Pyramidal Lattice Truss Research Articles

A homogenization method for natural frequencies and damping analysis of composite pyramidal lattice truss sandwich structures based on representative volume elements

A homogenization method for the vibration analysis of periodic sandwich panels is presented. Periodic boundary conditions are applied to a representative volume element (RVE) of the structures. The complex responses of the RVE under eight sinusoidal excitations are calculated and the complex stiffness matrix of the sandwich panels is obtained by the direct-solution steady-state dynamic analysis (DSDA) using the finite element method (FEM) in the frequency domain. Based on equivalent single-layer (ESL) theory and finite element-modal strain energy (FE-MSE) method, the natural frequencies, the mode shapes and the loss factors of the structures are obtained by shell models. The effectiveness of the homogenization method is validated by using pyramidal lattice truss sandwich panels made of carbon fiber reinforced plastics (CFRP). The results obtained by the homogenization method are compared with those obtained by experiments and solid models. The effects of the number of cells and damping layers are discussed.

Additively Manufactured Lattice Truss Sandwich Cylinder and Free Vibration Behaviors

In aerospace engineering, it is attractive to combine additive manufacturing (AM) with lightweight design to reduce the weight of primary load-bearing structures. In this paper, a double-layer pyramidal lattice truss sandwich cylinder was designed and printed by selective laser melting (SLM) method, which has advantages in integrally manufacturing end frames and bolt holes. With diameter of 0.493 m, this cylinder is one of the lattice truss sandwich structures with the largest diameter at present. Free vibration testing was carried out to reveal the free vibration responses of the cylinder. The first-order vibration turns from a circle to an oval in the plane of the cross section. The fundamental frequency is 133.9 Hz. An equivalent shell free vibration theory was proposed and finite element models (FEMs) based on discrete model and equivalent shell model were applied to predict the natural frequencies and mode shapes of the cylinder. Advantages of the AM method in making light and stiff large-sized aerospace structures are confirmed through this research.

Effect of high-low temperature on the compressive and shear performances of composite sandwich panels with pyramidal lattice truss cores

Composite sandwich panels with pyramidal lattice truss cores (CSPPLTCs) were manufactured employing waterjet-cutting technology and interlocking assembly. The effect of high-low temperature environments on the out-of-plane compressive and shear performance of the panels was studied using theoretical and experimental methods. In particular, the out-of-plane compressive stiffness, strength of sandwich panels with pyramidal lattice truss cores, their shear stiffness, and strength in high-low temperature environments were predicted using theoretical equations. The study found that in low-temperature environments, the movement of molecular chain segments in the epoxy is hindered, futhermore, the mismatched thermal expansivity of carbon fiber and epoxy resin leads to the improvement of interface bonding performance, thus improving the out-of-plane compressive and shear performance of CSPPLTCs; in high temperature environments, the movement of molecular chain segments in the epoxy gets more active and tends to move freely, so the resin turns into a flexible state with high elasticity from the stiff glass state, which finally causes a deterioration in out-of-plane compressive and shear performance of CSPPLTCs. According to observations, the failure mode depends on temperature environments. Brittle fracture and crushing failure happen in the composite struts at low temperature; plastic microbuckling may happen in the composite struts at high temperature.

Delamination Testing of AlSi10Mg Sandwich Structures with Pyramidal Lattice Truss Core made by Laser Powder Bed Fusion

Sandwich structures possess a high bending stiffness compared to monolithic structures with a similar weight. This makes them very suitable for lightweight applications, where high stiffness to weight ratios are needed. Most common manufacturing methods of sandwich structures involve adhesive bonding of the core material with the sheets. However, adhesive bonding is prone to delamination, a failure mode that is often difficult to detect. This paper presents the results of delamination testing of fully additive manufactured (AM) AlSi10Mg sandwich structures with pyramidal lattice truss core using Laser Powder Bed Fusion (LPBF). The faces and struts are 0.5 mm thick, while the core is 2 mm thick. The inclination of the struts is 45°. To characterise the bonding strength, climbing drum peel tests and out-of-plane tensile tests are performed. Analytical formulas are derived to predict the expected failure loads and modes. The analytics and tests are supported by finite element (FE) calculations. From the analytic approach, design guidelines to avoid delamination in AM sandwich structures are derived. The study presents a critical face sheet thickness to strut diameter ratio for which the structure can delaminate. This ratio is mainly influenced by the inclination of the struts. The peel tests resulted in face yielding, which can also be inferred from the analytics and numerics. The out-of-plane tensile tests didn’t damage the structure.

Effect of localized defects on mechanical and creep properties for pyramidal lattice truss panel structure by analytical, experimental and finite element methods

The localized defects, including the ruptured truss and debonding joint, have been severely threatening the structural integrity of the pyramidal lattice truss panel structure (PLTPS). In this paper, a series of analytical models, i.e., equivalent elastic modulus, plastic and creep strain rate models, were developed to study the effects of localized defects on the mechanical properties and creep performance of the PLTPS, which have been verified by the experiments and finite element (FE) simulation. Based on the experimental data, the equivalent elastic modulus model was modified when the defect fraction exceeds the threshold value. The complete stress–strain curve was plotted by the proposed analytical models. At elevated temperature, both the analytical model and finite element results indicate that the equivalent creep rate increases exponentially with the increase of the defect fraction. In addition, for the long-term service, the total equivalent strain is the superposition of the steady-state creep strain and the saltatorial strain stimulated by the inconsecutive stress once the truss or joint fails, which is more susceptible to the effective stress comparing with the servicing time. The proposed analytical model which considering the effect of localized defects of the PLTPS provides an efficient criterion to justify whether the structure with certain defects satisfies the engineering requirements.

