Nonlinear dynamical behavior of shallow cylindrical reticulated shells

By using the method of quasi-shells , the nonlinear dynamic equations of three-dimensional single-layer shallow cylindrical reticulated shells with equilateral triangle cell are founded. By using the method of the separating variable function, the transverse displacement of the shallow cylindrical reticulated shells is given under the conditions of two edges simple support. The tensile force is solved out from the compatible equations, a nonlinear dynamic differential equation containing second and third order is derived by using the method of Galerkin. The stability near the equilibrium point is discussed by solving the Floquet exponent and the critical condition is obtained by using Melnikov function. The existence of the chaotic motion of the single-layer shallow cylindrical reticulated shell is approved by using the digital simulation method and Poincare mapping.

Experimental study of wind loads on cylindrical reticulated shells

The cylindrical reticulated shell structures without side walls, which are normally arranged in pairs, are usually used as dry-coal sheds in a thermal power plant. The wind loads of these shells do not exist in standards or codes. Therefore, this study investigates the mean and fluctuating wind loads on a cylindrical reticulated shell with a rise-to-span ratio of 0.39 through a series of wind tunnel tests. The characteristics of the wind pressures on the upper and lower surfaces and the net pressures are presented. The results show that the wind direction and another shell structure significantly affect the wind loads on the principal shell. The most unfavorable wind direction is around 30~, whereas the effects of the wind field and the height of the coal stack are small. The surfaces of the shells are divided into nine blocks, and the block mean and fluctuating （rms） pressure coefficients suitable for engineering applications are given as references for wind load codes.

A new neural-network-based method for structural damage identification in single-layer reticulated shells

Single-layer reticulated shells(SLRSs)find widespread application in the roofs of crucial public structures,such as gymnasiums and exhibition center.In this paper,a new neural-network-based method for structural damage identification in SLRSs is proposed.First,a damage vector index,NDL,that is related only to the damage localization,is proposed for SLRSs,and a damage data set is constructed from NDL data.On the basis of visualization of the NDL damage data set,the structural damaged region locations are identified using convolutional neural networks(CNNs).By cross-dividing the damaged region locations and using parallel CNNs for each regional location,the damaged region locations can be quickly and efficiently identified and the undamaged region locations can be eliminated.Second,a damage vector index,DS,that is related to the damage location and damage degree,is proposed for SLRSs.Based on the damaged region identified previously,a fully connected neural network(FCNN)is constructed to identify the location and damage degree of members.The effectiveness and reliability of the proposed method are verified by considering a numerical case of a spherical SLRS.The calculation results showed that the proposed method can quickly eliminate candidate locations of potential damaged region locations and precisely determine the location and damage degree of members.

Numerical analysis of aluminum alloy reticulated shells with gusset joints under fire conditions

In this study,a numerical analysis was conducted on aluminum alloy reticulated shells(AARSs)with gusset joints under fire conditions.First,a thermal-structural coupled analysis model of AARSs considering joint semirigidity was proposed and validated against room-temperature and fire tests.The proposed model can also be adopted to analyze the fire response of other reticulated structures with semi-rigid joints.Second,a parametric analysis was conducted based on the numerical model to explore the buckling behavior of K6 AARS with gusset joints under fire conditions.The results indicated that the span,height-to-span ratio,height of the supporting structure,and fire power influence the reduction factor of the buckling capacity of AARSs under fire conditions.In contrast,the reduction factor is independent of the number of element divisions,number of rings,span-to-thickness ratio,and support condition.Subsequently,practical design formulae for predicting the reduction factor of the buckling capacity of K6 AARSs were derived based on numerical analysis results and machine learning techniques to provide a rapid evaluation method.Finally,further numerical analyses were conducted to propose practical design suggestions,including the conditions of ignoring the ultimate bearing capacity analysis of K6 AARS and ignoring the radiative heat flux.

