Power Secant Method applied to natural frequency extraction of Timoshenko beam structures

This work deals with an improved plane frame formulation whose exact dynamic stiffness matrix (DSM) presents, uniquely, null determinant for the natural frequencies. In comparison with the classical DSM, the formulation herein presented has some major advantages: local mode shapes are preserved in the formulation so that, for any positive frequency, the DSM will never be ill-conditioned; in the absence of poles, it is possible to employ the secant method in order to have a more computationally efficient eigenvalue extraction procedure. Applying the procedure to the more general case of Timoshenko beams, we introduce a new technique, named ""power deflation"", that makes the secant method suitable for the transcendental nonlinear eigenvalue problems based on the improved DSM. In order to avoid overflow occurrences that can hinder the secant method iterations, limiting frequencies are formulated, with scaling also applied to the eigenvalue problem. Comparisons with results available in the literature demonstrate the strength of the proposed method. Computational efficiency is compared with solutions obtained both by FEM and by the Wittrick-Williams algorithm.

A contribution to the exact modal solution of in-plane beam structures

The exact vibration modes and natural frequencies of planar structures and mechanisms, comprised Euler-Bernoulli beams, are obtained by solving a transcendental. nonlinear, eigenvalue problem stated by the dynamic stiffness matrix (DSM). To solve this kind of problem, the most employed technique is the Wittrick-Williams algorithm, developed in the early seventies. By formulating a new type of eigenvalue problem, which preserves the internal degrees-of-freedom for all members in the model, the present study offers an alternative to the use of this algorithm. The new proposed eigenvalue problem presents no poles, so the roots of the problem can be found by any suitable iterative numerical method. By avoiding a standard formulation for the DSM, the local mode shapes are directly calculated and any extension to the beam theory can be easily incorporated. It is shown that the method here adopted leads to exact solutions, as confirmed by various examples. Extensions of the formulation are also given, where rotary inertia, end release, skewed edges and rigid offsets are all included. (C) 2008 Elsevier Ltd. All rights reserved.

Optimal location of supports in beam structures using genetic algorithms

Real structures can be thought as an assembly of components, as for instances plates, shells and beams. This later type of component is very commonly found in structures like frames which can involve a significant degree of complexity or as a reinforcement element of plates or shells. To obtain the desired mechanical behavior of these components or to improve their operating conditions when rehabilitating structures, one of the eventual parameters to consider for that purpose, when possible, is the location of the supports. In the present work, a beam-type structure is considered, and for a set of cases concerning different number and types of supports, as well as different load cases, the authors optimize the location of the supports in order to obtain minimum values of the maximum transverse deflection. The optimization processes are carried out using genetic algorithms. The results obtained, clearly show a good performance of the approach proposed. © 2014 IEEE.

Analysis of sandwich beam structures using kriging based higher order models

Functionally graded composite materials can provide continuously varying properties, which distribution can vary according to a specific location within the composite. More frequently, functionally graded materials consider a through thickness variation law, which can be more or less smoother, possessing however an important characteristic which is the continuous properties variation profiles, which eliminate the abrupt stresses discontinuities found on laminated composites. This study aims to analyze the transient dynamic behavior of sandwich structures, having a metallic core and functionally graded outer layers. To this purpose, the properties of the particulate composite metal-ceramic outer layers, are estimated using Mod-Tanaka scheme and the dynamic analyses considers first order and higher order shear deformation theories implemented though kriging finite element method. The transient dynamic response of these structures is carried out through Bossak-Newmark method. The illustrative cases presented in this work, consider the influence of the shape functions interpolation domain, the properties through-thickness distribution, the influence of considering different materials, aspect ratios and boundary conditions. (C) 2014 Elsevier Ltd. All rights reserved.

