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This study investigates the vibration characteristics of spinning annular disks with various boundary conditions aiming to investigate the effect of radius ratio parameter and the rotation speed on natural frequencies of a spinning disk analytically for nine different types of boundary conditions. The stress distributions on the disks are obtained for all boundary conditions. The Galerkin method is employed with polynomial functions as approximate displacement functions. Analytical results are presented and compared to the results of the finite element analyses as well as experimental ones. [ABSTRACT FROM AUTHOR]

Two essential tools for successfully optimizing a grillage are to evaluate both size and layout variables and to use an efficient optimization method suitable for this problem. In this study, a binary variant of the Jaya algorithm called JayaX is used to optimize the size and layout of grillages simultaneously. JayaX algorithm employs the logic "exclusive or" operator to balance exploration and exploitation during the optimization process. This study proposes a different approach for using the modification ratio in the "exclusive or" operator. The layout and size variables of the optimization problem are the number of beams in both directions and the cross sections of these beams, respectively. The minimum-weighted structure is aimed in the study considering displacement and strength constraints according to AISC-LRFD. Three examples from the literature were optimized using the coded algorithm. The efficiency of JayaX algorithm in a structural optimization problem and the effect of the simultaneous approach in grillage optimization are revealed. Furthermore, the importance of layout variables in grillage optimization is also clarified. [ABSTRACT FROM AUTHOR]

For rural bridges in Australia, a common design practice is pouring in-situ concrete on top of beams in order to tie all the beams together and distribute load. However, pouring concrete on-site creates more risk and contractors prefer to avoid it. Another method is using transverse post tensioning to tie beams. This article investigated the behaviour of transverse post-tensioning bars in providing load distribution between beams and ultimately comment on their effectiveness compared to in-situ poured decks. Currently, the industry has not completely investigated this matter in order to design post-tensioning accurately. Conservative estimates are currently used in industry today. Current practice is 50% of the design load on the beam where the load is applied in their design assumptions which is quite high. The team modelled concrete box girder bridges with transverse post-tensioning using grillage method. Several factors were investigated including bridge length and width, bridge skew and beam type. From the models, the team concluded that increasing the bridge span increases the load distribution, the load distribution difference is negligible for skew between 0 and 20 degrees and larger shear actions are observed with increased skew and width. It was determined that the worst-case total load on the beam where the load as applied was found to be 40.5%, 9.5% less than current practice. It is recommended that a similar investigation is conducted using a finite element method to gain a deeper understanding. [ABSTRACT FROM AUTHOR]

The paper deals with the analysis of lateral torsional buckling (LTB) of steel beams that are components of grillages. Such structures are constructed from primary substring beams and secondary coupling beams. One of the functions performed by secondary beams in grillages is point protection of primary beams against overall stability failure. Based on the LTB analysis of primary beams, the condition specified in the code PN-EN 1993-1-1 (EC-3) was verified. The condition concerns the maximum spacing of point lateral bracings that stabilise compression flanges of beams. Critical moments of LTB for those beams were determined employing two methods. The first method involved the use of equivalent (simplified) loading diagram and the author-developed analytic formula. The other method employed LTBeamN and Abaqus (FEM) software, in which the whole beam was modelled together with bracings. Beam loading diagrams most frequently used in engineering practice were taken into account. Coefficients of LTB were determined in accordance with EC-3. A good congruence of results was obtained, which confirmed the correctness of the equivalent (simplified) beam loading diagram. The condition specified in the code PN-EN 1993-1-1 (EC-3) was also confirmed.

The paper deals with the analysis of lateral torsional buckling (LTB) of steel beams that are components of gril-lages. Such structures are constructed from primary substring beams and secondary coupling beams. One of the functions performed by secondary beams in grillages is point protection of primary beams against overall stability failure. On the basis of the LTB analysis of primary beams, the condition specified in the code PN-EN 1993--1-1 (EC-3) was verified. The condition concerns the maximum spacing of point lateral bracings that stabilise the compression flanges of beams. Critical moments of LTB for those beams were determined employing two methods. The first method involved the use of equivalent (simplified) loading diagram and the analytic formula developed by the authors. The other method employed the LTBeamN and Abaqus (FEM) software, in which the whole beam was modelled together with bracings. The beam loading diagrams most frequently used in engineering practice were taken into account. Coefficients of LTB were determined in accordance with EC-3. A good congruence of results was obtained, which confirmed the correctness of the equivalent (simplified) beam loading diagram. The condition specified in the code PN-EN 1993--1-1 (EC-3) was also confirmed. [ABSTRACT FROM AUTHOR]

The purpose of the paper is to present the method implemented for a global optimization of grillage-type pile foundations introducing two advanced metaheuristics: AAGA and AGADS. The suggested new optimization algorithm including the synergy of AAGA and AGADS demonstrates improved results comparing with former AGA and GADS. Compromise objective function to be minimized involves the maximum reactive force in piles and maximum bending moment in the connecting beams. The feasibility of a simple weighting technique for the objective function is proved by numerical investigation of objective function domain for several different topologies of foundations. Sizing problem of connecting beams is solved together with the optimization problem. The original finite element program was employed for solution of direct problem. [ABSTRACT FROM AUTHOR]