Shape optimization of aluminium alloy spherical reticulated shells considering nonlinearities

This study proposes a shape optimization method for K6 aluminum alloy spherical reticulated shells with gusset joints,considering geometric,material,and joint stiffness nonlinearities.The optimization procedure adopts a genetic algorithm in which the elastoplastic non-linear buckling load is selected as the objective function to be maximized.By confinement of the adjustment range of the controlling points,optimization results have enabled a path toward achieving a larger elastoplastic non-linear buckling load without changing the macroscopic shape of the structure.A numerical example is provided to demonstrate the effectiveness of the proposed method.In addition,the variation in structural performance during optimization is illustrated.Through parametric analysis,practical design tables containing the parameters of the optimized shape are obtained for aluminum alloy spherical shells with common geometric parameters.To explore the effect of material nonlinearity,the optimal shapes obtained based on considering and not considering material non-linear objective functions,the elastoplastic and elastic non-linear buckling loads,are compared.

NONLINEAR BENDING THEORY OF DIAGONAL SQUARE PYRAMID RETICULATED SHALLOW SHELLS

Double-deck reticulated shells are a main form of large space structures. One of the shells is the diagonal square pyramid reticulated shallow shell, whose its upper and lower faces bear most of the load but its core is comparatively flexible. According to its geometrical and mechanical characteristics, the diagonal square pyramid reticulated shallow shell is treated as a shallow sandwich shell on the basis of three basic assumptions. Its constitutive relations are analyzed from the point of view of energy and internal force equivalence. Basic equations of the geometrically nonlinear bending theory of the diagonal square pyramid reticulated shallow shell are established by means of the virtual work principle.

Nonlinear free vibration of reticulated shallow spherical shells taking into account transverse shear deformation

This paper deals with nonlinear free vibration of reticulated shallow spherical shells taking into account the effect of transverse shear deformation. The shell is formed by beam members placed in two orthogonal directions. The nondimensional fundamental governing equations in terms of the deflection, rotational angle, and force function are presented, and the solution for the nonlinear free frequency is derived by using the asymptotic iteration method. The asymptotic solution can be used readily to perform the parameter analysis of such space structures with numerous geometrical and material parameters. Numerical examples are given to illustrate the characteristic amplitudefrequency relation and softening and hardening nonlinear behaviors as well as the effect of transverse shear on the linear and nonlinear frequencies of reticulated shells and plates.

Optimal topology design of replaceable bar dampers of a reticulated shell based on sensitivity analysis

In this study,a method for control of reticulated shells is proposed and its practicality is demonstrated.The control is implemented by replacing selected bars of the shell with passive viscoelastic dampers.By applying the eigenvalue perturbation technique and the earthquake spectrum concept,the sensitivities of various topologies of the shell are analyzed,and the optimal topology is determined by taking their symmetries into consideration.The results of this research show that common damper topologies are not effective for all types of responses and recorded earthquakes.The optimal topology identifi ed requires a minimal number of dampers for each type of earthquake record.The displacement control effect of the dynamic responses of the optimal topology is 10% – 20%; the acceleration control effect is also about 10% – 20%; and the axial force control effect is as much as 30% – 45%.Furthermore,the incremental dynamic analysis(IDA) method is used to investigate the stability of the controlled shell.The results show that the dynamic stability of the controlled shell is well preserved when it is vibrated under vibration and is better than the uncontrolled shell.The ultimate load increased by 10% and the elements entered into the plastic stage when the peak acceleration reached 580 Gal,which is 200 Gal larger than the uncontrolled shell.

Research on mode localization of reticulated shell structures

Reticulated shell structures （RSSs） are characterized as cyclically periodic structures. Mistuning of RSSs will induce structural mode localization. Mode localization has the following two features： some modal vectors of the structure change remarkably when the values of its physical parameters （mass or stiffness） have a slight change; and the vibration of some modes is mainly restricted in some local areas of the structure. In this paper, two quantitative assessment indexes are introduced that correspond to these two features. The first feature is studied through a numerical example of a RSS, and its induced causes are analyzed by using the perturbation theory. The analysis showed that internally, mode localization is closely related to structural frequencies and externally, slight changes of the physical parameters of the structure cause instability to the RSS. A scaled model experiment to examine mode localization was carried out on a Kiewit single-layer spherical RSS, and both features of mode localization are studied. Eight tests that measured the changes of the physical parameters were carried out in the experiment. Since many modes make their contribution in structural dynamic response, six strong vibration modes were tested at random in the experimental analysis. The change and localization of the six modes are analyzed for each test. The results show that slight changes to the physical parameters are likely to induce remarkable changes and localization of some modal vectors in the RSSs.

