Lattice Cylindrical Shell Research Articles

Compression properties and energy absorption of Gyroid lattice cylindrical shells filled thin-walled tubes fabricated by selective laser melting

In recent years, lattice cylindrical shells (LCSs) based on the triply periodic minimal surfaces (TPMS) have been researched in the energy absorption (EA) field due to their distinctive mechanical properties. However, LCS structures will generate severe lateral expansion and localized fragmentation during compressive deformation, resulting in a significant decrease on compression performance. To further improve EA properties, Gyroid LCS filled thin-walled tubes (LCS-T) are proposed and produced by selective laser melting (SLM). In this work, the influence of the interaction (hollow thin-walled tubes + LCSs core) of the Gyroid LCS-T with different filling radii on the compressive properties and EA were investigated by the quasi-static compression experiments and finite element simulation systematically. The results showed that the Gyroid LCS-T based on AlMgScZr alloy fabricated by SLM had high connection strength and no obvious defects. The specific EA (SEA) of Gyroid LCS-T with radius of 3, 6, and 9 increased by 42.1%, 49.3%, and 53.3%, respectively, compared to thin-walled tubes. Compared to the sum of all components individually, the Gyroid LCS-T achieved superior performance in both compressive properties and EA by transferring stresses from the LCS interior to the thin-walled tube. Furthermore, the gradient design realized adjustment of the structural deformation and improved EA with about 1.24 times compared to uniform structure. This research offered visionary insights into designing energy-absorbing structures and optimizing parameters for LCS-T.

Design of lattice cylindrical shell meta-structures for broadband vibration reduction and high load-bearing capacity

In this paper, a new type of lattice cylindrical shell meta-structure (LCSM) with broadband vibration reduction and high load-bearing ability is designed. In particular, the proposed curved shell meta-structure is constructed by combining lattice structure and mechanical metamaterial with elastic bandgap properties. The dispersion curves of shell structure are obtained by combining Bloch's theorem with the coordinate transformation method. The vibration transmission properties and load-bearing performance of the LCSM and the sandwich LCSM are studied numerically and experimentally. The results reveal that the proposed meta-structure has excellent vibration isolation performance at broadband frequencies, and the change of structural parameters can be used to regulate the frequency range of bandgap. Especially, the existence of curvature makes the bandgap of the shell structure inevitably change when the circumferential size of the shell is changed. Moreover, the meta-structure can maintain certain broadband vibration reduction properties when increasing the load-bearing capacity. This work offers an innovative method to develop multi-functional lattice shell structures with both load-bearing and broadband vibration isolation properties.

Two-level homogenization and multi-failure analyses of hierarchical lattice stiffened cylinder

In this research, the equivalent method and multi-failure mechanism of hierarchical Isogrid stiffened cylinders (HISCs) were investigated. Two-level homogenization technique was proposed to analyze the stiffness and stresses of the HISC. Five failure modes and criteria, including global buckling, primary mono-cell buckling, secondary mono-cell buckling, primary rib buckling and material failure were proposed to distinguish the failure mode and predict the load capacity. The method was verified by experimental and numerical investigations. The study deepens the understanding of controlling ability of hierarchical structures on buckling behaviors and predicting failure with properties approaching the actual performance, and gives a guidance to ultralight design of large-diameter lattice cylindrical shells with higher accuracy.

Study on the collapse performances of fabricated single-layer spatial network structures based on discrete beam elements

Using discrete beam elements to simulate the mechanical properties of assemble joints, the collapse performances of free-form, cylindrical, and K6 spherical surface latticed shells were analyzed. The effects of grid sizes, rise-span ratios, and connection behaviors on structural collapse performances were discussed. The main conclusions were obtained: (1) By conducting an integral scaled model test of a free-form latticed shell, the accuracy of the collapse analysis model with discrete beam elements was verified. (2) Multiple collapse shapes were obtained for the latticed shells with various structural parameters. To ensure an excellent collapse-resistant capacity, the grid size should not exceed 4 m, and the rise-span ratio is suggested as 1/4 for the cylindrical latticed shells, and the grid size should not be greater than 3 m, and the rise-span ratio should not be less than 1/4 for the spherical surface latticed shell. (3) The connection behaviors of assemble joints significantly influence the structural collapse-resistant capacity. When the stiffness and bearing capacity of the assemble joint drop to 50% of the joint designed based on “strong joints and weak tubes”, the robustness index decreases rapidly. However, more than 80% of the collapse load is still reserved for the cylindrical latticed shell and approximately 60% for the spherical surface latticed shell.

