Lattice Domes Research Articles

劣化型履歴を有するブレース架構で支持された複層ラチスドームの地震応答と静的地震荷重の推定

This paper investigated earthquake responses of the latticed domes supported with braces of deteriorated stress-strain relationships due to buckling, followed by a proposal for estimation method of static seismic loads. The method for proposal is based on an equivalent linearization method, where nonlinear stress-strain relationships are linearized using an equivalent stiffness. First, two main modes, obtained in the equivalent linearization, were selected and superposed for representing the dynamic behavior, and two types of static seismic load depending on the intensities of input earthquake motions were proposed: One is a seismic load considering mainly the effects of horizontal sway motions and the other one is a seismic load reflecting the effects of the anti-symmetric motions induced by horizontal earthquake motions. Second, the seismic loads were applied in the pushover analysis of the domes, and the responses were compared with those calculated using a time history dynamic analysis. Finally, the proposed method was proved accurate and efficient for estimating static seismic loads as well as for structural proportioning of the members of latticed domes.

水平方向単一パルス波を受ける単層ラチスドームの動的座屈性状

This paper is intended as an investigation of the elasto-plastic dynamic buckling behavior of single layer lattice domes with substructures under horizontal single pulse waves. A single pulse wave is regarded as one wave of the earthquake motion or the wind load. The input waveform of single pulse wave is a half-sine pulse. Numerical analysis method is a time history response analysis taking into account the geometrical and material nonlinearities. From the results of numerical studies, the effects of the half subtended angle of dome and the duration of the half-sine pulse on the dynamic buckling behavior are made clear, and the relationship between the dynamic buckling behavior under earthquake motion and under half-sine pulse will be discussed.

Wind-induced dynamic response and its load estimation for structural frames of single-layer latticed domes with long spans

The main purpose of this study is to discuss the design wind loads for the structural frames of single-layer latticed domes with long spans. First, wind pressures are measured simultaneously at many points on dome models in a wind tunnel. Then, the dynamic response of several models is analyzed in the time domain, using the pressure data obtained from the wind tunnel experiment. The nodal displacements and the resultant member stresses are computed at each time step. The results indicate that the dome`s dynamic response is generally dominated by such vibration modes that contribute to the static response significantly. Furthermore, the dynamic response is found to be almost quasi-static. Then, a series of quasi-static analyses, in which the inertia and damping terms are neglected, is made for a wide range of the dome`s geometry. Based on the results, a discussion is made of the design wind load. It is found that a gust effect factor approach can be used for the load estimation. Finally, an empirical formula for the gust effect factor and a simple model of the pressure coefficient distribution are provided.

Structural optimization for specified nonlinear buckling load factor

The author’s method of design sensitivity analysis of nonlinear coincident buckling load factors and corresponding optimization method of finite dimensional elastic structures are shown to be applicable to a structure with moderately large number of degrees of freedom. The sensitivity formulations are written in general form for coincident buckling load factors including limit points and bifurcation points. Optimum designs are found for a spherical latticed dome subjected to a concentrated load and distributed loads, respectively. The results are compared with those by linear eigenvalue formulation. An approximate optimal solution against nonlinear buckling can be obtained by only scaling the solution under linear eigenvalue formulation even for the case where the effect of prebuckling deformation is very large. It is shown that the proposed method is practically applicable to optimum design with coincident critical points especially for the case of hill-top branching where bifurcation points are located at the limit point. In this case, imperfection sensitivity is not enhanced as a result of optimization. The reduction of maximum load factor due to a minor imperfection is shown to be in the same order as that to a major imperfection. Therefore symmetric imperfection as well as asymmetric imperfection should be considered in estimating the maximum loads.

中間荷重を受ける単層ラチスドームの座屈荷重の推定法に関する研究

The present paper studies the effects of the intermediate loads along members on the ultimate strength, that is, elasto-plastic buckling strength of single layer lattice domes and proposes an effective method to evaluate the buckling strength based on column buckling strength for members which is used to size the member sections. The method is based fundamentally on a concept of column buckling strength in terms of generalized slenderness that includes the effects of shell-like buckling with nonlinear effects before ultimate loads. The results presented in the paper confirm that the proposed method works well for the estimation.

Wind-induced dynamic behavior and its load estimation of a single-layer latticed dome with a long span

This paper describes the results of some basic investigations on the wind-induced dynamic behavior and the resultant load estimation of a single-layer latticed dome with a long span. The wind pressures at many locations on dome models were measured simultaneously in a wind tunnel. The dynamic response of several dome models was analyzed in the time domain by using a finite element method. For generating a time history of the wind load vector, which consisted of concentrated loads at all internal nodes, the proper orthogonal decomposition (POD) technique was applied to the wind pressure data obtained from the wind tunnel experiment. The nodal displacements and the resultant member stresses, both axial and bending, were computed at each time step. Based on the results, the characteristics of the wind-induced dynamic response of the dome are discussed. In the analysis, special attention is paid to the vibration modes that dominate the dynamic response. Furthermore, a brief discussion is made of the load estimation for the dome. A simple model for estimating the design wind load, expressed as an effective load, is proposed.

