F.J.M.Q. de Melo

A reduced integration mindlin beam element for linear elastic stress analysis of curved pipes under generalized in-plane loading

Abstract This paper presents a ring element for the analysis of in-plane bending of curved pipes. The element is derived from the arch bending theory using short, straight elements as an approach to the curved structure. Each curved pipe element is considered as a straight thin-walled C 0 -continuity beam element for the purpose of the derivation of the beam stiffness matrix terms. The assumption of the straight elements does not involve ovalization and warping of the transverse section; for the stiffness terms concerning the distortion of the transverse section, the pipe element is assumed curved. This method leads to the important advantage of generating a zero stress field along the curved centroidal line of the element under pure in-plane bending and to the satisfaction of the ‘patch test’.

Experimental modal analysis of a synthetic composite femur

In this paper we describe the experimental characterization of the modal parameters of a synthetic composite femur model widely used in biomechanical research studies. The objective of the experimental procedure was to identify the natural frequencies and mode shapes of an unconstrained (free-free) femur. The experimental data were compared with the same obtained in an analog study performed with a fresh cadaveric femur bone. Other objective of the study was to investigate modal analysis as a technique to validate a finite element model of a composite femur with isotropic material properties.

Determination of flexibility factors in curved pipes with end restraints using a semi-analytic formulation

Piping systems are structural sets used in the chemical industry, conventional or nuclear power plants and fluid transport in general-purpose process equipment. They include curved elements built as parts of toroidal thin-walled structures. The mechanical behaviour of such structural assemblies is of leading importance for satisfactory performance and safety standards of the installations. This paper presents a semi-analytic formulation based on Fourier trigonometric series for solving the pure bending problem in curved pipes. A pipe element is considered as a part of a toroidal shell. A displacement formulation pipe element was developed with Fourier series. The solution of this problem is solved from a system of differential equations using mathematical software. To build-up the solution, a simple but efficient deformation model, from a semi-membrane behaviour, was followed here, given the geometry and thin shell assumption. The flexibility factors are compared with the ASME code for some elbow dimensions adopted from ISO 1127. The stress field distribution was also calculated.

The dynamic analysis of piping systems using pseudo-dynamic techniques

This paper describes an application of pseudo-dynamic techniques to the dynamic analysis of piping structures. Essentially it consists in coupling a direct time integration algorithm, such as the Newmark method, to an experimental step. At each time step the integration algorithm generates a displacement vector of the structure, which is prescribed for the test specimen. This is mounted in a rigid test rig fitted with a set of displacement actuators and load cells at the level of the structure degrees of freedom. The load cells allow the reading of the internal restoring force vector, which is fed back to the direct time integration algorithm in an actual time step. Further calculations for the velocity and acceleration vectors will define a new structure configuration by evaluating a new displacement vector referred to the next time step. This procedure makes it possible to assess experimentally a realistic stress distribution at sections of complex shape piping parts. The method is a precise tool in dynamic analysis and, on being carried out in a quasi-static procedure, it operates with less expensive equipment than is necessary in real dynamic test.

Rational split of the strain tensor in elastoplastic damage mechanics

The basic step in constructing a sound non-linear constitutive model is in accounting for the inelastic deformations. Different investigators partition the state tensors in various ways. This paper discusses the specific implications and limitations of such partitioning of the infinitesimal strain tensor in view of the irreversible changes taking place at a material point. Emphasis is placed on those models which take into consideration the process of damage. It is demonstrated that the damage process affects both the elastic and the plastic behaviours and the most proper partitioning of the strain tensors assumes elastic-damage and plastic-damage constituents. The constraints posed by the use of a single damage variable are elaborated using the concepts of thermodynamics. It is shown that two damage variables are required to depict completely the loading-unloading-reloading of a general non-linear elastoplastic-damaged material. This is further illustrated by deriving a new elastoplastic damage constitutive equation.

The linear elastic in-plane bending of curved hollow profiles having a thin-walled rectangular section:

Abstract This paper presents a simple solution for the flexibility calculation of curved profiles having a rectangular thin-walled cross-section. Some assumptions related to geometric details about the shape of the deformed structure are included in the present analysis, aiming at an economic and accurate solution. Results concerning the distortion of the transverse section are compared with the corresponding data from the solution with a thin shell finite element analysis. A flexibility factor for the structure analysed here is presented as a graphical result.

Assessment of the Displacement Field Along a Surface Crack in a Flat Plate Using Optical Techniques

Structural components may contain cracks, and for these components a crack tip represents a highly singular stress. The evaluation of the associated strain gradient is difficult to achieve with experimental discrete methods. An efficient alternative are the optical techniques which are non-contact, and so delivering continuous information of the displacement fields and associated derivatives for strain evaluation. This paper describes some experimental methods to fully characterize the displacement field near a crack tip existing in flat plates. Three optical field techniques based on image analysis were used in the present work; respectively, Electronic Speckle Pattern Interferometry, Moiré Interferometry, and Digital Image Correlation. These methods allow different resolutions which can be adjusted according to the expected strain gradient. While the first method depends on the laser wavelength and position of the illumination sources, the second depends on the grating pitch and the last on the surface texture or painted speckle. Algorithms to derivate and filtering the displacement field are developed to compute the strain field and will be used for further works.

A semi-membrane ring element for the linear elastic stress analysis of pipe elbows under in-plane bending

Abstract A semi-membrane deformation ring element is presented. The displacement field involves a combination of first degree interpolation polynomials for the longitudinal direction and Fourier series in the meridional or transverse section. The possible boundary conditions for these kind of shells, namely rigid or warping endflanges and tangent terminations, are readily inserted in this ring element. Results concerning transverse section stresses and flexibility factors are calculated and discussed.

The stress and flexibility analysis of thin-walled curved pipes under out-of-plane bending with the semi-membrane ring element

Abstract A semi-membrane curved ring element, described in a previous paper, is reformulated to take into account more general loading conditions, such as the out-of-plane bending. A new displacement field was defined so that the out-of-plane bending moment could be considered. Results concerning transverse section stresses and flexibility factors are presented and discussed.