Dynamic behaviour of soft core sandwich beam structures using kriging-based layerwise models

Sandwich structures with soft cores are widely used in applications where a high bending stiffness is required without compromising the global weight of the structure, as well as in situations where good thermal and damping properties are important parameters to observe. As equivalent single layer approaches are not the more adequate to describe realistically the kinematics and the stresses distributions as well as the dynamic behaviour of this type of sandwiches, where shear deformations and the extensibility of the core can be very significant, layerwise models may provide better solutions. Additionally and in connection with this multilayer approach, the selection of different shear deformation theories according to the nature of the material that constitutes the core and the outer skins can predict more accurately the sandwich behaviour. In the present work the authors consider the use of different shear deformation theories to formulate different layerwise models, implemented through kriging-based finite elements. The viscoelastic material behaviour, associated to the sandwich core, is modelled using the complex approach and the dynamic problem is solved in the frequency domain. The outer elastic layers considered in this work may also be made from different nanocomposites. The performance of the models developed is illustrated through a set of test cases. (C) 2015 Elsevier Ltd. All rights reserved.

Decentralized model reference control of flexible cable-stayed beam structures

A decentralized model reference controller is designed to reduce the magnitude of the transversal vibration of a flexible cable-stayed beam structure induced by a seismic excitation. The controller design is made based on the principle of sliding mode such that a priori knowledge

Automated formulation of optimisation models for steel beam structures

Over 70% of the total costs of an end product are consequences of decisions that are made during the design process. A search for optimal cross-sections will often have only a marginal effect on the amount of material used if the geometry of a structure is fixed and if the cross-sectional characteristics of its elements are property designed by conventional methods. In recent years, optimalgeometry has become a central area of research in the automated design of structures. It is generally accepted that no single optimisation algorithm is suitable for all engineering design problems. An appropriate algorithm, therefore, mustbe selected individually for each optimisation situation. Modelling is the mosttime consuming phase in the optimisation of steel and metal structures. In thisresearch, the goal was to develop a method and computer program, which reduces the modelling and optimisation time for structural design. The program needed anoptimisation algorithm that is suitable for various engineering design problems. Because Finite Element modelling is commonly used in the design of steel and metal structures, the interaction between a finite element tool and optimisation tool needed a practical solution. The developed method and computer programs were tested with standard optimisation tests and practical design optimisation cases. Three generations of computer programs are developed. The programs combine anoptimisation problem modelling tool and FE-modelling program using three alternate methdos. The modelling and optimisation was demonstrated in the design of a new boom construction and steel structures of flat and ridge roofs. This thesis demonstrates that the most time consuming modelling time is significantly reduced. Modelling errors are reduced and the results are more reliable. A new selection rule for the evolution algorithm, which eliminates the need for constraint weight factors is tested with optimisation cases of the steel structures that include hundreds of constraints. It is seen that the tested algorithm can be used nearly as a black box without parameter settings and penalty factors of the constraints.

Decentralized model reference control of flexible cable-stayed beam structures

A decentralized model reference controller is designed to reduce the magnitude of the transversal vibration of a flexible cable-stayed beam structure induced by a seismic excitation. The controller design is made based on the principle of sliding mode such that a priori knowledge

Analysis, reliability and optimization of reinforced concrete 2-D structures

In this paper a consistent analysis of reinforced concrete (RC) two-dimensional (2-D) structures,namely slab structures subjected to in-plane and out-plane forces, is presented. By using this method of analysis the well established methodology for dimensioning and verifying RC sections of beam structures is extended to 2-D structures. The validity of the proposed analysis results is checked by comparing them with some published experimental test results. Several examples show some of these proposed analysis features, such as the influence of the reinforcement layout on the service and ultimate behavior of a slab structure and the non straightforward problem of the optimal dimension at a slab point subjected to several loading cases. Also, in these examples, the method applications to design situations as multiple steel families and non orthogonal reinforcement layout are commented.

A consistent method of analysis of RC shell structures

In this paper some topics related to the design of reinforced concrete (RC) shells are addressed. The influence of the reinforcement layout on the service and ultimate behavior of the shell structure is commented. The well established methodology for dimensioning and verifying RC sections of beam structures is extended. In this way it is possible to treat within a unified procedure the design and verification of RC two dimensional structures, in particular membrane and shell structures. Realistic design situations as multiple steel farnilies and non orthogonal reinforcement layout can be handled. Finally, some examples and applications of the proposed methodology are presented.