Non-Linear Vibration of Rectangular Reticulated Shallow Shell Structures

This paper deals with non-linear vibration of rectangular reticulated shallow shells by applying non-linear elastic theory of such structures established by the author .Us-ing the assumed (generalized)Fourier series solutions for transverse deflection (latticejoint transverse displacement )and force function,weighted means of the trial functions lead to the relations among the coefficients related to the solutions and vibration equ-ation which determines the unknown time function,and then the amplitude -frequeney relations for free vibration and forced vibration due to harmonic force are derived withthe aid of the regular perturbation method and Galerkin procedure,respectively.Nu-merical examples are given as well.

The Coupling Effect of Spatial Reticulated Shell Structure with Cables

The spatial reticulated shell structure with cables (RSC) is a kind of coupling working system, which consists of flexible cables, reticulated shell structure (RS) and tower columns. The dynamic analysis of RSC based on the coupling model was carried out. Three kinds of elements such as the spatial bar element, cable element and beam element were introduced to analyze the reticulated shell, cable and tower column respectively. Furthermore, such parameter influences as structural boundary conditions, grid configuration, the span-to-depth ratio and the arrangement of cable system upon structural dynamics were analyzed. The structural vibration modes can be divided into four groups based on some numerical examples. And the frequencies in the same group are very close while the frequencies in different groups are different from each other obviously. It is clear that the sequence of the appearance of the each mode group heavily depends on the comparative stiffness of the tower column system, RS and cables.

NON-LINEAR ELASTIC THEORY OF RECTANGULAR RETICULATED SHALLOW SHELL STRUCTURES

Based on fundamental assumptions, an analysis of the constitutive relations be-tween the internal.forces and deformations of discrete rectangular recirculated struturesis given.On the basis of this,an equivalent continuum model is adopted and the ap-plication of the principle of virtual work leads to non-linear governing equations and corresponding boundary conditions.

Wind-induced vibration of single-layer reticulated shell structures

Aiming at the dynamic response of reticulated shell structures under wind load,systematic parameter analyses on wind-induced responses of Kiewitt6-6 type single-layer spherical reticulated shell structures and three-way grid single-layer cylindrical reticulated shell structures were performed with the random simulation method in time domain,including geometric parameters,structural parameters and aerodynamic parameters.Moreover,a wind-induced vibration coefficient was obtained,which can be a reference to the wind-resistance design of reticulated shell structures.The results indicate that the geometric parameters are the most important factor influencing wind-induced responses of the reticulated shell structures;the wind-induced vibration coeffi-cient is 3.0-3.2 for the spherical reticulated shell structures and that is 2.8-3.0 for the cylindrical reticula-ted shell structures,which shows that the wind-induced vibration coefficients of these two kinds of space frames are well-proportioned.

Nonlinear stability of double-deck reticulated circular shallow spherical shell

Based on the variational equation of the nonlinear bending theory of doubledeck reticulated shallow shells, equations of large deflection and boundary conditions for a double-deck reticulated circular shallow spherical shell under a uniformly distributed pressure are derived by using coordinate transformation means and the principle of stationary complementary energy. The characteristic relationship and critical buckling pressure for the shell with two types of boundary conditions are obtained by taking the modified iteration method. Effects of geometrical parameters on the buckling behavior are also discussed.

