Complex Support Conditions Research Articles

A nonlinear finite element framework for static and dynamic analysis of structural cables with deviating supports

Structural cables are important load-bearing members in many light-weight and slender structures. The mechanical behaviour of tension cables is complex as it is dominated by geometric nonlinearities, complex support conditions and uncertainties arising from the composition of the cable cross section. Numerous models to describe static and dynamic cable behaviour were developed, differing in the model assumptions and the simplifications made. Most common are geometrical linearisation, dimensional reduction, and the disregard of localised support and stiffness effects. Some models take a combination of some geometric nonlinearities, cable bending stiffness and certain boundary effects into account. This paper first presents a literature review aimed at systematically categorising cable force identification models. Based on this, the paper proposes a novel numerical cable modelling framework that allows for accurate predictions of static and dynamic cable response, e.g. for the use in the inverse system identification techniques of Structural Health Monitoring. The saddled cable model is based on a nonlinear Finite Element formulation to account for the geometric and mechanical effects of deviating supports on structural cables even for very large sag cables. After validation with analytical solutions, the models show that the effect of self-weight distribution and cable bending stiffness considerably affects the identified internal force distribution, contact length on the saddle and cable form. Further, the model is used to predict the tension force based on the identified natural frequencies of an external tendon installed on a bridge. Compared with the actual tension force, the saddled cable model provided very high prediction accuracy, even when compared with other cable models. Therefore, it is shown to be very accurate and can be used to determine force-response relationships used in system identification techniques when increased accuracy is needed for such complex cable arrangements.

The General Method for the fire design of I-section web-tapered beams

The present investigation describes a numerical and parametric study on the validation of the General Method (GM) for the fire design of web-tapered steel beams using GMNIA.The GM covers the safety check of structural elements with complex support conditions and/or of non-prismatic members, as the non-uniform geometry prevents the use of the standard verification clauses. However, the fire part of the Eurocode 3 (EN 1993-1-2) provides no further indication regarding its applicability at elevated temperatures, apart from adapting the methodology to fire using the reduction factors for steel material properties, which is identified as a gap in the current version of the norm.However, previous investigation by the authors have shown overly conservative results for the adapted General Method and a calibration of the EN 1993-1-2 buckling curve has previously been proposed, although the parametric study was not representative enough for full validation.With that in mind, supported by an extensive numerical framework of over 25000 laterally restrained and unrestrained tapered beams at elevated temperatures, a precise and accurate calibration of the General Method is developed in the scope of this work.

The General Method for the fire design of I‐section web‐tapered beams

AbstractThe present investigation describes a numerical and parametric study on the validation of the General Method (GM) for the fire design of web‐tapered steel beams using GMNIA. The GM (clause 6.3.4 of EN 1993‐1‐1) covers the safety check of structural elements with complex support conditions and/or of non‐prismatic members. However, the fire part of the Eurocode 3 (EN 1993‐1‐2) gives no further indication regarding its applicability at elevated temperatures, apart from adapting the methodology to fire using the reduction factors for steel material properties, which is identified as a gap in the current version of the norm.Previous investigations by the authors have shown overly conservative results for the General Method and a calibration of the EN 1993‐1‐2 buckling curve has previously been proposed, although the parametric performed in that study was not extensive enough for a full validation. With that in mind, the present paper has improved these shortcomings by further upgrading the Eurocode 3 formulation and validating the proposal against numerical data from more than 25000 GMNIA simulations.

The General Method for the fire design of slender I-section web-tapered columns

The purpose of this paper is to validate the General Method for the stability check of unrestrained I-section web-tapered columns in fire situation. The General Method (clause 6.3.4 of EN 1993-1-1) covers the safety check of structural elements with complex support conditions and/or of non-prismatic members. However, the fire part of the Eurocode 3 (EN 1993-1-2) gives no further indication regarding the applicability of the method at elevated temperatures, apart from adapting the methodology to fire using the reduction factors for steel material properties, which is identified as a gap in the current version of the norm. To ascertain the validity of said adaptations, the ultimate capacity of members at elevated temperature has been obtained numerically with GMNI-Analyses and a parametric investigation incorporating I-section web-tapered columns built from slender (class 4) cross-sections has been carried out, with special attention to the influence of local buckling on member stability. It has been demonstrated that a straightforward application of the temperature-reduced mechanical properties of steel in the General Method results in an unsafe methodology, therefore justifying improvements to the procedure. In this work, this is done by i) proposing a novel methodology for the calculation of the in-plane load amplifier αult,k and ii) recalibrating the EN 1993-1-2 buckling curve. Not only does this new procedure improve the accuracy of the methodology but it also foregoes the otherwise necessary evaluation of the critical cross-section along the column.