The aim of the article is to report a technology for the optimization of grillage-type foundations seeking for the least possible reactive forces in the piles for a given number of piles and in the absolute value of the bending moments when connecting beams of the grillage. Mathematically, this seems to be the global optimization problem possessing a large number of local minima points. Both goals can be achieved choosing appropriate pile positions under connecting beams; however, these two problems contradict to each other and lead to diff erent schemes for pile placement. Therefore, we suggest using a compromise objective function (to be minimized) that consists of the largest reactive force arising in all piles and that occurring in the absolute value of the bending moment when connecting beams, both with the given weights. Bending moments are calculated at three points of each beam. The design parameters of the problem are positions of the piles. The feasible space of design parameters is determined by two constraints. First, during the optimization process, piles can move only along connecting beams. Therefore, the two-dimensional grillage is “unfolded” to the one-dimensional construct, and supports are allowed to range through this space freely. Second, the minimum allowable distance between two adjacent piles is introduced due to the specific capacities of a pile driver. Also, due to some considerations into the scheme of pile placement, the designer sometimes may introduce immovable supports (usually at the corners of the grillage) that do not participate in the optimization process and always retain their positions. However, such supports hinder to achieve a global solution to a problem and are not treated in this paper. The initial data for the problem are as follows: a geometrical scheme of the grillage, the given number of piles, a cross-section and material data on connecting beams, the minimum possible distance between adjacent supports and loading data given in the form of concentrated loads or trapezoidal distributed loadings. The results of the solution are the required positions of piles. This solution can serve as a pilot project for more detailed design. The entire optimization problem is solved in two steps. First, the grillage is transformed into the one-dimensional construct and the optimizer decides about a routine solution (i.e. the positions of piles in this construct). Second, backward transformation returns pile positions into the two-dimensional grillage and the “black-box” finite element program returns the corresponding objective function value. On the basis of this value, the optimizer predicts new positions of piles etc. The finite element program idealizes connecting beams as beam elements and piles – as mesh nodes of the finite element with a given boundary conditions in the form of vertical and rotational stiff ness. Since the problem may have several tens of design parameters, the only choice for optimization algorithms is using stochastic optimization algorithms. In our case, we use the original elitist real-number genetic algorithm and launch the program sufficient number of times in order to exclude large scattering of results. Three numerical examples are presented for the optimization of 10-pile grillage: when optimizing purely the largest reactive force, purely the largest in the absolute value of the bending moment and both parameters with equal weights. Momentų ir reakcijų minimizavimas rostverkiniuose pamatų sijynuose genetiniu algoritmu Santrauka Straipsnyje na grinėjamas rostverkinių pamatų optimizavimas, siekiant kuo mažesnių reaktyvinių jėgų poliuose, esant duotajam polių skaičiui, ir kuo mažesnių absoliutiniu dydžiu lenkimo momentų sijyno jungiamosiose sijose. Optimizavimo uždavinio tikslo funkciją sudaro didžiausia visuose poliuose atraminė reakcija ir didžiausias absoliutiniu dydžiu lenkimo momentas jungiamosiose sijose. Abu dėmenys imami su tam tikrais svoriais. Momentai skaičiuojami trijuose kiekvienos sijos taškuose. Uždavinio projektavimo kintamieji yra polių padėtys po jungiamosiomis sijomis. Optimizavimo uždavinys sprendžiamas genetiniu algoritmu, į kurio formulavimą įtraukiama išankstinė žinoma informacija apie uždavinį. Reakcijų ir momentų skaičiavimo uždavinys skaičiuojamas baigtinių elementų metodu. Ši programa jungiama prie optimizavimo algoritmo juodosios dėžės principu. Pateikiami nedidelės apimties sijyno skaitiniai pavyzdžiai. Tokie skaičiavimai galėtų būti kaip bandomieji detalesnio sijyno projektavimo sprendiniai. First Published Online: 16 May 2013 Reikšminiai žodžiai: globalusis optimizavimas, genetiniai algoritmai, sijynų optimizavimas, baigtinių elementų metodas.

Reinforced concrete four-pile caps under wall loading occur in heavily loaded foundations in bridge construction. The failure mode of shear across the full width of the cap may occur in these deep structural elements. A statically determinate two-way grillage model, comprising orthogonal deep beam grillage elements obeying a predetermined test observing deflection pattern and boundary conditions, is established to solve the structure's shear capacity. The model gives more accurate and faster solutions than the traditional strut-and-tie method and commercial nonlinear numerical modeling.A key step to solving the model is a linear constitutive (load-deflection) relationship developed for the grillage elements. The grillage model is verified against laboratory experiments for nine pile caps at the University of Southampton (UoS) with the results of a numerical modeling parametric study. A Visual Basic Userform-based design software is developed, incorporating the model and enabling engineers to obtain the shear capacity, full-field reinforcement stress distribution, and cap deflections within seconds. [ABSTRACT FROM AUTHOR]

A new facility for testing pipes under deep burial has been developed. However, before the facility was commissioned, the influence of the loading scheme and boundary conditions on the pipe behaviour was investigated so that the most appropriate experimental setup could be developed. Two- and three-dimensional finite element analyses were used to assess the impact of the top and side boundary conditions on both flexible and rigid pipes with varying diameters. The vertical overburden pressures expected in the field are simulated using actuators applying vertical forces to two steel grillages. The numerical results show that the use of two independent grillages on the surface produced a more uniformly distributed 'overburden' pressure, a novel approach that performs significantly better than previous loading systems. Proximity of the test facility's walls to the pipes was also investigated and found to have less than a 0.2% impact on pipe response when compared to simulations of field geometries. Results examining five different approaches to reducing the effect of sidewall friction were compared to the case of zero friction (i.e. the field case), and it was found that while lubricating the wall to create a friction angle of 5° over the full height produced the most accurate results, lubrication of only the top 2.5 m of the wall also produces thrust forces and bending moments within 10% of values from the zero-friction case. Finally, the effect of the position of the pipe within the test cell was investigated, where pipe testing with 0.3 m of bedding is expected to produce results like those for pipes close to rock foundations in the field. These results are already being used to inform testing procedures using this unique facility. [ABSTRACT FROM AUTHOR]

The thin-walled deck grillages are prone to deformation in lifting process of ship blocks construction due to huge rope tension loads. Optimizing hoisting scheme with the aid of CAE analysis techniques before implementing is conductive to controlling structure deformation. A deformation prediction method based on generative adversarial network (Def-GAN) is developed in this paper to perform quick-response and precise deformation predictions under a given hoisting scheme of deck grillages. This artificial intelligence network model has an adversarial architecture and comprises a pair of submodels, namely generator and discriminator. The datasets including lifting conditions and deformation distributions of deck grillages are set up to train and test the Def-GAN model. The deformation distributions in datasets are obtained from a series of FEM analyses. An image coding and mapping algorithm is employed to deal with input data of lifting conditions and output data of deformation distributions respectively. The results show that the predictive model achieved an R-squared accuracy of 0.997 and a mean squared error of 0.005 compared to numerical results for the test dataset. In addition to predicting deformation of grillages lifting, the Def-GAN model is a promising candidate tool for hoisting scheme optimization. • Data-driven Def-GAN network consisting of the generator and discriminator is established. • Lifting deformations of deck grillages are predicted by the developed network model. • Influence of various lifting conditions on the robustness of predictive model is analyzed. • Prediction accuracy of the well-trained model is verified by an independent database. [ABSTRACT FROM AUTHOR]

