Limit analysis of masonry walls using discontinuity layout optimization and homogenization

A numerical limit analysis model for masonry walls subject to in-plane loading is posed as a discontinuity layout optimization (DLO) problem, with the masonry conveniently modeled using a smeared continuum (“macromodeling”) approach and a homogenized yield surface. Unlike finite element limit analysis, DLO is formulated entirely in terms of discontinuities and can produce accurate solutions for problems involving singularities naturally, without the need for mesh refinement. In the homogenized model presented, masonry joints are reduced to interfaces, with sliding governed by an associative friction flow rule and blocks are assumed to be infinitely resistant. The model takes account of the interlock ratio of the masonry blocks, their aspect ratio and the cohesion and coefficient of friction of interfaces in both the vertical and horizontal directions. Results from the proposed model are compared with those from the literature, showing that complex failure mechanisms can be identified and that safe estimates of load carrying capacity can be obtained. Finally, to demonstrate the utility of the proposed modeling approach, it is applied to more complex problems involving interactions with other elements, such as voussoir arches and weak underlying soil layers.     

System reliability of timber trusses based on non-linear structural modelling

Structural design is today concerned with single component performance where each limit state is related to a single mode of failure of a single component. Further, in limit state codes the strength variables are related to a deterministic value (usually the 5-percentile). However, in a structure with a number of elements, two different effects (called system effects) can be found:

Strength and ductility of FRP web-bonded RC beams for the assessment of retrofitted beam–column joints

It is generally accepted that beam–column joints are critical elements of reinforced concrete (RC) buildings subjected to lateral loads, and that they may require specific design treatment following the accepted design philosophy of the strong-columnweak-beam. In earthquake-prone regions, the joints must be designed to allow the dissipation of large amounts of energy into the neighbouring elements without a significant loss of strength and ductility. The frames are often designed carefully based on the strong-column–weak-beam concept and their joints detailed accordingly. Sometimes, though, the detailing is inadequate (example, RC joints designed to earlier codes have insufficient lateral resistance). Web-bonded FRP (fibre reinforced plastic) is one of the few possible strengthening methods that can be used when an inadequately detailed joint is damaged causing severe degradation of the joint’s structural strength. In this paper, the results of some tests on FRP strengthened specimens are presented. The results show that the method is effective and capable of restoring or even upgrading the strength of the system. In addition, using the basic principles of equilibrium and compatibility, an analytical model is presented that simplifies the analysis and design of this strengthening scheme. Based on the model, a range of design graphs are presented for selection of the type and the amount of FRP required upgrading an existing joint to a specified moment capacity and curvature ductility.     

The effect of controlled shot peening on fusion welded joints

This work examines the effect of controlled shot peening (CSP) treatment on the fatigue strength of an ASTM A516 grade 70 carbon steel welded joint. Metallurgical modifications, hardness, elemental compositions, and internal discontinuities, such as porosity, inclusions, lack of penetration, and undercut found in treated and untreated fusion welded joints, were characterized. The fatigue results of as-welded and peened skimmed joints were compared. It was observed that the effect of the CSP and skimming processes improved the fatigue life of the fusion weld by 50% on MMA-welded, 63% on MIG-welded, and 60% on TIG-welded samples.     

A fully smoothed XFEM for analysis of axisymmetric problems with weak discontinuities

In this paper, we propose a fully smoothed extended finite element method for axisymmetric problems with weak discontinuities. The salient feature of the proposed approach is that all the terms in the stiffness and mass matrices can be computed by smoothing technique. This is accomplished by combining the Gaussian divergence theorem with the evaluation of indefinite integral based on smoothing technique, which is used to transform the domain integral into boundary integral. The proposed technique completely eliminates the need for isoparametric mapping and the computing of Jacobian matrix even for the mass matrix. When employed over the enriched elements, the proposed technique does not require sub‐triangulation for the purpose of numerical integration. The accuracy and convergence properties of the proposed technique are demonstrated with a few problems in elastostatics and elastodynamics with weak discontinuities. It can be seen that the proposed technique yields stable and accurate solutions and is less sensitive to mesh distortion. Copyright © 2016 John Wiley & Sons, Ltd.     