General Method for the fire design of tapered steel columns: Out‐of‐plane flexural buckling

ABSTRACTThe General Method (GM) covers the safety check of structural elements with complex support conditions and/or of non‐prismatic members. However, it's not widely validated at normal temperature and is inexistent in fire part of the Standard EN 1993‐1‐2. With that in mind, this investigation aims at proposing and validating the GM to perform the safety check of unrestrained tapered columns at elevated temperatures. This is done, first, by including, in the original formulation, the reduction of steel material properties with the temperature, and later by improving the EN 1993‐1‐2 out‐of‐plane buckling curve.With this novel approach, the GM shows good agreement to numerical results and produces accurate predictions of out‐of‐plane resistance for tapered columns at elevated temperatures.

Buckling resistance of non-uniform steel members based on stress utilization: General formulation

In Eurocode 3 (2005) the buckling curve approach is adopted for verification of prismatic columns and beams. It has the flexibility of adjusting imperfection factors according to their sections, steel grade and other relevant parameters. However, for generic single members, built-up or not, uniform or not, with complex support conditions or not, the available possibilities for such cases are the General Method given in clause 6.3.4 of Eurocode 3 (2005) or advanced numerical simulations. The applicability of the general method, however, is limited and in some aspects inconsistent (Simões da Silva et al., (2010)). As an alternative, the stability of non-uniform members can be analysed using numerical GMNIA which is a time-consuming procedure and the output is highly dependent on the experience of the user.In this paper, a novel general formulation for stability design of steel columns, beams and beam-columns with variable geometry, loads and complex support conditions is presented. The verification is based on the buckling mode as shape of the initial imperfection with an amplitude previously calibrated for the standard prismatic simply-supported columns and beams in Eurocode 3. The verification is performed as an interaction equation where the first and second order contributions to the longitudinal stress utilization are added for each cross-section along the member length. Several aspects regarding the member behaviour in the context of a specific buckling mode are discussed and finally, validation of the approach is carried out to show its consistency and accuracy.

The influence of thermal actions and complex support conditions on the mechanical state of sandwich structure

The influence of thermal actions and complex support conditions on the mechanical state of sandwich structure

A Canonical Biomechanical Vocal Fold Model

The present article aimed at constructing a canonical geometry of the human vocal fold (VF) from subject-specific image slice data. A computer-aided design approach automated the model construction. A subject-specific geometry available in literature, three abstractions (which successively diminished in geometric detail) derived from it, and a widely used quasi two-dimensional VF model geometry were used to create computational models. The first three natural frequencies of the models were used to characterize their mechanical response. These frequencies were determined for a representative range of tissue biomechanical properties, accounting for underlying VF histology. Compared with the subject-specific geometry model (baseline), a higher degree of abstraction was found to always correspond to a larger deviation in model frequency (up to 50% in the relevant range of tissue biomechanical properties). The model we deemed canonical was optimally abstracted, in that it significantly simplified the VF geometry compared with the baseline geometry but can be recalibrated in a consistent manner to match the baseline response. Models providing only a marginally higher degree of abstraction were found to have significant deviation in predicted frequency response. The quasi two-dimensional model presented an extreme situation: it could not be recalibrated for its frequency response to match the subject-specific model. This deficiency was attributed to complex support conditions at anterior-posterior extremities of the VFs, accentuated by further issues introduced through the tissue biomechanical properties. Increating canonical models by leveraging advances in clinical imaging techniques, the automated design procedure makes VF modeling based on subject-specific geometry more realizable.

