• Coupled systems mechanics
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• v.12 no.4
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• pp.297-313
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• 2023

This paper deals with delamination analysis of non-linear viscoelastic multilayered beam subjected to bending in the plane of the layers. For this purpose, first, a non-linear viscoelastic model is presented. In order to take into account the non-linear viscoelastic behaviour, a non-linear spring and a non-linear dashpot are assembled in series with a linear spring connected in parallel to a linear dashpot. The behaviours of the non-linear spring and dashpot are described by applying non-linear stress-strain and stress-rate of strain relationships, respectively. The constitutive law of the model is derived. Due to the non-linear spring and dashpot, the constitutive law is non-linear. This law is used for describing the time-dependent mechanical behaviour of the beam under consideration. The material properties involved in the constitutive law vary along the beam length due to the continuous material inhomogeneity of the layers. Solution of the strain energy release rate for the delamination is obtained by analyzing the balance of the energy with considering of the non-linear viscoelastic behaviour. The strain energy release rate is found also by using the complementary strain energy for verification. A parametric study is carried-out by using the solution obtained. The solutions derived and the results obtained help to understand the time-dependent delamination of non-linear viscoelastic beams under loading in the plane of layers.

• Computers and Concrete
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• v.15 no.4
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• pp.547-562
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• 2015

A two-dimensional multi-layered finite elements modeling of reinforced concrete structures at non-linear behaviour under monotonic and cyclical loading is presented. The non-linearity material is characterized by several phenomena such as: the physical non-linearity of the concrete and steels materials, the behaviour of cracked concrete and the interaction effect between materials represented by the post-cracking filled. These parameters are taken into consideration in this paper to examine the response of the reinforced concrete structures at the non-linear behaviour. Four examples of application are presented. The numerical results obtained, are in a very good agreement with available experimental data and other numerical models of the literature.

• Structural Engineering and Mechanics
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• v.18 no.5
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• pp.565-589
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• 2004

The present paper concerns the macroscopic overall description of rheologic properties for steel wire and synthetic fibre cables under variable loading actions according to non-linear creep and/or relaxation theory. The general constitutive equations of non-linear creep and/or relaxation of tension elements - cables under one-step and the variable stress or strain inputs using the product and two types of additive approximations of the kernel functions are presented in the paper. The derived non-linear constitutive equations describe a non-linear rheologic behaviour of the cables for a variable stress or strain history using the kernel functions determined only by one-step - constant creep or relaxation tests. The developed constitutive equations enable to simulate and to predict in a general way non-linear rheologic behaviour of the cables under an arbitrary loading or straining history. The derived constitutive equations can be used for the various tension structural elements with the non-linear rheologic properties under uniaxial variable stressing or straining.

• Steel and Composite Structures
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• v.20 no.2
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• pp.379-397
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• 2016

Due to creep and shrinkage of the concrete core, concrete-filled steel tubular (CFST) arches continue to deform in the long-term under sustained loads. This paper presents analytical investigations of the effects of geometric nonlinearity on the long-term in-plane structural performance and stability of three-pinned CFST circular arches under a sustained uniform radial load. Non-linear long-term analysis is conducted and compared with its linear counterpart. It is found that the linear analysis predicts long-term increases of deformations of the CFST arches, but does not predict any long-term changes of the internal actions. However, non-linear analysis predicts not only more significant long-term increases of deformations, but also significant long-term increases of internal actions under the same sustained load. As a result, a three-pinned CFST arch satisfying the serviceability limit state predicted by the linear analysis may violate the serviceability requirement when its geometric nonlinearity is considered. It is also shown that the geometric nonlinearity greatly reduces the long-term in-plane stability of three-pinned CFST arches under the sustained load. A three-pinned CFST arch satisfying the stability limit state predicted by linear analysis in the long-term may lose its stability because of its geometric nonlinearity. Hence, non-linear analysis is needed for correctly predicting the long-term structural behaviour and stability of three-pinned CFST arches under the sustained load. The non-linear long-term behaviour and stability of three-pinned CFST arches are compared with those of two-pinned counterparts. The linear and non-linear analyses for the long-term behaviour and stability are validated by the finite element method.

• Coupled systems mechanics
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• v.10 no.1
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• pp.1-19
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• 2021

Composite nature of the masonry structures in general causes complex and non-linear behaviour, especially in intense vibration conditions. The presence of different types and forms of structural elements and different materials is a major problem for the analysis of these type of structures. For this reason, the analysis of the behaviour of masonry structures requires a combination of experimental tests and non-linear mathematical modelling. The famous UNESCO Heritage Old Bridge in Mostar was selected as an example for the analysis of the global behaviour of reinforced stone arch masonry bridges. As part of the experimental research, a model of the Old Bridge was constructed in a scale of 1:9 and tested on a shaking table platform for different levels of seismic excitation. Non-linear mathematical modelling was performed using a combined finite-discrete element method (FDEM), including the effect of connection elements. The paper presents the horizontal displacement of the top of the arch and the failure mechanism of the Old Bridge model for the experimental and the numerical phase, as well as the comparison of the results. This research provided a clearer insight into the global behaviour of stone arch masonry structures reinforced with steel clamps and steel dowels, which is significant for the structures classified as world cultural heritage.