Linear random vibration by stochastic reduced‐order models

A practical method is developed for calculating statistics of the states of linear dynamic systems with deterministic properties subjected to non‐Gaussian noise and systems with uncertain properties subjected to Gaussian and non‐Gaussian noise. These classes of problems are relevant as most systems have uncertain properties, physical noise is rarely Gaussian, and the classical theory of linear random vibration applies to deterministic systems and can only deliver the first two moments of a system state if the noise is non‐Gaussian. The method (1) is based on approximate representations of all or some of the random elements in the definition of linear random vibration problems by stochastic reduced‐order models (SROMs), that is, simple random elements having a finite number of outcomes of unequal probabilities, (2) can be used to calculate statistics of a system state beyond its first two moments, and (3) establishes bounds on the discrepancy between exact and SROM‐based solutions of linear random vibration problems. The implementation of the method has required to integrate existing and new numerical algorithms. Examples are presented to illustrate the application of the proposed method and assess its accuracy. Copyright © 2009 John Wiley & Sons, Ltd.     

Super-resolving random-Gaussian apodized photon sieve

A novel apodized photon sieve is presented in which random dense Gaussian distribution is implemented to modulate the pinhole density in each zone. The random distribution in dense Gaussian distribution causes intrazone discontinuities. Also, the dense Gaussian distribution generates a substantial number of pinholes in order to form a large degree of overlap between the holes in a few innermost zones of the photon sieve; thereby, clear zones are formed. The role of the discontinuities on the focusing properties of the photon sieve is examined as well. Analysis shows that secondary maxima have evidently been suppressed, transmission has increased enormously, and the central maxima width is approximately unchanged in comparison to the dense Gaussian distribution. Theoretical results have been completely verified by experiment.     

Weak discontinuities in magneto-gasdynamics with finite electrical conductivity

Following Elcrat[6] the phenomena associated with the weak discontinuities in inviscid non-heat conducting gas with finite electrical conductivity have been studied here. The differential equations for growth and decay of weak discontinuities have been formulated. In order to integrate them in full generality they are transformed to an equation along the bi-characteristic curve in the characteristic manifold Σ = US(t). These equations have been solved completely. The criteria for decay or “blow up” of weak discontinuities are given. The role of finite electrical conductivity is to cause damping.     

Accurate evaluation of 3D stress fields in adhesive bonded joints via higher-order FE models

Abstract

The accurate representation of the 3D stress fields at the bonded areas of adhesive joints is essential for their design and strength evaluation. In the present study, higher-order beam models developed in the framework of the Carrera Unified Formulation are employed to reduce the complexity and computational cost of numerical simulations on adhesive joints. The different components of the adhesive joint, i.e. adherends and adhesive, are modeled as beams with independent kinematics based on the Hierarchical Legendre Expansion (HLE). HLE models make use of a hierarchical polynomial expansion over the cross-section of the beam, thus allowing for the control of the accuracy of the stress solutions via the polynomial expansion. Recalling the Finite Element method, the beam axis is discretized by means of 1D elements. In this manner, generic geometries of the adhesive bonded joints can be studied. The proposed model is assessed through comparison against numerical and analytical references from the literature for single lap and double lap joints. Finally, a detailed 3D analysis is performed on the single lap joint problem, showing that the stress gradients along the adhesive are correctly and efficiently described if the proposed methodology is employed.     

Probabilistic analysis of multi-step failure process of a laminated composite in bending

This paper presents results of a theoretical and experimental analysis of the random bending strength of laminated composites. Multi-layered composites with a periodic structure of sublaminates are considered in a combined loading (bending action and plane stress) state. The random strength response of the composites is analyzed on the basis of a multi-step failure probabilistic model. Here, the multi-step failure is considered as a process in which the failure of some single structural elements (sublaminates, laminae) leads to load redistribution onto other intact elements. A numerical algorithm based on the Monte Carlo technique and respective computer code are offered. The effect of scatter of structure parameters and number of sublaminates on the bending strength distribution is analyzed in detail. Experimental confirmation is considered on an example of uniaxial bending of laminated carbon-fiber-reinforced plastics. A method for evaluation of reliability in a random combined loading is also suggested.     

