are presented and discussed. The efficiency and convergence of the proposed method in vibration analysis of uniform and non-uniform Euler-Bernoulli beams are checked. The application of this technique in a frame is also presented. Findings – The present paper concentrates on developing the C1 element of the adaptive GFEM for vibration analysis of Euler-Bernoulli beams and frames. The GFEM, which was conceived on the basis of the partition of unity method, allows the inclusion of enrichment functions that contain a priori knowledge about the fundamental solution of the governing differential equation. The proposed enrichment functions are dependent on the geometric and mechanical properties of the element. This approach converges very fast and is able to approximate the frequency related to any vibration mode. Originality/value – The main contribution of the present study consisted in proposing an adaptive GFEM for vibration analysis of Euler-Bernoulli uniform and non-uniform beams and frames. The GFEM results were compared with those obtained by the h and p-versions of FEM and the c-version of the CEM. The adaptive GFEM has shown to be efficient in the vibration analysis of beams and has indicated that it can be applied even for a coarse discretization scheme in complex practical problems. [ABSTRACT FROM AUTHOR]

This work deals with an enrichment technique of the finite element solution to the free vibration problems, called the composite element method [J. Sound Vibration 218 (1998) 619, 659, Key Engrg. Mater. 145–149 (1998) 773]. The enrichment of the solution space is obtained combining the FEM and the high accuracy of closed form solutions from the classical theory. The analytical solutions must be in accordance with some special boundary conditions in such a way they do not change the nodal values of FEM and, also, they must be the solutions to the frequency equation. The CEM can be improved using two types of approach: h and c-versions. The h-version, the same as FEM, consists of the refinement of the element mesh. The c-version is the increase of degrees of freedom related to the classical theory. Truss and beams elements are used in order to verify the numerical efficiency of the CEM. Some examples are presented and the frequencies and mode shapes of vibration obtained by CEM are compared with the FEM solution, and also the classical theory. The numerical results have shown that CEM is more accurate than FEM with the same number of total degrees of freedom. The CEM is also more accurate to determine higher frequencies than the FEM, except for the last ones. The results suggest that, for higher frequencies, numerical instabilities are presented. [Copyright &y& Elsevier]

This paper introduces a new type of Finite Element Method (FEM), called Composite Element Method (CEM). The CEM was developed by combining the versatility of the FEM and the high accuracy of closed form solutions from the classical analytical theory. Analytical solutions, which fulfil some special boundary conditions, are added to FEM shape functions forming a new group of shape functions. CEM results can be improved using two types of approach: h-version and c-version. The h-version, as in FEM, is the refinement of the element mesh. On the other hand, in the c-version there is an increase of degrees of freedom related to the classical theory (c-dof). The application of CEM in vibration analysis is thus investigated and a rod element is developed. Some samples which present frequencies and vibration mode shapes obtained by CEM are compared to those obtained by FEM and by the classical theory. The numerical results show that CEM is more accurate than FEM for the same number of total degrees of freedom employed. It is observed in the examples that the c-version of CEM leads to a super convergent solution. [ABSTRACT FROM AUTHOR]

Arches and curved beams are solved here by the G/XFEM in the context of free vibration problems. This hierarchical enrichment method has been used in many complex applications, however it has not been examined for dynamic of curved beams yet. The focus of the present work is to apply the G/XFEM for free vibration analysis of thin and thick curved beam models. The accuracy of frequencies values, the convergence to reach them, and the frequency spectrum are some of the points to be discussed. Four examples are carried out and the results are compared with standard FEM, the p -Fourier Method and analytical solutions. Even with coarse meshes, G/XFEM presents competitiveness and can reach good precision for large range of frequencies with few enrichment levels. It is also shown that the ill conditioning of mass and stiffness matrices for higher enrichment levels does not affect the G/XFEM competitiveness, since it converges faster with few enrichment levels. • The first application of G/XFEM for free vibration analysis of curved beams. • The bibliographic review showing a pioneer application of the method. • A brief theoretical review for thin and thick curved beams formulations. • The main aspects of G/XFEM formulation in the context of the Partition of Unity. • The proposed approach shows best convergence rates than other methods in addition to high precision. [ABSTRACT FROM AUTHOR]

The stable Generalized Finite Element Method, SGFEM, has been used for numerical stabilization of the generalized finite element method during enrichment process of shape functions. However, some troubles persist in dynamic analysis. The flat-top strategy is an alternative to hold up the SGFEM but, despite its good performance in quasi-static problems, for dynamic problems some points remain opened, such as the accuracy of natural frequencies, the computational effort to reach a desired degree of precision (for each natural frequency), and the conditioning of mass and stiffness matrices. The main objective of this work is to assess the performance of the flat-top SGFEM in the context of free vibration analysis Based in many numerical simulations, the sensitivity of the method is verified for different parameters, such as, the size of the flat-top partition of unity (PU) intervals, the smoothness of enriched functions, and the stabilization parameter. Despite the flat-top SGFEM improves the numerical stability for modal analysis, it is shown that the convergence rates can be degraded. [ABSTRACT FROM AUTHOR]