Dimensionless analysis of constrained damping treatments

One of the most effective ways of controlling vibrations in plate or beam structures is by means of constrained viscoelastic damping treatments. Contrary to the unconstrained configuration, the design of constrained and integrated layer damping treatments is multifaceted because the thickness of the viscoelastic layer acts distinctly on the two main counterparts of the strain energy the volume of viscoelastic material and the shear strain field. In this work, a parametric study is performed exploring the effect that the design parameters, namely the thickness/length ratio, constraining layer thickness, material modulus, natural mode and boundary conditions have on these two counterparts and subsequently, on the treatment efficiency. This paper presents five parametric studies, namely, the thickness/length ratio, the constraining layer thickness, material properties, natural mode and boundary conditions. The results obtained evidence an interesting effect when dealing with very thin viscoelastic layers that contradicts the standard treatment efficiency vs. layer thickness relation; hence, the potential optimisation of constrained and integrated viscoelastic treatments through the use of properly designed thin multilayer configurations is justified. This work presents a dimensionless analysis and provides useful general guidelines for the efficient design of constrained and integrated damping treatments based on single or multi-layer configurations. (C) 2012 Elsevier Ltd. All rights reserved.

Teräspalkkirakenteiden palomitoitus hiilivetypalossa

Työn tavoitteena oli kehittää teräspalkkirakenteiden palosuunnittelua ja palosuojauksen toteutusta öljynjalostamolla käytettävien kantavien teräspalkkirakenteiden osalta. Lisäksi tavoitteena oli luoda suunnitteluohjeen runko palomitoituksen toteuttamiseksi Neste Engineering Oy:ssä. Ongelmakohtia työssä olivat rakenteiden kapasiteettien tarkka määritys, toimivien toteutusratkaisujen etsiminen, sekä öljynjalostamolla mitoituspalona käytettävän hiilivetypalon SFS-ENV-1992-1-2 käyttö yleisemmin mitoituspalona käytettävän standardipalo ISO-834 sijaan. Työssä perehdyttiin kirjallisuuden perusteella eri palosuojausmenetelmiin. Tarkemman jatkotutkimuksen kohteeksi otettiin jo käytössä hyväksi havaittu teräsputkipalkkien sisäpuoleinen betonitäyttö. Menetelmässä teräsputkipalkin oletetaan kantavan kuormat normaalitilassa ja sisällä olevan raudoitetun betonin palossa. Palkkirakenteiden kapasiteettimitoitus määritettiin laskennallisesti poikkileikkauksille. Mitoitus perustuu palkissa tapahtuvien sisäisten venymien ja puristumien tarkasteluun, sekä poikkileikkauksen tarkan lämpötilajakauman huomioimiseen. Raudoitustankojen ankkurointia palkki-pilari-liitoksessa kehitettiin valmistuksen kannalta yksioikoisemmaksi ja helpommin toteutettavaksi. Palkkien raudoituksiin suunniteltiin kierremuhvijatkoksella toteutettava ankkurointimenetelmä, jolla palkkien raudoitustangot saadaan ankkuroitua täydestä kapasiteetistaan tapauskohtaisesti pilarin vastakkaisella puolella olevaan palkkiin tai ankkurointikappaleella pilariin. Teräsputkipilarin betonivalun vaihtoehtoisiin menetelmiin tutustuttiin. Pilarin alapäähän asennettavan venttiilin läpi tapahtuva täyttö helpottaa betonointityövaihetta. Tutkimuksen tuloksena luotiin suunnitteluohjeen runko, jonka pohjalta voidaan tehdä lopullinen ohje. Myös työn tuloksena saatu laskentaohjelma palkkien momentti-kapasiteetin ja pilarin nurjahduskuorman laskemiseksi helpottaa suunnittelua. Raudoituksen ankkurointiin ja betonointiin esitettyjen menetelmien toimivuus on syytä kokeilla käytännössä ja tehdä jatkokehitys näistä saatavien kokemusten pohjalta.