Energy absorption of diamond lattice cylindrical shells under axial compression loading

A mapping method was proposed to construct the lattice cylindrical shell (LCS) based on the triply periodic minimal surfaces (TPMS). The diamond lattice cylindrical shell (D-LCS) was designed using the proposed method and fabricated by selective laser melting (SLM). The experimental tests were conducted to investigate the energy absorption performance of these structures under quasi-static axial compression loading. The finite element (FE) models were established and validated using experimental results. Furthermore, the influence of the design parameters on the deformation modes and energy absorption performances of the D-LCSs were studied by parametric studies. The results showed that the D-LCS exhibited superior energy absorption performances compared with its counterparts. The relative density, cell size, radial variation coefficient, and mapping angle had significant effects on the deformed modes and energy absorption performances of the D-LCS structures. The findings of this study were expected to facilitate the design of the D-LCS structures for energy absorption applications.

Unusual deformation patterns in a second-gradient cylindrical lattice shell: Numerical experiments

Numerical experiments reveal unusual deformation patterns in a cylindrical lattice shell, modeled as a curved two-dimensional second-gradient elastic surface.

The connection performance and bearing capacity of a single-layer combined lattice shell with aluminium alloy honeycomb panels

To take full advantage of the lightweight and high strength characteristics of aluminium alloy honeycomb panels and to overcome the shortcoming of the low elastic modulus of the aluminium alloy lattice shell, the present study proposes a new aluminium alloy combined lattice shell (AACLS) structure, which consists of aluminium honeycomb panels and an aluminium alloy lattice shell that jointly resist the load. In the present study, a cylindrical combined lattice shell with a span of 4.4 m was designed and fabricated to carry out the bearing capacity test, and on this basis, the load bearing characteristics and the failure mechanism of this new type of spatial structure are described. The test results show that because the honeycomb panels acted as an integral part of the structure, the overall stiffness and stable bearing capacity of this new type of combined lattice shell were significantly improved compared to those of a panel-free single-layer aluminium alloy lattice shell with the same span. Using the connection performance simulation method proposed in the present study, the load bearing performance of the combined cylindrical lattice shell was well simulated, with an error of only 2% between the calculated and tested ultimate bearing capacities. Parametric analysis was carried out to investigate the effects of the boundary conditions, rise-to-span ratio, and geometric imperfections on the performance of the combined lattice shell. Based on the finite element analysis results of 552 numerical examples and using the probability-based partial factor design method, a simplified method for calculating the stable bearing capacity of the combined lattice shell is proposed, which provides a theoretical basis for the engineering design and specification development of this new type of combined structure in the future.

Damage identification of single-layer cylindrical latticed shells based on the model updating technique

Damage identification of single-layer cylindrical latticed shells based on the model updating technique

Assessment and design considerations for single layer cylindrical lattice shells subjected to seismic loading

This paper examines the main considerations related to the seismic design and assessment of single layer steel cylindrical lattice shells, and offers recommendations for their practical application. Geometric configurations covering a wide range of rise to span ratios are considered within the investigation. An insight into the relative influence of seismic loading on shell design, in comparison to gravity conditions, is firstly provided through the use of digital parametric engineering procedures. This is followed by linear elastic response assessments which are used to propose a simplified procedure for estimating the internal seismic forces for the purpose of member sizing in early design stages. Suitable approaches for pushover analysis are then discussed and used to identify inherent plastic mechanisms. The results of incremental nonlinear dynamic analysis, using a suite of fourteen records, are also employed in order to validate the findings and to further assess the ultimate response under realistic seismic loading conditions. Based on the findings, representative ranges for behaviour factors and displacement modification coefficients are derived alongside discussions on their implementation within codified seismic design procedures. Apart from providing recommendations for simplified design approaches, the assessments presented in this paper can also be used to support detailed performance based guidelines as well as for informing geometry and size optimisation strategies.