Lattice‐Dome Design Using a Knowledge‐Based System Approach

In the design of lattice domes, design engineers need expertise in areas such as configuration processing, nonlinear analysis, and optimization. These are extensive numerical, iterative, and time‐consuming processes that are prone to error without an integrated design tool. This article presents the application of a knowledge‐based system in solving lattice‐dome design problems. An operational prototype knowledge‐based system, LADOME, has been developed by employing the combined knowledge representation approach, which uses rules, procedural methods, and an object‐oriented blackboard concept. The system's objective is to assist engineers in lattice‐dome design by integrating all design tasks into a single computer‐aided environment with implementation of the knowledge‐based system approach. For system verification, results from design examples are presented.

Imperfection-Sensitive Overall Buckling of Single-Layer Lattice Domes

In this paper, the effects of geometric imperfections on the nonlinear buckling behavior of rigidly jointed single-layer lattice domes under vertical loading have been studied. A commercially available finite-element code has been used. Numerical experiments using varying levels of imperfection, chosen to be of the same forms as various linear buckling eigenmodes, have demonstrated the complexity of the buckling behavior. Lower bounds to the imperfection sensitivity of elastic overall buckling loads have been shown to result from the reduced stiffness analysis which is a simple extension to the classical linear buckling analysis. In addition an alternative elastic and plastic interaction empirical formula based upon the reduced stiffness loads has been seen to predict the lower bounds in the relatively large level of geometric imperfections.

大規模スペースフレームの動的解析に対するPCクラスタによる並列化システムの開発 : その1 改良した反復解法による並列化動的解析手法の効果について

In recent years, large-scale numerical analysis in structural design are increasingly demanded because of the necessity of realizing dynamic response analysis with elastic plastic behaviors in large-scale space frame structures. In order to realize large-scale numerical analysis, the developments of new high performance computing system without super-computers are desired. In several approaches, a parallel computing system is especially gathering the most attention for engineers. Thus the purpose of this study is to develop a parallel processing system for the dynamic analysis by using a PC cluster, which is a group of personal computers connected to a network mutually. Furthermore the calculating ability of the system is investigated by the numerical experiments for single layer lattice domes in this paper. It is demonstrated that the iteration method proposed to the dynamic analysis for structures is suitable for parallel calculations. Accordingly it was found through numerical experiments that the ability of parallel computing in this system produce good results and that parallel calculations using PC cluster with four personal computers reduce total analysis times to about 54% for models with different number of freedoms.

Advanced plastic hinge analysis for the design of tubular space frames

The basic theory of a two-surface plastic hinge analysis program is presented, focusing on the inelastic stiffness formulation of a three-dimensional beam–column element. Material non-linear behaviour is considered by allowing yielding to occur at the element end and mid-length sections. Simple beams and columns were analysed to demonstrate the capability of the analysis model in predicting the bending and buckling behaviour of frame members. Several tubular space frame structures, including tubular braced frames, a lattice dome and a barrel vault with pre-tensioned cables, were analysed to illustrate the qualities and limitations of the analyses in predicting the systems' strength and behaviour. The design implication of geometrical imperfections on the limit load of the system is also highlighted.

Integrated Design System for Lattice Domes

In structural design, the preliminary synthesis stage derives judgmental knowledge from engineering heuristic and experience which are usually expressed in symbolic form. On the other hand, detailed design involves extensive numerical processing. An integrated computer-aided design system should be able to handle both symbolic and numerical processings. It must also be able to integrate engineering databases and CAD packages within a single environment. The knowledge-based system approach provides a venue for achieving all these requirements. This paper presents a prototype knowledge-based system for lattice design that can perform several essential tasks including preliminary synthesis, numerical model generation, nonlinear finite element analysis, code compliance checking and member sizing. The system user is guided throughout the design session by interactive graphical user interfaces which facilitate the design process.

Application of Scissors Type Deployabe System to Single-layer Latticed Dome

Application of Scissors Type Deployabe System to Single-layer Latticed Dome

部材に分布荷重が作用するラチス構造の弾性座屈挙動

While the possibility of large space structural systems is pursued, it is important to study a new structural system as well as a new performance of materials. One of possible structural systems that have been developed is the hybrid system combining a space frame structure with a cladding, for example, a concrete slab, steel panels or membrane. In this case, constituent members of the structure are subjected to laterally distributed load due to the dead and live load. Then in this paper, the elastic buckling behavior of latticed structures is theoretically investigated on the condition that constituent members are subjected to laterally distributed load by using the proposed tangent stiffness equations of beam-column members. The treated latticed structures are double-layer latticed grids, cylindrical latticed shells and single-layer latticed domes.