Failure of heterogeneous materials: 3D meso‐scale FE models with embedded discontinuities

We present a meso‐scale model for failure of heterogeneous quasi‐brittle materials. The model problem of heterogeneous materials that is addressed in detail is based on two‐phase 3D representation of reinforced heterogeneous materials, such as concrete, where the inclusions are melt within the matrix. The quasi‐brittle failure mechanisms are described by the spatial truss representation, which is defined by the chosen Voronoi mesh. In order to explicitly incorporate heterogeneities with no need to change this mesh, some bar elements are cut by the phase‐interface and must be split into two parts. Any such element is enhanced using both weak and strong discontinuities, based upon the Incompatible Mode Method. Furthermore, a dedicated operator split solution procedure is proposed to keep local any additional computation on elements with embedded discontinuities. The results for several numerical simulations are presented to illustrate the capabilities of the proposed model to provide an excellent representation of failure mechanisms for any different macroscopic loading path. Copyright © 2010 John Wiley & Sons, Ltd.     

Delamination analysis of composites by new orthotropic bimaterial extended finite element method

The extended finite element method (XFEM) is further improved for fracture analysis of composite laminates containing interlaminar delaminations. New set of bimaterial orthotropic enrichment functions are developed and utilized in XFEM analysis of linear‐elastic fracture mechanics of layered composites. Interlaminar crack‐tip enrichment functions are derived from analytical asymptotic displacement fields around a traction‐free interfacial crack. Also, heaviside and weak discontinuity enrichment functions are utilized in modeling discontinuous fields across interface cracks and bimaterial weak discontinuities, respectively. In this procedure, elements containing a crack‐tip or strong/weak discontinuities are not required to conform to those geometries. In addition, the same mesh can be used to analyze different interlaminar cracks or delamination propagation. The domain interaction integral approach is also adopted in order to numerically evaluate the mixed‐mode stress intensity factors. A number of benchmark tests are simulated to assess the performance of the proposed approach and the results are compared with available reference results. Copyright © 2011 John Wiley & Sons, Ltd.     

Discrete and continuum methods for numerical simulations of non‐linear wave propagation in discontinuous media

The main objective of this paper is to develop a methodology to model dynamic loading of various discontinuous media. Two methods for modeling non‐linear waves in a media with multiple discontinuities are considered. The first one, a discrete method, is based on the Simple Common Plane contact algorithm. This method can be applied both to compliant contacts characterized by finite thickness and elastic moduli (such as joints in geomechanics) as well as to non‐compliant frictional contacts traditionally described by the slide lines in finite element/finite difference codes. The second one, a continuum method, assumes that the contacts are not compliant and can be modeled as one or several weakness planes cutting through the elements of the computational mesh. Both discrete and continuum methods described in the paper can be applied to derive equivalent continuum properties for media with multiple discontinuities. An example of such application for a randomly jointed media is given in the paper. Copyright © 2010 John Wiley & Sons, Ltd.     

Mixed-mode crack growth in bonded composite joints under standard and impact-fatigue loading

Carbon fibre reinforced polymers (CFRPs) are now well established in many high-performance applications and look set to see increased usage in the future, especially if lower cost manufacturing and solutions to certain technical issues, such as poor out-of-plane strength, can be achieved. A significant question when manufacturing with CFRP is the best joining technique to use, with adhesive bonding and mechanical fastening currently the two most popular methods. It is a common view that mechanical fastening is preferred for thicker sections and adhesive bonding for thinner ones; however, advances in the technology and better understanding of ways to design joints have lead to increasing consideration of adhesive bonding for traditionally mechanically fastened joints. In high-performance applications fatigue loading is likely and in some cases repetitive low-energy impacts, or impact fatigue, can appear in the load spectrum. This article looks at mixed-mode crack growth in epoxy bonded CFRP joints in standard and impact fatigue. It is shown that the back-face strain technique can be used to monitor cracking in lap-strap joints (LSJs) and piezo strain gauges can be used to measure the strain response of impacted samples. It is seen that there is significant variation in the failure modes seen in the samples and that the crack propagation rate is highly dependent on the fracture mode. Furthermore, it is found that the crack propagation rate is higher in impact fatigue than in standard fatigue even when the maximum load is significantly lower.     