Abstract Laboratory-grown cone-shaped ice specimens (1 m diameter) were utilized to load large structural grillages into a plastic response domain. The scantlings of the grillages were typical of a transversely framed mid-body ice belt arrangement of a 10,000 ton Ice Class PC6 vessel. The maximum loads reached levels well beyond the elastic limit of the material and any acceptable plastic design point. The tests allowed for an evaluation of highly non-linear structural behavior and overload capacity considering the simultaneous failure of ice. Two separate large structural grillage tests were carried out with ice specimens loaded at a quasi-static loading rate (0.5 mm/s). The first set of tests were performed in two loading steps at identical loading positions at the mid-span of the central stiffener. The second set of tests were carried out in three loading steps at different loading positions along the span of the central stiffener of the grillage as a sequence of right-off, center, and left-off center. The experiments led to unique insight into the overload response and load carrying capacity of a large structural grillage as well as the effect of prior plastic damage on the structural behavior. Load-deflection curves and deformed shapes measured by MicroScribe® were compared with the results of nonlinear finite element (FE) analysis. The FE analysis results show a strong agreement with the physical experiments, which confirms that the nonlinear FE analysis is a suitable tool for the analysis of ice-strengthened ship structures subjected to extreme ice loading. Highlights • Lab-grown ice specimen were utilized to load the grillages into a plastic response domain. • Maximum loads reached levels beyond the elastic limit of the material. • Highly non-linear structural behavior and overload capacity considering ice failure were evaluated. • Effect of prior plastic damage on the structure was investigated and discussed. • Results of FE analysis showed a good agreement compared with the physical experimental results. [ABSTRACT FROM AUTHOR]

Grillages are often used to form bridge decks and other constructions. However, following a period of intensive research activity in the 1970s, comparatively little attention has been paid to optimizing the layout of grillages in recent years. In this contribution a new numerical procedure is proposed which takes advantage of the adaptive solution scheme previously developed for truss layout optimization problems, enabling very large scale problems to be solved. A key benefit of the proposed numerical procedure is that it is completely general, and can therefore be applied to problems with arbitrary loading and boundary conditions. Also, unlike some previously proposed procedures, the sizes of individual beams can readily be discerned. To demonstrate its efficacy the numerical procedure is applied to a range of grillage layout design problems, including load dependent problems which could not be solved using traditional methods. It is shown that important phenomena such as “beam-weaves” can be faithfully captured and new high-precision numerical benchmark solutions are provided. [ABSTRACT FROM AUTHOR]

Overload response of the stiffening frames in ship side structure due to ice loading is an important design consideration for ships operating in ice infested waters. By overload, we mean loads that are larger than assumed by the rules. Therefore, the response of ice strengthened grillage frames is investigated under a range of idealized rectangular pressure patches and by assuming different boundary conditions for the structural units. A flat, representative grillage of an ice-strengthened ship is considered and analysed using non-linear Finite Element Method. The response of the grillage frames is compared with the isolated frame response. Two frame types are considered: flatbars and L-frames. Finite element simulations revealed that patch length has strong effect on the frame deformation mode. The key characteristic that differentiates the response under shorter and longer patches is the longitudinal membrane stretching of the shell plating. Longer patches tend to suppress this deformation mode that leads to similar frame behaviour observed in isolated frame analysis. It is further shown that overload capacity of grillage frames reduces with increasing patch length to levels observed in isolated frame analysis. Analysis of plastic strain development in the frames and plating revealed that plastic strain localized faster in frames, but shell plating is more sensitive to patch height variations. This renders frames more susceptible to fracture than plating. Finally, the local failure mechanisms of the L-frames tend to diminish the load sharing capability and so negatively affects the overload behaviour. [ABSTRACT FROM AUTHOR]

This paper presents experimental and numerical investigation results for the plastic response of steel grillages, represented by one longitudinal stiffener and two transverse stiffeners of stiffened plates, used on ships or offshore structures under repeated mass impacts. The repeated mass impact scenario adopted in this paper could represent the repetition of impacted loads on marine structures due to contact with ice floes and floating objects during service. Repeated impact tests on grillage models at room and sub-zero temperatures (−50 °C) were conducted by releasing a knife-edge striker using a drop testing machine. The ends of the grillage models were firmly fixed onto a strong bed with support fixtures. To evaluate the repeated impact performance of the tested models, permanent deflections were measured after each impact test. Additionally, numerical simulations were performed using the commercial software package ABAQUS/Explicit to predict the extent of damage to the tested models caused by repeated impacts. In the calculations, the material properties of tested models were used to determine the strain hardening and strain rate hardening model using the equations recently proposed by the authors. Also, a simple analytical approach has been proposed to predict the damage evolution of the grillage subjected to repeated mass impacts. Reasonable agreement was achieved between the predictions and test results. The results showed that when the structure was repeatedly impacted, permanent deflections of the grillage significantly increased with increasing impact force. The permanent deflections tended to have certain values when the number of impacts increased. Based on the numerical results (which were substantiated with the experimental results), further calculations were then carried out to examine impact responses in greater detail and assess the effects of variations in boundary conditions and strain rate definitions on the response of grillages to repeated mass impacts. [ABSTRACT FROM AUTHOR]

An efficient computational technique for nonlinear analysis of reinforced concrete (RC) beam-slab systems (rectangular grids) using grillage analogy is proposed. A load-controlled algorithm has been adopted for tracing the complete loaddeflection response till the ultimate load, under inonotonic loading. Material modelling of reinforced concrete in the present study includes nonlinear stress-strain behaviour such as cracking of concrete, yielding of steel and tensionstiffening effect. The proposed methodology has been validated against the test data reported in the literature as well as the experiments conducted for the present study. The numerically generated load-deflection curves are found to be in good agreement with the experimental results. The main advantages of this procedure is that it gives a more accurate estimation of short-term deflections under service loads, and a more realistic distribution of moments and shear forces at the limit state of collapse. Further, the algorithm can be conveniently used in reliability analysis of reinforced concrete beam-slab systems. [ABSTRACT FROM AUTHOR]