入力低減型支持機構を有する大スパンドーム構造物の地震応答性状 : 免震層の降伏せん断力係数の影響について

The purpose of this paper is to study the effect of a seismic isolation system on the responses of the space frame structures where hysteresis dampers are installed to reduce the responses due to horizontal earthquake motion. This system is applied to a latticed dome with about 300m span, and dynamic response analysis of the system is carried out to illustrate the effectiveness. From the results of the numerical studies with dome, it is confirmed that the seismic isolation system with hysteresis dampers effectively suppress the vertical and horizontal acceleration responses of the dome subjected to horizontal earthquakes.

Long-Span Lattice Roof for the Nagoya Dome

The Nagoya Dome is a multi-purpose stadium that can accommodate 40,500 spectators for a baseball game. Its steel roof has a hermetic quality with excellent sound insulating performance, since the dome is adjacent to a residential neighbourhood. A single-layer steel lattice dome has been adopted for the roof structure, both to minimize shadow effects from sunlight and to achieve the required ceiling height of at least 60 m for baseball. The roof has a span of 187.2 m, which makes it one of the largest single-layer lattice dome structures in the world. The roof area is approximately 29,000 m² with a glass skylight at the center occupying about 5,000 m². A retractable screen beneath the skylight controls the transmission of sunlight into the dome.

Wave Propagation Behaviour of Spatial Structures: Impact Response Analysis of Single Layer Lattice Domes

Many researchers have investigated the wave propagation behaviors of continuum spatial structures such as plate and cylindrical shell. But due to the numerical difficulty, there is very little research related to discrete spatial structures. The objective of this paper is to examine wave propagation behavior of single layer lattice domes subject to vertical impact load at the centre node. In the first part, an analytical method based on the Fourier transform and a matrix method is presented. In the second part, an impacted two dimensional lattice beam is analyzed in order to estimate the validity of the analytical program. In the last part, nine types of single layer lattice domes are analyzed to estimate the effect of member distribution density, member arrangement pattern and the jointing system, etc., upon the wave propagation behavior.

Wind loads and wind-induced dynamic behavior of a single-layer latticed dome

This paper describes the results of some basic investigations on wind loads and wind-induced dynamic behavior of a rigidly jointed single-layer latticed dome with a long span. First, the wind pressures were measured simultaneously at many points on a dome model in a turbulent boundary layer which simulated the natural wind over typical urban terrain. In the wind tunnel experiments, nine models with different rise/span and wall-height/span ratios were tested. In order to investigate the structure of the pressure field on the dome, the proper orthogonal decomposition (POD) technique was applied to the pressure data. The effect of dome geometry on the structure of the pressure field is briefly discussed. Then, the dynamic response of nine latticed domes with a span of 120 m was analyzed in the time domain. The equation of motion for the structural frame of the dome was numerically integrated by using the Newmark's β method; the wind loads, expressed as the concentrated loads at the interior nodes of the network, were generated by superimposing the first eight eigenfunctions of pressure, which were obtained from the above mentioned POD analysis. The results indicate that the dynamic response is dominated by several vibration modes; that is, the first three or four axisymmetric modes and a few lower asymmetric modes with small wave numbers both in the circumferential and in the radial direction.

緩みのある接合特性を有する単層ラチスドームの弾塑性挙動シミュレーション法

In the former study on the numerical simulation for the partial beam with the ball-joint connection, the ability of the numerical modeling was proven by the present authors. By using the similar method, the estimative ability of the present simulation method for the practical latticed dome is investigated through comparative analyses between numerical analyses and experiments. The numerical analyses are executed with parameters, looseness, initial compressive force at the connectors and initial deflection at noticeable node of the dome. Through comparison between the experiments and the numerical simulations, the structural behaviours of the tested steel single layered latticed domes with ball-joint connections are also precisely discussed

集中荷重と分布荷重を受ける剛接合単層ラチスドームの変形特性に関する実験的・理論的研究

The deflection behavior of rigidly jointed single-layer latticed domes with several triangular networks subjected to a vertical concentrated load and/or uniform pressure have been studied experimentally. On comparing of the experimental results with calculated ones of finite element method, close agreements between them were obtained. The results indicate that the dome tends to buckle more easily as the distributed load increases and that the buckling characteristics depend on the Shell-likeness Factor S. In applying a concentrated load to the apex of the dome, the deflection characteristics standardize those for the other junctions.

Complete Load-Deflection Response and Initial Imperfection Analysis of Single-Layer Lattice Dome

The whole process of load-deflection response is analyzed for two single-layer lattice dome of big size as practical examples. The nonlinear behaviours of the perfect domes and their deflection shapes at several points after buckling are at first investigated. Two methods for imperfection analysis are then suggested. It is proved that single-layer lattice dome is very sensitive to initial imperfections and the suggested methods can be applied to real analysis.