A semi-analytical method for the free vibration analysis of thick double-shell systems

A semi-analytical method is extended to analyze the natural frequencies and mode shapes of thick double-shell systems. On the basis of the semi-analytical method for the state-vector equation of circular cylindrical shells, the mathematical model for thick double-shell systems is established. The main advantage of such model is that the finite element mesh is only used in the curved surface of shells and the number of variables is independence of the wall thickness of cylindrical shells. Moreover, the presented method is also suitable for the cases of various complex support conditions and the arbitrary distributed interconnecting springs. To validate the present method, several examples are calculated numerically. Some special phenomena on the mode shapes of thick double-shell systems are found.

Discrete singular convolution and its application to the analysis of plates with internal supports. Part 1: Theory and algorithm

AbstractThis paper presents a novel computational approach, the discrete singular convolution (DSC) algorithm, for analysing plate structures. The basic philosophy behind the DSC algorithm for the approximation of functions and their derivatives is studied. Approximations to the delta distribution are constructed as either bandlimited reproducing kernels or approximate reproducing kernels. Unified features of the DSC algorithm for solving differential equations are explored. It is demonstrated that different methods of implementation for the present algorithm, such as global, local, Galerkin, collocation, and finite difference, can be deduced from a single starting point. The use of the algorithm for the vibration analysis of plates with internal supports is discussed. Detailed formulation is given to the treatment of different plate boundary conditions, including simply supported, elastically supported and clamped edges. This work paves the way for applying the DSC approach in the following paper to plates with complex support conditions, which have not been fully addressed in the literature yet. Copyright © 2002 John Wiley & Sons, Ltd.

Finite strip method for the free vibration and buckling analysis of plates with abrupt changes in thickness and complex support conditions

The free vibration problem of a stepped plate supported on non-homogeneous Winkler elastic foundation with elastically mounted masses is formulated based on Hamilton's principle. The stepped plate is modelled by finite strip method. To overcome the problem of excessive continuity of common beam vibration functions at the location of abrupt change of plate thickness, a set of C 1 continuous functions have been chosen as the longitudinal interpolation functions in the finite strip analysis. The C 1 continuous functions are obtained by augmenting the relevant beam vibration modes with piecewise cubic polynomials. As these displacement functions are built up from beam vibration modes with appropriate corrections, they possess both the advantages of fast convergence of harmonic functions as well as the appropriate order of continuity. The method is further extended to the buckling analysis of rectangular stepped plates. Numerical results also show that the method is versatile, efficient and accurate.

Structural acoustics and vibration behavior of complex panels

Among the many mechanical parameters that influence structure-borne sound are the effects of stiffeners, added mass and complex support conditions along the structure boundaries. In the present paper, these effects are incorporated into a model of sound radiation in air from a complex, baffled, rectangular panel under harmonic point force or point moment excitation. A complex panel is thus defined as a panel which is stiffened lengthwise and widthwise by flexural-torsional beams, which carries point masses and which is elastically restrained against transverse displacement and rotation along the edges. The vibration of the panel assumes no fluid loading and is solved using the Rayleigh-Ritz method with simple polynomial trial functions. The expressions of the kinetic and strain energies associated with stiffeners, added mass and elastic boundary conditions, are detailed. A simple computation scheme is used to derive the farfield sound pressure from the transverse displacement of the panel. Numerical results are shown in terms of the mean quadratic velocity of the panel, radiated sound power and radiation efficiency for a variety of situations including force or moment excitation, simply-supported, clamped or free edges, addition of stiffeners and addition of a point mass, and are used to draw some useful guidelines in practice.

Analysis of stiffened shear-flexible orthotropic panels

A modified Ritz method is presented for the analysis of stiffened shear-flexible orthotropic panels subjected to mixed boundary conditions. The method is based on a modified version of the principle of minimum potential energy, which, in contrast to the classical principle, does not require the independent variables to a priori fulfill all geometric boundary conditions Because of this, relatively simple trial functions can be used even for the most complex support conditions. Efficiency and reliability of the method are demonstrated on the basis of several representative examples.

Flexural free vibrations of rectangular plates with complex support conditions

The spline finite strip method of analysis is introduced and applied to the study of flexural free vibration response of thin rectangular plates with complex support conditions. Examples are given to demonstrate the versatility, accuracy and efficiency of the method.