Laser fabrication and characterization of sub-millimeter joints between polyimide and Ti-coated borosilicate glass

Laser-fabricated joints of sub-millimeter widths between biocompatible, dissimilar materials have the potential for application as encapsulation of miniature implantable biomedical devices. In this work, we briefly describe the laser joining method of a very promising system, polyimide/titanium-coated borosilicate glass, and present results from characterization of such laser joints by means of mechanical failure (tensile) tests, optical and scanning electron microscopy, X-ray photoelectron spectroscopy (XPS) and Raman spectroscopy. Our results suggest that the formation of the joints is a result of the creation of strong chemical bonds between Ti-containing species and certain polymeric functional groups. Mechanical tensile strength failure testing showed that such joints experience some degradation as a result of soaking in physiological solutions. This degradation is limited and, even after relatively long-term exposure the joints retain considerable strength.     

钎缝间隙对316L不锈钢真空钎焊接头组织的影响

采用镍基钎料BNi2+40%BNi5对316L不锈钢进行真空钎焊。主要通过光学显微镜、电子探针显微分析仪、硬度计等研究了3种钎缝间隙下钎焊接头的显微组织、钎缝成分分布以及钎缝显微硬度。结果表明316L不锈钢的钎焊接头主要由固溶体、共晶组织及网状化合物组成,硼、硅是导致化合物相产生的主要合金元素;随着钎缝间隙的减小,钎焊接头中金属间化合物相的含量逐渐减小,当钎缝间隙为30μm时,接头组织基本为固溶体。     

Microstructure and mechanical properties of dissimilar materials joints between T92 martensitic and S304H austenitic steels

In this paper, T92 martensitic steel and S304H austenitic steel were welded by gas tungsten arc welding (GTAW) process. Microstructural features and mechanical properties of T92 and S304H dissimilar materials joints were investigated. The results showed that the part of the joints with relatively weak tensile strength was T92 coarse-grained heat affected zone (CGHAZ), while the part of the joints which revealed relatively weak toughness was weld metal. The decrease of tensile strength in T92 CGHAZ was due to its coarse tempered martensite structure. Weak toughness of the joints was resulted from the coarse dendritic austenite of the weld metal. However, the weld metal in transverse direction of the joints was provided higher tensile strength by the orientation distribution of grains compared with T92 CGHAZ.     

Application of the weakest link analysis to the area of fatigue design of steel welded joints

A new approach in the area of fatigue life assessment of steel welded joints is being proposed with the following features: (i) methodology of fatigue life calculation is independent from geometry of welded element; (ii) fatigue life assessment is based on fatigue characteristic of introduced efficient material – suitable for different steel welded joints; (iii) the fatigue life assessment is carried on the desired level of failure probability.In the proposed method a material volume surrounding the weld is divided into volume elements and regarded as a serial system having its definition in the reliability theory (the weakest link concept). Failure probability distribution of the welded structure is characterized by the proposed S–N curve for efficient material and the shape parameter introduced to describe the volume effect.     

Mechanical characterization by dynamical tensile loading of 2017 aluminium alloy joints welded by diffusion bonding

The mechanical properties of diffusion-welded joints of 2017 aluminium-copper alloys have been studied under dynamic loading with the help of a Hopkinson bar linear assembly. With the aim of comparing with previous results obtained under static loading, the strength, failure elongation and failure energy were evaluated in the welding temperature range from 475 to 600 °C. Measurements of the above mechanical properties were also performed on treated specimens which were base-material specimens subjected to the same thermal cycle as the welded samples. It was found that for a welding temperature above 525 °C the strength of the welded joints could reach values of the same order of magnitude as those of the treated samples. In contrast, the failure elongation and failure energy remained clearly lower, whatever the welding temperature was. For a given value of the welding pressure, the welding temperature dependence rate of the dynamic strength was shown to be increased with increasing welding time. With regard to the failure elongation or the relatively weak influence of the welding pressure on the joint strength, the spread in the experimental results (probably arising from the brittle nature of the sample failure mode) does not allow a clear conclusion. In spite of this restriction, it can be concluded that differences in the mechanical properties of the diffusion-welded joints could be evidenced by dynamic loading tests, even if no significant differences could be observed under static loading.