In this paper, the welding process of a bottom grillage constrained by a pin jig is simulated through an improved thermal elasto-plastic finite element method (FEM). Shell elements with section integration are adopted to enhance simulation efficiency. The spring-back deflections after pin jig being removed and the welding deformation under unconstrained condition are calculated. The influence of mechanical restrains on the welding deformation of the bottom grillage is studied through comparison. The constraint forces of pin jig in whole welding process are obtained from the simulation. The results show that the spring-back deformation of this bottom grillage is significant and the mechanical constraints of pin jig cannot mitigate the welding distortion of this structure effectively. The maximum constraint forces of connection plate occur at the moments when welding torch approaches the adjacent structural components. [ABSTRACT FROM PUBLISHER]

A steel-concrete composite waffle floor system (SCCWFS) that consists of orthogonal steel beams and a flat RC slab has potential applications in long-span building floors because of its large loading capacity, low depth-to-span ratio, and excellent ductility, as demonstrated by a previous experimental program. According to the test results, the spatial composite effect between the orthogonal steel beams and concrete slab significantly influences the performance of the SCCWFS. However, the complexity of the spatial composite effect in the SCCWFS makes it much more difficult to determine the rigidity and the internal force distribution in a routine design practice than the one-way steel-concrete composite floor or the RC waffle slab. To address this problem, a parameterized grillage method is developed in which intrinsic factors are defined to describe the critical properties of the deformation pattern, the reaction force and moment distribution of the SCCWFS; relation factors are defined to relate these properties of the SCCWFS to that of its corresponding steel grillage. Based on the parameterized grillage method, parametric analyses are conducted using a beam-shell mixed finite-element (FE) model and the influence of various parameters on intrinsic and relation factors is investigated, in which the beam height, slab thickness, length-to-width ratio, and so on are shown to be of importance. The data of a total of 5190 numerical models associated with seven parameters covering almost all the practical cases are then obtained, and a step-shaving procedure is proposed to derive formulas that are influenced by multiple variables. Based on the parameterized grillage method and the step-shaving procedure, formulas to predict the vertical displacements, reaction force and moment distribution of the SCCWFS are derived and verified. Finally, design procedures, recommendations and simplified forms of the formulas are proposed, in which the formulas are proved to have an error of approximately 10%. [ABSTRACT FROM AUTHOR]

Modified genetic algorithm with special phenotypes' selection and crossover operators with default specified rules is proposed in this paper thus refusing the random crossover. The suggested crossover operator enables wide distribution of genes of the best phenotypes over the whole population. During selection and crossover, the best phenotypes of the newest population and additionally the genes of the best individuals of two previous populations are involved. The effectiveness of the modified algorithm is shown numerically on the real-life global optimization problem from civil engineering - the optimal pile placement problem under grillage-type foundations. This problem is a fair indicator for global optimization algorithms since the ideal solutions are known in advance but with unknown magnitudes of design parameters. Comparison of the proposed algorithm with 6 other stochastic optimization algorithms clearly reveals its advantages: at similar accuracy level the algorithm requires less time for tuning of genetic parameters and provides narrower confidence intervals on the results than other algorithms. [ABSTRACT FROM AUTHOR]

Passivated emitter and rear cell (PERC) solar cells are currently being introduced into mass production. In this paper, we report a novel PERC solar cell design that applies a screen-printed rear Al finger grid instead of the conventional full-area aluminum (Al) rear layer while using the same PERC manufacturing sequence. We name this novel cell concept PERC+ because it offers several advantages. In particular, the Al paste consumption of the PERC+ cells is drastically reduced to 0.15 g instead of 1.6 g for the conventional PERC cells. The Al fingers create 2-µm-deeper aluminum back surface fields, which increases the open-circuit voltage by 4 mV. The five-busbar Al finger grid enables bifacial applications of the PERC+ cells with front-side efficiencies up to 20.8% and rear-side efficiencies up to 16.5% measured with a black chuck. The corresponding bifaciality is 79%. When applied in monofacial modules where the white back sheet acts as external rear reflector, the efficiency of the PERC+ cells is estimated to 20.9%, which is comparable with conventional PERC cells. Whereas Institute for Solar Energy Research Hamelin developed the aforementioned PERC+ results, SolarWorld independently pioneered a very similar bifacial PERC+ cell process starting in 2014. Transfer into mass production has been successfully accomplished, and novel glass-glass bifacial PERC+ modules have been launched at the Intersolar 2015 based on a most simple, lean, and cost-effective bifacial cell process. These new bifacial PERC+ modules show an increase in annual energy yield between 5% and 25% in simulations, which is confirmed by first outdoor measurements. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The purpose of the paper is to present technology applied for the global optimization of grillage-type pile foundations (further grillages). The goal of optimization is to obtain the optimal layout of pile placement in the grillages. The problem can be categorized as a topology optimization problem. The objective function is comprised of maximum reactive force emerging in a pile. The reactive force is minimized during the procedure of optimization during which variables enclose the positions of piles beneath connecting beams. Reactive forces in all piles are computed utilizing an original algorithm implemented in the Fortran programming language. The algorithm is integrated into the MatLab environment where the optimization procedure is executed utilizing a genetic algorithm. The article also describes technology enabling the integration of MatLab and Fortran environments. The authors seek to evaluate the quality of a solution to the problem analyzing experimental results obtained applying the proposed technology.