• Structural Engineering and Mechanics
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• v.10 no.2
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• pp.181-195
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• 2000

A two-step procedure for the application of non linear constrained programming to the limit analysis of rigid brick-block systems with no-tension and frictional interface is implemented and applied to various masonry structures. In the first step, a linear problem of programming, obtained by applying the upper bound theorem of limit analysis to systems of blocks interacting through no-tension and dilatant interfaces, is solved. The solution of this linear program is then employed as initial guess for a non linear and non convex problem of programming, obtained applying both the 'mechanism' and the 'equilibrium' approaches to the same block system with no-tension and frictional interfaces. The optimiser used is based on the sequential quadratic programming. The gradients of the constraints required are provided directly in symbolic form. In this way the program easily converges to the optimal solution even for systems with many degrees of freedom. Various numerical analyses showed that the procedure allows a reliable investigation of the ultimate behaviour of jointed structures, such as stone masonry structures, under statical load conditions.

• International Journal of Concrete Structures and Materials
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• v.11 no.2
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• pp.261-273
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• 2017

The control of the deformative behaviour of pre-stressed concrete roof elements for a satisfactory service performance is a main issue of their structural design. Slender light-weight wing-shaped roof elements, typical of the European heritage, are particularly sensitive to this problem. The paper presents the results of deformation measurements during storage and of both torsional-flexural and purely flexural load tests carried out on a full-scale 40.5 m long innovative wing-shaped roof element. An element-based simplified integral procedure that de-couples the evolution of the deflection profile with the progressive shortening of the beam is adopted to catch the experimental visco-elastic behaviour of the element and the predictions are compared with normative close-form solutions. A linear 3D fem model is developed to investigate the torsional-flexural behaviour of the member. A mechanical non-linear beam model is used to predict the purely flexural behaviour of the roof member in the pre- and post-cracking phases and to validate the loss prediction of the adopted procedure. Both experimental and numerical results highlight that the adopted analysis method is viable and sound for an accurate simulation of the service behaviour of precast roof elements.

• Steel and Composite Structures
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• v.4 no.6
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• pp.489-507
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• 2004

The flexibility of the connection between steel and concrete largely influences the global behaviour of the composite beam. Therefore the way the connection is modelled is the key issue in its structural analysis. Here we present a new strain-based finite element formulation in which we consider non-linear material and contact models. The computational efficiency and accuracy of the formulation is proved with the comparison of our numerical results with the experimental results of Abdel Aziz (1986) obtained in a full-scale laboratory test. The shear connectors are assumed to follow a non-linear load-slip relationship proposed by Ollgaard et al. (1971). We introduce the notion of the generalized slip, which offers a better physical interpretation of the behaviour of the contact and gives an additional material slip parameter. An excellent agreement of experimental and numerical results is obtained, using only a few finite elements. This demonstrates that the present numerical approach is appropriate for the evaluation of behaviour of planar composite beams and perfect for practical calculations.

• Structural Engineering and Mechanics
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• v.85 no.1
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• pp.89-104
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• 2023

This work presents a proposal for employing reduced numerical integration in the formulation of the 4-node quadrilateral solid finite element. The use of these low-order integration rules leads to numerical instabilities such as those producing the hourglass effect. The proposed procedure allows evaluating a given constitutive model only in one integration point, achieving an attractive computational cost reduction and, also, successfully controls the hourglass effect. A validation of the proposal is included and discussed throughout the paper. To show the efficiency of the proposal, several application examples of masonry structures are studied and discussed. To represent the non-linear mechanical behaviour of masonry a plastic-damage model is implemented within the application of this sub-integration scheme. Also, in order to have a full and computationally efficient strategy to determine the behaviour of masonry structures, involving its evolution to collapse, a homogenization technique with a macro-modeling approach is used. The methodology discussed throughout this paper demonstrates a substantial computational cost reduction and an improved approximation of the non-linear problem evidenced by a reduction of up to 85% of the computational time for some cases.

• Wind and Structures
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• v.29 no.5
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• pp.339-359
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• 2019

Pre-stressed concrete poles are among the supporting systems used to support transmission lines. It is essential to protect transmission line systems from harsh environmental attacks such as downburst wind events. Typically, these poles are designed to resist synoptic wind loading as current codes do not address high wind events in the form of downbursts. In the current study, the behavior of guyed pre-stressed concrete Transmission lines is studied under downburst loads. To the best of the authors' knowledge, this study is the first investigation to assess the behaviour of guyed pre-stressed concrete poles under downburst events. Due to the localized nature of those events, identifying the critical locations and parameters leading to peak forces on the poles is a challenging task. To overcome this challenge, an in-house built numerical model is developed incorporating the following: (1) a three-dimensional downburst wind field previously developed and validated using computational fluid dynamics simulations; (2) a computationally efficient analytical technique previously developed and validated to predict the non-linear behaviour of the conductors including the effects of the pretension force, sagging, insulator's stiffness and the non-uniform distribution of wind loads, and (3) a non-linear finite element model utilized to simulate the structural behaviour of the guyed pre-stressed concrete pole considering material nonlinearity. A parametric study is conducted by varying the downbursts locations relative to the guyed pole while considering three different span values. The results of this parametric study are utilized to identify critical downburst configurations leading to peak straining actions on the pole and the guys. This is followed by comparing the obtained critical load cases to new load cases proposed to ASCE-74 loading committee. A non-linear failure analysis is then conducted for the three considered guyed pre-stressed concrete transmission line systems to determine the downburst jet velocity at which the pole systems fail.