Roberto Dalledone Machado

Structural dynamic analysis for time response of bars and trusses using the generalized finite element method

The Generalized Finite Element Method (GFEM) can be viewed as an extension of the Finite Element Method (FEM) where the approximation space is enriched by shape functions appropriately chosen. Many applications of the GFEM can be found in literature, mostly when some information about the solution is known a priori. This paper presents the application of the GFEM to the problem of structural dynamic analysis of bars subject to axial displacements and trusses for the evaluation of the time response of the structure. Since the analytical solution of this problem is composed, in most cases, of a trigonometric series, the enrichment used in this paper is based on sine and cosine functions. Modal Superposition and the Newmark Method are used for the time integration procedure. Five examples are studied and the analytical solution is presented for two of them. The results are compared to the ones obtained with the FEM using linear elements and a Hierarchical Finite Element Method (HFEM) using higher order elements.

Modified Local Green's Function Method (MLGFM). Part I. Mathematical background and formulation

The MLGFM is an integral numerical method, established as an extension of the Galerkin BEM, which has produced considerable research in many fields of engineering analysis. Although many researchers have presented numerical results using this technique, there has been no attempt yet to present a work discussing the mathematical background of the method. This work is divided in two parts (in two different papers). The first fills the gap mentioned above. The second presents a compilation of some significant results obtained by the application of the MLGFM to potential and Mindlin plate problems.

GFEM for modal analysis of 2D wave equation

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 concer...

The Generalized Finite Element Method Applied to Free Vibration of Framed Structures

The vibration analysis is an important stage in the design of mechanical systems and buildings subject to dynamic loads like wind and earthquake. The dynamic characteristics of these structures are obtained by the free vibration analysis. The Finite Element Method (FEM) is commonly used in vibration analysis and its approximated solution can be improved using two refinement techniques: h and p-versions. The h-version consists of the refinement of element mesh; the p-version may be understood as the increase in the number of shape functions in the element domain without any change in the mesh. The conventional p-version of FEM consists of increasing the polynomial degree in the solution. The h-version of FEM gives good results for the lowest frequencies but demands great computational cost to work up the accuracy for the higher frequencies. The accuracy of the FEM can be improved applying the polynomial p refinement. Some enriched methods based on the FEM have been developed in last 20 years seeking to increase the accuracy of the solutions for the higher frequencies with lower computational cost. Engels (1992) and Ganesan & Engels (1992) present the Assumed Mode Method (AMM) which is obtained adding to the FEM shape functions set some interface restrained assumed modes. The Composite Element Method (CEM) (Zeng, 1998a and 1998b) is obtained by enrichment of the conventional FEM local solution space with non-polynomial functions obtained from analytical solutions of simple vibration problems. A modified CEM applied to analysis of beams is proposed by Lu & Law (2007). The use of products between polynomials and Fourier series instead of polynomials alone in the element shape functions is recommended by Leung & Chan (1998). They develop the Fourier p-element applied to the vibration analysis of bars, beams and plates. These three methods have the same characteristics and they will be called enriched methods in this chapter. The main features of the enriched methods are: (a) the introduction of boundary conditions follows the standard finite element procedure; (b) hierarchical p refinements are easily implemented and (c) they are more accurate than conventional h version of FEM. At the same time, the Generalized Finite Element Method (GFEM) was independently proposed by Babuska and colleagues (Melenk & Babuska, 1996; Babuska et al., 2004; Duarte et al., 2000) and by Duarte & Oden (Duarte & Oden, 1996; Oden et al., 1998) under the following names: Special Finite Element Method, Generalized Finite Element Method, Finite Element Partition of Unity Method, hp Clouds and Cloud-Based hp Finite Element Method.

Experimental Aspects in the Vibration-Based Condition Monitoring of Large Hydrogenerators

Based on experimental observations on a set of twenty 700 MW hydrogenerators, compiled from several technical reports issued over the last three decades and collected from the reprocessing of the vibration signals recorded during the last commissioning tests, this paper shows that the accurate determination of the journal bearings operating conditions may be a difficult task. It shows that the outsize bearing brackets of large hydrogenerators are subject to substantial dimensional changes caused by external agents, like the generator electromagnetic field and the bearing cooling water temperature. It also shows that the shaft eccentricity of a journal bearing of a healthy large hydrogenerator, operating in steady-state condition, may experience unpredictable, sudden, and significant changes without apparent reasons. Some of these phenomena are reproduced in ordinary commissioning tests or may be noticed even during normal operation, while others are rarely observed or are only detected through special tests. These phenomena modify journal bearings stiffness and damping, changing the hydrogenerator dynamics, creating discrepancies between theoretical predictions and experimental measurements, and making damage detection and diagnostics difficult. Therefore, these phenomena must be analyzed and considered in the application of vibration-based condition monitoring to these rotating machines.

Modelagem numérica de vigas mistas aço-concreto

The use of composite structures is increasingly present in the constructions of Civil Engineering. Steel-concrete composite beams, in particular, are structures consisting of two materials, a profile metal, located in predominantly region of tension, and a section of concrete, located predomi- nantly in compressed region, connected by metallic devices called shear connectors. The main functions of the connectors are: allow the joint work of slab-beam, restrict the longitudinal slipping and uplifting at the interface of the elements, and absorb shear forces. In this context, this work presents three-dimensional numerical models of composite steel-concrete beams, in order to simulate their structural behavior, with emphasis at the slab-beam interface. Simulations had been carried out by means of the ANSYS software, version 10.0, based on Finite Element Method. Results were compared with those provided by Standard Codes and with references found in the literature. Reported results demonstrate that the numerical approach is a valid tool to analyze the behavior of steel-concrete composite beams.

The composite element method applied to free vibration analysis of trusses and beams

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.

An Introduction to the Composite Element Method Applied to the Vibration Analysis of Trusses

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.

Accurate assessment of natural frequencies for uniform and non-uniform Euler-Bernoulli beams and frames by adaptive generalized finite element method

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 ...

GFEM STABILIZATION TECHNIQUES APPLIED TO DYNAMIC ANALYSIS OF NON-UNIFORM SECTION BARS

The Finite Element Method FEM , although widely used as an approximate solution method, has some limitations when applied in dynamic analysis. As the loads excite the high frequency and modes, the method may lose precision and accuracy. To improve the representation of these highfrequency modes, we can use the Generalized Finite Element Method GFEM to enrich the approach space with appropriate functions according to the problem under study. However, there are still some aspects that limit the GFEM applicability in problems of dynamics of structures, as numerical instability associated with the process of enrichment. Due to numerical instability, the GFEM may lose precision and even result in numerically singular matrices. In this context, this paper presents the application of two proposals to minimize the problem of sensitivity of the GFEM: an adaptation of the Stable Generalized Finite Element Method for dynamic analysis and a stabilization strategy based on preconditioning of enrichment. Examples of one-dimensional modal and transient analysis are presented as bars with cross section area variation. Numerical results obtained are discussed analyzing the effects of the adoption of preconditioning techniques on the approximation and the stability of GFEM in dynamic analysis.