Much critical infrastructure, including bridges, wind turbine structures, dolphins and some other ocean engineering structures, is supported on large-diameter rigid monopiles. For such structures, compared with the gravitational loads, cyclic lateral loading may often be more critical for the analysis and design. The lateral load-carrying capacity of a pile depends on its geometry (dimensions), the soil properties and type of loading. In order to increase its lateral load-carrying capacity, it is necessary either to change the properties of the near-surface layers of soil or to change its geometry. This paper presents model studies investigating a novel technique to limit the lateral deflection (rotation) of a monopile under long-term cyclic lateral loading. The technique provides enhanced restraint of the monopile through the installation of four shorter piles, arranged in a cruciform, which attach to the head of the central monopile by way of a grillage. Different aspects of this modification, including its fabrication and attachment to the monopile, are presented. Its efficiency in reducing the monopile rotation under cyclic lateral loading is evaluated through a comprehensive testing programme, with reasonably encouraging results. [ABSTRACT FROM AUTHOR]

Simplified analysis methods derived in previous studies are employed for studying the progressive collapse behaviour of steel and composite buildings. A regular frame building is considered and various scenarios of sudden column removal, each affecting different floor areas in terms of geometry and boundary conditions, are applied. Descriptions of the pseudo-static responses of the various constitutive beams are obtained based on both detailed representations of the nonlinear static responses and by applying a new simplified approach proposed in a separate publication. Comparisons between the results of the two methods confirm that the simplified approach is capable of describing behaviour with reasonable accuracy. By employing a simplified multi-level assessment approach that has been previously derived at Imperial College, grillage-type approximations are obtained and used to examine the floor dynamic behaviour for the various column removal cases. It is found that, although the structural response varies depending on the location of the initial damage, substantial connection strength is required in all cases in order to provide resistance to progressive collapse. In addition, for average levels of connection ductility, failure most likely occurs prior to the development of tensile catenary action in the beams, which indicates that the provision of tying resistance may not be effective in enhancing robustness. Therefore, the combined action of flexure and compressive arching in the beams is likely to form the principal collapse resisting mechanism in common practical applications, which confirms similar conclusions made in previous studies at Imperial. The provision of adequate levels of connection moment capacity – in combination with sufficient ductility supply – is, therefore, the most effective way of securing structural robustness. [ABSTRACT FROM AUTHOR]

Across many industries damage events leading to a breach in structural integrity continue to occur. An area where this can lead to particularly unsafe conditions is in the maritime environment, where it may be difficult to rescue crew and cargo. In order to improve structural safety through design for the survivability or to assess the residual strength of a damaged vessel in an emergency response or salvage scenario, it is critical to understand the influence of the damage. This paper, for the first time, investigates the use of FEA on ultimate collapse strength of damaged steel grillages and the influence of the damage aperture on the developing failure modes within the structure. The study finds that the presence of damage, in the form of a hole, can lead to the failure mode changing as damage aperture size is increased leading to significant changes to the ultimate collapse strength of the structure. It concludes that to assess the damaged strength of steel plated structures, it is critical that modelling methods are able to capture and account for such mode changes in order to accurately assess the true residual strength of the structure. [ABSTRACT FROM AUTHOR]

Fluid structure interactions (FSI) has played an important role in many engineering applications ranging from aeroelasticity in aerospace engineering, wind turbines, civil engineering, bioengineering, etc. This paper focuses on FSI simulations of high speed compressible flows and its applications in studying blast impacts on flexible structures. Under the strong and high speed shock waves generated from blasts, engineering structures are deformed and possibly destructed causing damages to its surroundings. In this work, high speed compressible flows are simulated using a second order finite volume approach with HLLC flux scheme for strong shock capturing. High pressure loading from blast wave deforms structures and potentially causes severe damages. The structure responses are computed using dynamic finite element analysis. The interaction between flows and structures are coupled via exchange of information on loading conditions and structural deformations by a partitioned coupling scheme. The proposed FSI framework is applied for simulations of flat plate under explosive charge and explosion in a confined flexible cylinder. The results are well compared with literature and experimental data. [ABSTRACT FROM AUTHOR]

Current seismic design practice related to integral bridge girder-to-cap beam connections allows little or no lateral seismic load to be distributed beyond the girders immediately adjacent to the column. However, distribution results from several large-scale tests have shown that the distribution of column seismic moment typically engages all the girders. An approach utilizing simple stiffness models to predict distribution in integral bridge structures is presented in detail; distribution predictions based on grillage analyses also are compared. The experimental results and the analytical results from the stiffness and grillage models show that current design methods related to vertical load distribution are sufficiently accurate. However, when applied to the distribution of lateral load, similarly obtained results reveal that current design practice does not appropriately account for the amount of load that is distributed beyond the girders adjacent to the column to the nonadjacent girders. The current practice leads to excessive girder-to-cap connection reinforcement, increased girder depth, unnecessarily high seismic mass, and increased construction cost. Finally, this paper makes recommendations for more appropriate distribution of seismic lateral load in integral bridge superstructures. [ABSTRACT FROM AUTHOR]

The article studies the problem of the exact internal controllability on a gridwork structure that depends on two small parameters ε and δ. The controll is provided by the HUM method (Hilbert Uniqueness Method). We apply the homogenization methods: the energetic method of Tartar and the dilatation method. The limit problem is a problem of vibrations on a rectangle which is controlled by the limit of the control. [ABSTRACT FROM AUTHOR]

The purpose of the paper is to present technology applied for the global optimization of grillage-type pile foundations (further grillages). The goal of optimization is to obtain the optimal layout of pile placement in the grillages. The problem can be categorized as a topology optimization problem. The objective function is comprised of maximum reactive force emerging in a pile. The reactive force is minimized during the procedure of optimization during which variables enclose the positions of piles beneath connecting beams. Reactive forces in all piles are computed utilizing an original algorithm implemented in the Fortran programming language. The algorithm is integrated into the MatLab environment where the optimization procedure is executed utilizing a genetic algorithm. The article also describes technology enabling the integration of MatLab and Fortran environments. The authors seek to evaluate the quality of a solution to the problem analyzing experimental results obtained applying the proposed technology. Santrauka Straipsnyje pateikiama sijynų tipo pamatų (toliau sijynų) globalaus optimizavimo technologija. Optimizavimo tikslas – nustatyti optimalų polių išdėstymą sijynuose. Šis uždavinys priskiriamas topologijos optimizavimo uždavinių grupei. Tikslo funkciją sudaro maksimali poliuje kylanti atraminė reakcijos jėga, kuri minimizuojama optimizavimo procese. Šio uždavinio projektavimo kintamieji - polių padėtys po jungiančiosiomis sijyno sijomis. Tiesioginis reakcijų poliuose skaičiavimo uždavinys sprendžiamas originaliu algoritmu, sukurtu Fortran programavimo kalba. Šis algoritmas juodosios dėžės principu jungiamas prie MatLab aplinkos, kurioje genetiniu algoritmu sprendžiamas optimizavimo uždavinys. Straipsnyje taip pat aprašyta technologija, kuri leidžia sujungti Matlab ir Fortran aplinkas, t. y. iš Matlab aplinkos iškviesti Fortran paprogramį. Analizuodami eksperimentinius duomenis autoriai bando įvertinti gaunamų sprendinių kokybę. Raktiniai žodžiai: globalusis optimizavimas; genetiniai algoritmai; rostverkų optimizavimas; baigtinių elementų metodas; MatLab; Fortran