Shape optimization and buckling analysis of novel two-way aluminum alloy latticed shells

The circumferential profile of cylinder, as a classic shape, has been widely adopted in single-layer latticed shells. Previous research into these structures primarily concentrated on their buckling behavior. In this work, a novel two-way aluminum alloy cable-stiffened single-layer latticed shell is proposed to explore a shape optimization procedure of such structure. In addition, the buckling behavior of the optimized structures and classic cylindrical latticed shells are examined and compared. The optimization procedure adopts a linear algorithm, in which the structural strain energy is selected to be the optimization objective. Buckling analyses are also performed to compare the buckling behavior of this novel latticed shell with classic cylindrical and optimized shapes. The comparisons show that the load-carrying capacities are clearly enhanced by optimizing the shell shapes. The results presented in this article are anticipated to aid engineers in the design of two-way aluminum alloy latticed shells with an optimal shape.

Research on the progressive collapse resistance of single-layer cylindrical latticed shells with AH joints

Progressive collapse accidents of single-layer latticed shells introduce a serious threat to public safety. The progressive collapse-resisting capacity (PCRC) has gradually become an essential requirement in the design of spatial structures. In this study, the progressive collapse test and numerical simulation of a single-layer cylindrical latticed shell were conducted to evaluate the effect of the joint stiffness on the PCRC of fabricated single-layer latticed shells. A combined spring model was established to simulate the semi-rigid performance of fabricated joints in the FEA. The failure mechanism of single-layer cylindrical latticed shells with different joint systems was thoroughly discussed from multiple perspectives. The results show that the combined spring model can accurately simulate the progressive collapse of a single-layer latticed shell with semi-rigid joints. The progressive collapse of the cylindrical latticed shell with type-II AH joints showed brittle features during the test. Most joints experienced connection failure. Although the rigid jointed shell and latticed shell with type-II AH joints have much higher PCRC, the semi-rigid jointed shell with type-I AH joints has better ductility during progressive collapse. This paper offers a reference for the progressive collapse-resisting design of latticed shells with fabricated joints.

Quasi-static compression and hygrothermal stability of BMI/CE co-cured composite lattice cylindrical shell

Composite lattice cylindrical shell is a typical lightweight structure, which has been widely used in aerospace structures in recent years. In this paper, combined with the high temperature resistance of bismaleimide (BMI) resin and the dimensional stability of cyanate ester (CE) resin, it is proposed to cure T800 carbon fiber/CE composite composed grid and T800 carbon fiber/BMI composite composed skin at one time. The stability of shell height, out-of-roundness and axial pressure resistance of T800/BMI shell, T800/CE shell and T800/BMI-CE shell under hygrothermal conditions are compared and analyzed by experiment and simulation, and the mechanism and feasibility of this design method are verified and discussed.

Evaluation of Load Factor to Be Applied in Buckling Design of Cylindrical Lattice Shells Under Asymmetric Snow Load

The load factor is one of the keys in anti-buckling design for safety together for construction cost, and studies have been becoming demanded in a recent situation that super large and super light spatial structures have been constructed. This paper investigates the relationship between reliability index β and snow load factor γs for anti-buckling design of a simply supported cylindrical lattice shell roof under simultaneous action of both dead load and asymmetric snow load. The cylindrical lattice shell analyzed is composed of an equilateral triangle grid of which members are of steel circular hollow sections. Members are connected rigidly to nodes at their both ends. The snow distribution as a main target is assumed in a way that the snow depth on the half of the arch-like roof is half of the amount on the other half roof. The snow fall depth is here assumed 50cm evaluated as 100-year return period, and its probability is assumed as Gumbel distribution with 100-year reference period. The probability distribution of buckling strength Pcr including geometrical and material nonlinearities is approximately evaluated based on a first-order perturbation. The reliability is calculated based on AFOSM, and the relationship in a form of β to γs is finally expressed for design use.