Lujasta rakenneteräksestä tehdyn rakenteen vikasietoisuuden määritys

Tässä työssä tutkittiin Ruukin valmistamista lujista Optim 700 MC Plus sekä Optim 700 QL teräksistä tehtyjen hitsattujen palkkirakenteiden vikasietoisuutta sekä murtumiskäyttäytymistä laboratoriossa suoritettujen täyden mittakaavan kokeiden avulla. Koerakenteet suunniteltiin siten, että rakenteen kylmämuovauksen sekä hitsauksen vaikutukset yhdessä rakenteen geometrian vaikutuksen kanssa heikentävät rakenteen murtumissitkeyttä rakenteeseen tehdyn teräväkärkisen alkusärön tasossa. Suunnitellussa koesarjassa varioidaan testauslämpötilan lisäksi hitsauksen lämmöntuontia sekä koerakenteeseen tehtävän alkusärön kokoa. Tässä työssä tavoitteena oli yleisesti esittää menettely hitsatun säröllisen teräsrakenteen kestävyyden arviointia varten. Optim 700 MC Plus teräksestä tehdyn koerakenteen käyttäytymistä tutkittiin laskennallisesti murtumismekaniikan avulla. Laadittujen FEM - mallien avulla laskettiin rakenteen murtumisparametrien arvot kummallekin tutkittavalle teräkselle. Optim 700 MC Plus materiaalista valmistetuille koerakenteen säröalueen rakennedetaljia vastaavalle koekappaleille suoritettiin murtumissitkeyskokeita. Murtumissitkeyskokeista saatujen tulosten avulla pystyttiin kuvaamaan täyden mittakaavan koerakenteessa olevan särön murtumiskäyttäytymistä mitoitusmenetelmissä. Koerakenteelle laskettiin tässä työssä kriittisen särökoon ja sitä vastaavan kuorman arvot perustuen rakenteen oletettuun hauraaseen, epästabiiliin sitkeään sekä plastiseen murtumiskäyttäytymiseen. Tässä työssä testattiin molemmista tutkittavista materiaaleista valmistetut täyden mittakaavan koerakenteet -40 °C lämpötilassa. Molemmat testatut rakenteet käyttäytyvät mitattujen siirtymätulosten perusteella melko hauraasti. Optim 700 MC Plus materiaalille saatujen laskentatulosten voidaan todeta testatun koekappaleen perusteella soveltuvan hauraasti käyttäytyvän rakenteen mitoitukseen.

Experimental damage detection using system norms

Nowadays there is great interest in structural damage detection in systems using nondestructive tests. Once the failure is detected, as for instance a crack, it is possible to take providences. There are several different approaches that can be used to obtain information about the existence, location and extension of the fault in the system by non-destructive tests. Among these methodologies, one can mention different optimization techniques, as for instance classical methods, genetic algorithms, neural networks, etc. Most of these techniques, which are based on element-byelement adjustments of a finite element (FE) model, take advantage of the dynamic behavior of the model. However, in practical situations, usually, is almost impossible to obtain an accuracy model. In this paper, it is proposed an experimental technique for damage location. This technique is based on H: norm to obtain the damage location. The dynamic properties of the structure were identified using experimental data by eigensystem realization algorithm (ERA). The experimental test was carried out in a beam structure through varying the mass of an element. For the output signal was used a piezoelectric sensor. The signal of input of sine form was generated through SignalCalc® software.

Cálculo de estructuras de barras incluyendo efectos dinámicos de interacción suelo-estructura. Modelo mixto de elementos finitos y elementos de contorno.

[EN] This work presents a 2D finite elements - boundary elements coupling model for the harmonic analysis of beam structures founded on viscoelastic domains. The beam structure is modeled by finite elements, whereas the soil is modeled as a homogeneous isotropic viscoelastic boundary element region. The coupling is enforced through a rigid boundary in which equilibrium and compatibility conditions are applied. Formulation and implementation are presented together with some application examples.