Rational and sophisticated structural solutions are essential requirements for structural designers, as a consequence of architectural design evolution and new building management concepts. Thus, waffle slabs turn out to be an interesting alternative, despite their laborious numerical modeling. It is necessary to increase knowledge about the structural behavior of and improve the theoretical models used for the simulation of these slabs. To better understand the behavior of RC waffle slabs, and more realistically quantify stresses and displacements of this kind of element under actual work conditions, a real-scale ribbed slab was tested and the results are presented in this paper. The chosen structure, designed to serve as a parking floor, was instrumented with strain and deflection gauges to assess the deformations and deflections developed under some induced loading conditions. A grillage model and a three-dimensional finite-element model were used for the numerical study. The data collected indicates that both strategies can be used to obtain adequate estimates of deflections and bending moments. [ABSTRACT FROM AUTHOR]

Influence of grouping of the bridge piers on scour of the ground surface is investigated. Experimental research results of influence of bridge pier as three-row much pile grillage, which is placed behind of prismatic pier, on a form and depths local and global scours are presented. [ABSTRACT FROM AUTHOR]

Abstract: Lightweight for transport facility and reduced assembling and erection time are the main requirements to deployable bridges for emergency purposes which can be easily satisfied by using GFRP profiles. A reduced scale model of the truss girder component of a thirty meters span bridge has been tested in laboratory. The prototype bridge is composed of a GFRP grid floor deck supported by prestressed truss girders which are mounted by assembling GFRP tubular profiles and steel joints with bearing type connections. Structural tests first focused on the behavior of a 13m span simply supported truss girder model fabricated in the reduced geometric scale 1:2.3. This paper presents the description and the results obtained from numerical modeling and from experimental tests performed on the truss girder assembled with three distinct connection details between GFRP tubes and steel joints. The experimental results showed that improved performance of the connections make the proposed conceptual design plainly appropriate to be used as truss girders of a new concept of composite deployable bridge that can carry heavy vehicle loading. [Copyright &y& Elsevier]

Highlights: [•] The use of grillage analysis to predict the nonlinear seismic behaviour of flat plates was validated. [•] The effective slab width required to calculate the lateral stiffness of a flat plate system was examined. [•] Expressions to estimate the nominal and factored effective slab width were proposed. [•] The effective slab width was found to increase with the increase of flat plate span. [•] The ratio of Beff to B was found to decrease with the increase of bay width. [ABSTRACT FROM AUTHOR]

Member grouping of a steel grillage system has an important effect in the minimum weight design of these systems. In the present research, this effect is investigated using an optimum design algorithm which is based on two stochastic search techniques called particle swarm (PSO) and harmony search (HS) optimization methods. The optimum design problem of a grillage system is formulated by implementing LRFD-AISC (Load and Resistance Factor Design-American Institute of Steel Construction) limitations. It is decided that W-Sections are to be adapted for the longitudinal and transverse beams of the grillage system. 272 W-Section beams given in LRFD code are collected in a pool and the optimum design algorithm is expected to select the appropriate sections from this pool so that the weight of the grillage is the minimum correspondingly the design limitations implemented from the design code are satisfied. The solution for this discrete programming problem is determined by using the PSO and HS algorithms. Design example is presented to demonstrate the effect of beam spacing and performances of stochastic search techniques in the optimum design of grillage systems. [ABSTRACT FROM AUTHOR]

The article analyzes the optimization of grillage-type foundations seeking for the least possible reactive forces in the poles for a given number of poles and for the least possible bending moments of absolute values in the connecting beams of the grillage. Therefore, we suggest using a compromise objective function (to be minimized) that consists of the maximum reactive force arising in all poles and the maximum bending moment of the absolute value in connecting beams; both components include the given weights. The variables of task design are pole positions under connecting beams. The optimization task is solved applying the algorithm containing all the initial data of the problem. Reactive forces and bending moments are calculated using an original program (finite element method is applied). This program is integrated into the optimization algorithm using the “black-box” principle. The “black-box” finite element program sends back the corresponding value of the objective function. Numerical experiments revealed the optimal quantity of points to compute bending moments. The obtained results show a certain ratio of weights in the objective function where the contribution of reactive forces and bending moments to the objective function are equivalent. This solution can serve as a pilot project for more detailed design. Santrauka Straipsnyje nagrinėjamas rostverkinių pamatų optimizavimas, siekiant kuo mažesnių reaktyvinių jėgų poliuose duotajam polių skaičiui ir kuo mažesnių absoliutiniu dydžiu lenkimo momentų sijyno jungiančiosiose sijose. Optimizavimo uždavinio tikslo funkciją sudaro didžiausia visuose poliuose atraminė reakcija ir didžiausias absoliutiniu dydžiu lenkimo momentas jungiančiosiose sijose; abu dėmenys imami su tam tikrais svoriais. Uždavinio projektavimo kintamieji yra polių padėtys po jungiančiosiomis sijomis. Optimizavimo uždavinys sprendžiamas genetiniu algoritmu, į kurio formulavimą įtraukiama išankstinė žinoma informacija apie uždavinį. Reakcijų ir momentų skaičiavimo uždavinys skaičiuojamas baigtinių elementų metodu. Ši programa jungiama prie optimizavimo algoritmo juodosios dėžės principu. Optimaliam taškų, kuriuose skaičiuojami lenkimo momentai, skaičiui nustatyti atliekami skaitiniai eksperimentai. Skaitiniais eksperimentais nustatytos sąlygos, kurioms esant reakcija ir momentas turi ekvivalentišką įtaką tikslo funkcijai. Tokie skaičiavimai galėtų būti kaip bandomieji sprendiniai detaliau projektuojant sijyną. Raktiniai žodžiai: globalusis optimizavimas, genetiniai algoritmai, sijynų optimizavimas, baigtinių elementų metodas