Collapse Mechanism of Single-Layer Cylindrical Latticed Shell under Severe Earthquake

In this paper, the results of finite element analyses of a single-layer cylindrical latticed shell under severe earthquake are presented. A 3D Finite Element model using fiber beam elements is used to investigate the collapse mechanism of this type of shell. The failure criteria of structural members are simulated based on the theory of damage accumulation. Severe earthquakes with peak ground acceleration (PGA) values of 0.5 g are applied to the shell. The stress and deformation of the shell are studied in detail. A three-stage collapse mechanism “double-diagonal -members-failure-belt” of this type of structure is discovered. Based on the analysis results, measures to mitigate the collapse of this type of structure are recommended.

Deformation behaviors and energy absorption of auxetic lattice cylindrical structures under axial crushing load

Auxetic lattice cylindrical shell consisting of re-entrant lattice cell has superior mechanics performance due to negative Poisson's ratio (NPR). In this work, finite element models were established and finite element method (FEM) was adopted to explore the deformation behaviors and energy absorption of re-entrant auxetic lattice cylindrical shells and the SILICOMB lattice cylindrical shell in different crushing velocity. Result indicated that the deformation behaviors of auxetic lattice cylindrical shells are expressed as NPR mode, and different deformation behaviors (‘Z’ mode, ring mode, diamond mode and mixed mode) of lattice sandwich cylindrical shells are mainly determined by the ratio of the core wall thickness to the skin. The SILICOMB lattice cylindrical shell has better performance than the conventional hexagon honeycomb lattice cylindrical shell when crushing under high velocity. Meanwhile, the SILICOMB sandwich cylindrical shell has the best performance on the specific energy absorption among these four configurations and the maximum increment is 20.77%. The design of the auxetic and the SILICOMB cylindrical shells may provide a new idea which can be applied in practical application as impact resistance structures on aerospace.

Numerical and experimental studies on compressive behavior of Gyroid lattice cylindrical shells

In this paper, Gyroid lattice cylindrical shell (LCS) specimens were designed by a newly proposed mapping methodology and were fabricated by selective laser melting (SLM) technology. Their energy absorption and deformation modes were investigated through quasi-static compression tests. A finite element model (FEM) was proposed, which was validated by the experimental results, for a further study on the compressive behavior of the Gyroid LCS. Based on the numerical study, it was found that Gyroid LCS showed superior energy absorption to the hexagonal LCS and triangular LCS with the same density. In addition, a parametric study indicated that main energy absorption factors, namely total energy absorption, specific energy absorption and mean crushing load, were in power function relationship with the relative density. Finally, it was found that thickness gradient and geometric gradient had significant effects on the failure modes of Gyroid LCS under compression. The research in this paper is expected to provide some guidance for the design of energy absorption devices or structures.

Reliability of stability of single-layer latticed shells with spatially correlated initial geometric imperfection modeled using conditional autoregressive model

Latticed shells are extensively used for large-span structures. Their design is often governed by the global instability requirement stipulated in the Chinese design code for the specified gravity load and initial geometric imperfection (IGI). However, the reliability-basis for the recommended design requirement that a critical load factor of 2 need to be achieved is unknown. In the present study, it is proposed that the spatially varying IGI can be adequately modeled using the conditional autoregressive model. It is shown that this model is sufficiently flexible in modeling spatially varying correlated imperfection and can cope with irregular grid systems. By using this model for IGI and considering global instability, the probability distributions of the load capacity and the failure probabilities of spherical and cylindrical latticed shells designed according to the Chinese design code are evaluated. The evaluation is also carried out by representing the IGI shape using the spatially independent Gaussian model and the first eigen buckling mode (1EBM) that is recommended by the design code. It is shown that the use of the 1EBM to represent the IGI shape does not necessarily lead to conservative estimates of the failure probabilities as compared to those obtained by considering spatially varying stochastic imperfection shapes. The results shown that the estimated failure probability is sensitive to the assumed stochastic model for and standard deviation of the IGI at each joint of the latticed shells. Furthermore, the failure probability of the spherical latticed shell differs from that of the cylindrical latticed shell. The reliability analysis results also indicate that the use of a critical load factor of 2 implemented in the code for design of the latticed shell, in general, lead to an annual failure probability for global instability less than 10−5. A sensitivity analysis indicates that the code recommended critical load factor can be reduced to 1.75 while achieving a target reliability index often adopted for design code calibration.