Non-uniform thermal behavior of single-layer spherical reticulated shell structures considering time-variant environmental factors: analysis and design

Contrary to conventional design methods that assume uniform and slow temperature changes tied to atmospheric conditions,single-layer spherical reticulated shells undergo significant non-uniform and time-variant temperature variations due to dynamic environmental coupling.These differences can affect structural performance and pose safety risks.Here,a systematic numerical method was developed and applied to simulate long-term temperature variations in such a structure under real environmental conditions,revealing its non-uniform distribution characteristics and time-variant regularity.A simplified design method for non-uniform thermal loads,accounting for time-variant environmental factors,was theoretically derived and validated through experiments and simulations.The maximum deviation and mean error rate between calculated and tested results were 6.1℃ and 3.7%,respectively.Calculated temperature fields aligned with simulated ones,with deviations under 6.0℃.Using the design method,non-uniform thermal effects of the structure are analyzed.Maximum member stress and nodal displacement under non-uniform thermal loads reached 119.3 MPa and 19.7 mm,representing increases of 167.5%and 169.9%,respectively,compared to uniform thermal loads.The impacts of healing construction time on non-uniform thermal effects were evaluated,resulting in construction recommendations.The methodologies and conclusions presented here can serve as valuable references for the thermal design,construction,and control of single-layer spherical reticulated shells or similar structures.

Stability analysis of ellipse- like suspen-dome structures with low rise-span ratio

To investigate the effects of initial geometric imperfection and material nonlinearity on the stability analysis of the suspen-dome, the steel roof of Jiangsu Culture Sports Center Gymnasium was utilized as a numerical model, and modal analyses were performed. Then, linear buckling analysis,geometric nonlinear stability analysis, geometric nonlinear stability analysis with initial imperfection, and double nonlinear analysis considering material nonlinearity and geometric nonlinearity were discussed in detail to compare the stability performance of the ellipse-like suspen-dome and the single-layer reticulated shell. The results showthat the cable-strut system increases the integrity of the suspen-dome, and moderates the sensibility of the single-layer reticulated shell to initial geometric imperfection. However, it has little influence on integral rigidity, fundamental vibration frequencies, linear ultimate live loads, and geometric nonlinear ultimate live loads without initial imperfection. When considering the material nonlinearity and initial imperfection, a significant reduction occurs in the ultimate stability capacities of these two structures. In this case, the suspen-dome with a lowrise-span ratio is sensitive to the initial imperfection and material nonlinearity. In addition, the distribution pattern of live loads significantly influences the instability modes of the structure, and the uniform live load with full span is not always the most dangerous case.

Principle and practice of coupling support of double yielding shell of soft rock roadway under high stress

In order to ensure the safety and stability of the soft rock roadway under high stress, based on the char- acteristics of the surrounding rock deformation and failure, this paper presented the support technology“coupling support of double yielding shell”, then gave the design method of inner and outer shells and analyzed the principle and requirements of the support technology by taking the -850 meast belt mad-way of Qujiang coal mine as the background. The field application results show that the support technol- ogy can control the soft rock roadway deformation better under high stress. The displacement between roadway sides was 851 mm, the displacement of the roof was 430 mm, and the displacement of the floor was 510 mm.

Samples Selection for Artificial Neural Network Training in Preliminary Structural Design

An artificial neural network (ANN) is applied in the preliminary structural design of reticulated shells. Major efforts are made to enhance the generalization ability of networks through well-selected train- ing samples. Number-theoretic methods (NTMs) are adopted to generate samples with low discrepancy, i.e., uniformly scattered in the domain, where discrepancy is a quantitative measurement of the uniformity. The discrepancy of the NTM-based sample set is 1/6-1/7 that of samples with equal spacing. In a case study, networks trained by NTM-based samples are compared with those trained by equal-spaced samples in generalizing performance. The results show that both the computational precision and stability of the former ANNs are more satisfactory than those of the latter. It is concluded that the flexibility of ANNs in generalizing can be effectively increased by use of uniformly distributed training samples rather than simply piling data. More reliable uniformity should be obtained, however, through NTMs instead of equal-spaced samples.