The aim is to investigate ways of increasing the efficiency of grillage optimization. Following this general aim, two well‐known optimization methods, namely the Genetic Algorithm (GA) and Simulated Annealing (SA), were compared using some standard medium size (10 and 15 piles) examples. The objective function was the maximal vertical reactive force at a support. Coordinates of piles were optimization variables. SA wins and was applied to real‐life problem (55 piles) by parallel computations performed using a powerful cluster. New element is comparison of SA with GA and application of SA to a practical problem of grillage optimization. Santrauka Straipsnio tikslas ‐ ištirti galimus rostverkiniu pamatu optimizavimo būdus. Siekiant šio tikslo du gerai žinomi optimizavimo metodai ‐ genetiniai algoritmai ir atkaitinimo modeliavimo algoritmas ‐ buvo palyginti vidutinio dydžio (10 ir 15 poliu) pavyzdžiams išspresti. Tikslo funkcija imama didžiausia atraminI poliaus reakcija. Projektavimo kintamieji ‐ poliu koordinatIs. Atkaitinimo modeliavimo metodas laimi, todel jis buvo pritaikytas praktiniam uždaviniui (55 poliai) spresti. Spresti buvo naudojamas klasteris. Naujumas ‐ genetiniu algoritmu palyginimas su atkaitinimo modeliavimo metodu bei atkaitinimo modeliavimo metodo pritaikymas sprendžiant praktini uždavini. Published Published Online: 14 Oct 2010 Reikšminiai žodžiai: rostverkai, atkaitinimo modeliavimas, globalus optimizavimas, baigtiniai elementai, genetiniai algoritmai

Aim of the article is to suggest technology for optimization of pile positions in a grillage-type foundations seeking for the minimum possible pile quantity. The objective function to be minimized is the largest reactive force that arises in any pile under the action of statical loading. When piles of the grillage have different characteristics, the alternative form of objective function may be employed: the largest difference between vertical reaction and allowable reaction at any pile. Several different allowable reactions with a given number of such piles may be intended for a grillage. The design parameters for the problem are positions of the piles. The feasible space of design parameters is determined by two constraints. First, during the optimization process piles can move only along the connecting beams. Therefore, the two-dimensional grillage is “unfolded” to a one-dimensional construct, and the supports are allowed to range through this space freely. Second, the minimum allowable distance between two adjacent piles is introduced due to the specific capacities of pile driver.The initial data for the problem are the following: the geometrical scheme of the grillage, the cross-section and material data of connecting beams, minimum possible distance between adjacent supports, characteristics of piles, and the loading data given in the form of concentrated loads or trapezoidal distributed loadings. The results of solution are the required number of piles and their positions.The entire optimization problem is solved in two steps. First, the grillage is transformed to a one-dimensional construct, and the optimizer decides about a routine solution (i.e. the positions of piles in this construct). Second, the backward transformation returns the pile positions into the two-dimensional grillage, and the “black-box” finite element program returns the corresponding objective function value. On the basis of this value the optimizer predicts the new positions of piles, etc. The finite element program idealizes the connecting beams as the beam elements and the piles – as the finite element mesh nodes with a given boundary conditions in form of vertical and rotational stiffnesses. The optimizing program is an elitist genetic algorithm or a random local search algorithm. At the beginning of problem solution the genetic algorithm is employed. In the optimization problems under consideration, the genetic algorithms usually demonstrate very fast convergence at the beginning of solution and slow non-monotonic convergence to a certain local solution point after some number of generations. When the further solution with a genetic algorithm refuses to improve the achieved answer, i.e. a certain local solution is obtained; the specific random search algorithm is used. The moment, at which the transition from genetic algorithm to the local search is optimal, is sought in the paper analyzing the experimental data. Thus, the hybrid genetic algorithm that combines the genetic algorithm itself and the local search is suggested for the optimization of grillages. Globalusis rostverkinių pamatų optimizavimas hibridiniu genetiniu algoritmu Santrauka Straipsnio tikslas – sukurti technologiją polių padėtims rostverkiniuose pamatuose optimizuoti. Siekiama minimizuoti polių skaičių rostverke. Tikslo funkcija imama didžiausia atraminė poliaus reakcija, kuri optimizavimo metu yra minimizuojama. Iš pradžių uždavinys sprendžiamas genetiniu algoritmu, o kai toliau genetinį algoritmą naudoti tampa neefektyvu, gautas rezultatas gerinamas specifiniu atsitiktinės lokalios paieškos algoritmu. Analizuodami eksperimentinius duomenis autoriai bando nustatyti momentą, kada reikia pereiti nuo genetinio algoritmo naudojimo prie lokalios paieškos algoritmo, kad geresnis rezultatas būtų pasiekiamas per kuo trumpesnį laiką. Bendrą algoritmą, sujungiantį genetinį algoritmą su lokalios paieškos algoritmu, autoriai vadina hibridiniu genetiniu algoritmu. First Published Online: 16 May 2013 Reikšminiai žodžiai: globalusis optimizavimas, genetiniai algoritmai, poliniai pamatai

In this paper, a new efficient optimization algorithm called Teaching-Learning-Based Optimization (TLBO) is used for the optimum design of grillage systems based on the LRFD-AISC (Load and Resistance Factor Design-American Institute of Steel Construction). Cross sectional area of W-shapes are considered as discrete design variables. Various grillage structures are designed to show the efficiency of the TLBO algorithm. The results obtained from this study are compared with those reported in the literature. It is concluded that the TLBO algorithm presented in this study can be effectively used in the optimal design of grillage structures. [ABSTRACT FROM AUTHOR]