Purpose: This study aims to present a new hybrid formulation based on non-uniform rational b-splines functions and enrichment strategies applied to free and forced vibration of straight bars and trusses. Design/methodology/approach: Based on the idea of enrichment from generalized finite element method (GFEM)/extended finite element method (XFEM), an extended isogeometric formulation (partition of unity isogeometric analysis [PUIGA]) is conceived. By numerical examples the methods are tested and compared with isogeometric analysis, finite element method and GFEM in terms of convergence, error spectrum, conditioning and adaptivity capacity. Findings: The results show a high convergence rate and accuracy for PUIGA and the advantage of input enrichment functions and material parameters on parametric space. Originality/value: The enrichment strategies demonstrated considerable improvements in numerical solutions. The applications of computer-aided design mapped enrichments applied to structural dynamics are not known in the literature. [ABSTRACT FROM AUTHOR]

Purpose: This paper aims to present an adaptive approach of the generalized finite element method (GFEM) for transient dynamic analysis of bars and trusses. The adaptive GFEM, previously proposed for free vibration analysis, is used with the modal superposition method to obtain precise time-history responses. Design/methodology/approach: The adaptive GFEM is applied to the transient analysis of bars and trusses. To increase the precision of the results and computational efficiency, the modal matrix is responsible for the decoupling of the dynamic equilibrium equations in the modal superposition method, which is used with only the presence of the problem's most preponderant modes of vibration. These modes of vibration are identified by a proposed coefficient capable of indicating the influence of each mode on the transient response. Findings: The proposed approach leads to more accurate results of displacement, velocity and acceleration when compared to the traditional finite element method. Originality/value: In this paper, the application of the adaptive GFEM to the transient analysis of bars and trusses is presented for the first time. A methodology of identification of the preponderant modes to be retained in the modal matrix is proposed to improve the quality of the solution. The examples showed that the method has a strong potential to solve dynamic analysis problems, as the approach had already proved to be efficient in the modal analysis of different framed structures. A simple way to perform h-refinement of truss elements to obtain reference solutions for dynamic problems is also proposed. [ABSTRACT FROM AUTHOR]

Purpose The purpose of this paper is to check the efficiency of isogeometric analysis (IGA) by comparing its results with classical finite element method (FEM), generalized finite element method (GFEM) and other enriched versions of FEM through numerical examples of free vibration problems.Design/methodology/approach Since its conception, IGA was widely applied in several problems. In this paper, IGA is applied for free vibration of elastic rods, beams and trusses. The results are compared with FEM, GFEM and the enriched methods, concerning frequency spectra and convergence rates.Findings The results show advantages of IGA over FEM and GFEM in the frequency error spectra, mostly in the higher frequencies.Originality/value Isogeometric analysis shows a feasible tool in structural analysis, with emphasis for problems that requires a high amount of vibration modes. [ABSTRACT FROM AUTHOR]

Purpose – The purpose of this paper is to present an application of the Generalized Finite Element Method (GFEM) for modal analysis of 2D wave equation. Design/methodology/approach – The GFEM can be viewed as an extension of the standard Finite Element Method (FEM) that allows non-polynomial enrichment of the approximation space. In this paper the authors enrich the approximation space with sine e cosine functions, since these functions frequently appear in the analytical solution of the problem under study. The results are compared with the ones obtained with the polynomial FEM using higher order elements. Findings – The results indicate that the proposed approach is able to obtain more accurate results for higher vibration modes than standard polynomial FEM. Originality/value – The examples studied in this paper indicate a strong potential of the GFEM for the approximation of higher vibration modes of structures, analysis of structures subject to high frequency excitations and other problems that concern high frequency oscillatory phenomena. [ABSTRACT FROM AUTHOR]

The Generalized/eXtended Finite Element Method (G/XFEM) has successfully been applied in the dynamic analysis of a variety of structures such as bars, trusses, beams, and two-dimensional (2D) problems. The G/XFEM has shown high convergence rates to approximate displacements and stresses in many problems, such as in Fracture Mechanics. For free vibration analyses, the G/XFEM also shows high convergence rates to approximate most of the natural frequencies but the error is still considerable for the highest ones. Dealing with transient analysis, the enrichment has usually been done for all elements of the mesh, which requires high computational efforts. Further, those frequencies that were poorly approximated, pollute and affect the final solution precision of the time response. To reduce such issues, a compound strategy is adopted joining selective enrichment and modal matrix reduction. Friberg Indicator is taken in the selective process. The proposed technique is examined for dynamic analysis of plane state problems. Some examples show that, even with a reduced number of degrees of freedom, more accurate approximations are obtained. The additional time for computation of selective parameters is offset by the reduction of the total time solution. Thus, all results have less total computational running time than the traditional G/XFEM. • The Friberg indicator is combined with the Generalized Finite Element Method. • Modal influence factor is tested in two-dimensional transient analysis. • A reduced and selective procedure is proposed for transient analysis. • The proposed technique provides promising results and reduced computational effort. [ABSTRACT FROM AUTHOR]

This paper presents a C 0 quadrilateral enriched element by the Generalized Finite Element Method, having trigonometric and exponential functions as enrichment functions, applied in free vibration analysis with distorted mesh. The stiffness and mass matrices are obtained by subintervals numerical integration. The efficiency of the enriched C 0 element is observed by solving several plane stress free vibrations problems. The analyses include uniform and non-uniform mesh models, and severely distorted meshes. Furthermore, the sensitivity of the enriched C 0 element is also analyzed. The results of the analyses are compared with other numerical formulations and show that the enriched C 0 element proposed in this paper has good performance. [ABSTRACT FROM AUTHOR]