Mechanical performance of AH joints and influence on the stability behaviour of single-layer cylindrical shells

Abstract Previous studies on the mechanical performance of AH (assembled hub) joints mainly focused on the axial capacity and the bending capacity of the joint system. However, the joint system in latticed shells is subjected to combined axial forces and bending moments in practice. In this paper, the mechanical performance of joints under eccentric load is investigated experimentally and numerically. The eccentric bearing capacity, as well as the failure mechanism of the novel joint system, are derived and compared with the axial loading and pure bending conditions. The correlation curve with 95% guaranteed rate is determined by non-linear regression analysis. On this basis, a combined non-linear spring model is established to simulate the mechanical performance of joints in single-layer cylindrical shells for stability analysis. The results indicate that for orthogonal type cylindrical latticed shells with diagonals or crossed cables, the stability reduction factor can reach a range of up to 0.8 to 0.96. However, for cylindrical latticed shells with lamella grids or three-way grids, the stability reduction factor is less than 0.62. This situation can be improved by strengthening the joint system or reducing the intersection angles of members. When the intersection angle decreases from 90° to 60°, the stability reduction factors of lamella shells will increase by 34%–47%. This means that cylindrical shells with AH joints have sufficient stability to meet engineering requirements by rational design.

Seismic performance of single layer steel cylindrical lattice shells

This paper examines the elastic and inelastic seismic behaviour of single layer steel cylindrical lattice shells. The main dynamic characteristics for this form of structure are firstly examined through a parametric assessment, which also leads to proposed expressions for estimating the fundamental period and mode of vibration. The seismic response of five typical shell configurations, representing a wide range of rise to span ratios, is then assessed within the linear elastic range under selected earthquake excitations. Particular focus is given to the relative influence of the horizontal and vertical seismic components on the internal actions. In order to provide a means for evaluating the underlying inelastic behaviour, a simple pushover approach, which is suitable for this structural form, is suggested using the forces obtained from the fundamental mode shape. The peak angle change is proposed as a damage parameter within the nonlinear analysis for characterising the inelastic global and local demands in shells of different geometries. Incremental dynamic analysis is subsequently carried out in order to evaluate the detailed nonlinear time history response. The results provide detailed insights into the influence of the horizontal and vertical excitations on the nonlinear seismic response, and illustrate the suitability of the peak angle change as an inelastic deformation measure for shells of different geometric configurations. The main findings from the linear and nonlinear assessments are highlighted within the discussions, with a view to providing guidance for performance based assessment procedures as well as simplified design approaches.

Shaking table test and numerical simulation of an isolated cylindrical latticed shell under multiple-support excitations

In order to study the influence of the ground motion spatial effect on the seismic response of large span spatial structures with isolation bearings, a single-layer cylindrical latticed shell scale model with a similarity ratio of 1/10 was constructed. An earthquake simulation shaking table test on the response under multiple-support excitations was performed with the high-position seismic isolation method using high damping rubber (HDR) bearings. Small-amplitude sinusoidal waves and seismic wave records with various spectral characteristics were applied to the model. The dynamic characteristics of the model and the seismic isolation effect on it were analyzed at varying apparent wave velocities, namely infinitely great, 1000 m/s, 500 m/s and 250 m/s. Besides, numerical simulations were carried out by Matlab software. According to the comparison results, the numerical results agreed well with the experimental data. Moreover, the results showed that the latticed shell roof exhibited a translational motion as a rigid body after the installation of the HDR bearings with a much lower natural frequency, higher damping ratio and only 1/2∼1/8 of the acceleration response peak values. Meanwhile, the structural responses and the bearing deformations at the output end of the seismic waves were greatly increased under multiple-support excitations.