An analytical method for control of the strength of a grillage (gross panel) under unidirectional in-plane axial load is proposed. It allows us to solve the following tasks: (i) calculation of the critical stiffness of transverse girders, (ii) calculation of the maximum unidirectional in-plane compression load when the structure's scantlings are known (iii) and calculation of the required structure's scantlings when the unidirectional in-plane compression load is given. The proposed procedure is helpful in the application of probabilistic methods without employing specialised computer programmes, which is an advantage when fast (although approximate) evaluation is needed for the grillage critical buckling strength (e.g. ship's deck structure) before applying the finite-element method (FEM) analysis. Results of analytical approach are compared and confirmed using FEM data. A probabilistic method for control of the strength of ship's deck structure under unidirectional in-plane axial load is proposed. It allows us to assess the effect of deterioration due to corrosion on the deck's buckling strength while avoiding the use of specialised computer programmes. [ABSTRACT FROM AUTHOR]

Abstract: In this paper a metric for assessing the producibility of a stiffened grillage structure in the early stage design is presented. This metric is comprised of seven separate producibility drivers that are dependent on the properties of the panel. The new producibility metric is compared with a traditional costing method in a two-objective genetic algorithm to show that there is a competition between the two methods, meaning that the new metric gives a designer additional information at the early design stage. The estimated costs versus producibility scores for several grillage sizes show that large gains in producibility can be made without large increases in estimated costs up until a critical point where a knee in the Pareto front occurs. Furthermore, it was found that the individual producibility elements are highly dependent on the size of the panel tested and the constraints the panel must meet. In general, producibility is a key factor to be considered in structural design and should be accounted for in any structural optimization. [Copyright &y& Elsevier]

Using the dip and strike angles method of representing the geometry of yield line pattern in terms of the dip and strike angles of the deflected slab segments, the yield line analysis of reinforced concrete slabs had been successfully computerized. In this study, the dip and strike angles method is generalized for applications to slabs with any number of arbitrary-shaped openings subjected to point, line, patch and uniformly distributed loads. As before, the external work done by applied loads and the internal energy dissipation along yield lines are evaluated as functions of the dip and strike angles, but to allow for the presence of openings, the external work done and internal energy dissipation within the openings are discounted. Based on the principle of virtual work, the load factor is evaluated in terms of the dip and strike angles and the yield line pattern is determined by minimizing the load factor with respect to the dip and strike angles. Examples of slabs with openings under various boundary conditions and loading patterns are presented to illustrate the applicability, efficiency and accuracy of the generalized method. [ABSTRACT FROM AUTHOR]

Abstract: The design process is becoming increasingly complex with designers balancing societal, environmental and political issues. Composite materials are attractive to designers due to excellent strength to weight ratio, low corrosion and ability to be tailored to the application. One problem with composite materials can be the low stiffness that they exhibit and as such for many applications they are stiffened. These stiffened structures create a complex engineering problem by which they must be designed to have the lowest cost and mass and yet withstand loads. This paper therefore examines the way in which rapid assessment of stiffened boat structures can be performed for the concept design stage. Navier grillage method is combined with genetic algorithms to produce panels optimised for mass and cost. These models are constrained using design rules, in this case ISO 12215 and Lloyd's Register Rules for Special Service Craft. The results show a method that produces a reasonable stiffened structure rapidly that could be used in advanced concept design or early detailed design to reduce design time. [Copyright &y& Elsevier]

Grillage topologies are commonly used in many composite structural applications to produce low mass designs that have a high stiffness. While composite failure criteria are being compared in many different simple structures, for example plates and tubes, literature must also compare more complicated applications, including grillages, as there are distinct differences in behaviour. This paper therefore performs analysis of grillage structures with more up to date failure criteria, taken from the world wide failure exercise, than previously investigated. The grillage theory selected is that of Navier theory with elastic equivalent properties due to its low computational expense for use with a genetic algorithm to optimise a composite structure. The results take an example from leisure boatbuilding showing the grillages produced from the different limit states, comparing the cost and mass. The final results show that the method allows a rapid analysis of grillages and that the selection of the limit state has an important effect on the optimised grillage topology. [ABSTRACT FROM AUTHOR]

Abstract: Numerical simulation is performed to analyze the hydrodynamic response of a net cage and submerged mooring grid system exposed to waves and current. A series of experiments are conducted to validate the numerical model of net cage and grid mooring system. The numerical results of this model correspond with those obtained from experimental observations. Then, the numerical simulation of a multi-cage and mooring system under the action of waves combined with current is conducted. The influence of waves and current directions and the length of grid lines on the cage responses are discussed. The twin mooring system and the orthogonal mooring system are compared. Results show that for the orthogonal mooring system, the maximum tension force on the anchor line of the four-cage system is less than four times of that of the single-cage system, when both waves and current travel along the x-axis. The minimum net cage volume holding coefficient of the single-cage system is smaller than that of the four-cage system. The amplitude of the mooring line tension force for the twin mooring system is larger than the orthogonal mooring system. [Copyright &y& Elsevier]

For the estimation of the strength of a structure, one could avoid detailed elastoplastic analysis and resort, instead, to direct limit analysis methods that are formulated within linear programming. This work describes the application of the force method to the limit analysis of three-dimensional frames. For the limit analysis of a framed structure, the force method, being an equilibrium-based approach, is better suited than the displacement method and results, generally, to faster solutions. Nevertheless, the latter has been used mostly, since it has a better potential for automation. The difficulty for the direct computerization of the force method is to automatically pick up the structure's redundant forces. Graph theory concepts may be used to accomplish this task, and a numerical procedure was proposed for the optimal plastic design of plane frames. An analogous approach is developed herein for the limit analysis of space frames which is computationally more cumbersome than the limit analysis of plane frames. The proposed procedure results in hypersparse matrices, and in conjunction with the kinematic upper bound linear program which is solved by a sparse solver, the proposed method appears computationally very efficient. It is also proved that it is much more effective than any displacement-based formulation. The robustness and efficiency of the approach are testified by numerical examples for grillages and multi-storey frames that are included. [ABSTRACT FROM AUTHOR]