Compression performances and failure modes of 3D printed pyramidal lattice truss composite structures

Lattice structures have several advantageous properties, including light weight, high specific strength, and high specific stiffness. 3D printing technology was used to prepare pyramidal structures with different strut diameters. Here, compression tests were used to study the effect of the relative density on the structural deformation mechanism, compression performance, and energy absorption characteristics. The 3D printed pyramidal structures with different strut diameters have three post-failure modes: fracture, stable deforming, and softening. The compression performance of the structure is greater at higher relative densities. The structure absorbs energy well at appropriate relative densities. The finite element method was used to characterize the compression behaviors of the lattice structures. A comparison of structures prepared by previous studies reveals that the 3D printed pyramidal structures prepared in this study have excellent energy absorption capacity in low-density structures.

Effect of elevated temperature on the out-of-plane compressive properties of nickel based pyramidal lattice truss structures with hollow trusses

In this study, the effect of elevated temperatures on the out-of-plane properties of nickel based pyramidal lattice truss structures with hollow trusses were investigated through theoretical analysis, experimental measurements and numerical prediction. It is found that, with the increase of temperature from 25 °C to 450 °C, the compressive strength, compressive modulus and energy absorption capacity of the sandwich structures fabricated via SLM additive manufacturing decrease by 37.98%, 33.25% and 38.36%, respectively. The theoretically predicted failure modes and compressive strength of the hollow lattice truss cores are in well agreement with experimental measurements and numerical predictions. Comparison with competing lightweight sandwich constructions reveals that the nickel based pyramidal lattice truss structure with hollow truss exhibits superiority in the specific strength under high temperature.

Characteristics of an improved boundary insert for sandwich panels with lattice truss cores

Composite sandwich panels with lattice truss cores have dramatic static and dynamic characteristics, which are widely used in aerospace industry. Owing to the inability to sustain localized loads of joining, valid inserts are required to enable the interconnection of the sandwich panels. The present study develops a novel boundary insert parallel to the facesheets for pyramidal lattice truss core sandwich panels. Analytical-mechanical models are addressed for the proposed boundary insert subjected to in-plane pull-out, in-plane shear as well as out-of-plane shear loads and experimental tests are carried out to characterize mechanical behaviors. Failure sequences and mechanisms are discussed comprehensively and good correspondence is obtained with analytical prediction. Finite element simulation models are developed for visualization of internal load distribution. Experimental results show that significant improvements in load capacities can be achieved by the developed boundary insert compared with the interconnection concepts for honeycomb sandwich panels.

Vibration characteristics of novel multilayer sandwich beams: Modelling, analysis and experimental validations

Multilayer sandwich structures have been extensively studied. However, very few results are reported on the vibration issues of some novel multilayer sandwich structures with lattice truss cores in the literature. To this aim, in this paper, the dynamic modellings of multilayer sandwich beams with pyramidal lattice truss cores are developed, and the vibration characteristics of multilayer lattice sandwich beams are numerically investigated and validated by vibration experiments. The deformation relations of multilayer sandwich beams are theoretically developed in this study, and consequently the constitutive relations of the truss core layers of multilayer sandwich beams are derived by using such a deformation energy based method. Hamilton’s principle and the assumed mode method are used to derive the equations of motion of the multilayer sandwich beams. The natural frequencies of the multilayer lattice sandwich beams are obtained and compared with those from the finite element method (FEM) and experimental tests, which all verified the correctness and feasibility of the proposed numerical method. Contributions of this study lie in the development of the novel deformation relations of multilayer sandwich beams, establishment of the dynamic models, and systematic analysis of vibration characteristics with both the numerical and experimental methods. The present work would facilitate the application of multilayer truss core sandwich structures in engineering fields.

A hybrid joining insert for sandwich panels with pyramidal lattice truss cores

Sophisticated and efficient technique of sandwich attachment for composite sandwich structure assembly is imperatively required by industries. Certain types of joining inserts are widely used to carry the localized loads, but little is known regarding to the joining method for composite lattice truss core sandwich structures. In this study, a novel hybrid insert fastener, which comprises a plurality of carbon-fiber-reinforced grid cells and a metallic part, is developed for pyramidal truss core sandwich structures. Finite element models are developed to predict the failure modes and the load capabilities of different insert locations. Static pull-out and shear experiments are carried out, and the failure behaviors for each load case are discussed. The results show that the shear performance is significantly improved, and the insert position greatly affects the static pull-out behavior. An optimization of the hybrid joining insert to enhance the pull-out characteristic is addressed and verified by the finite element analysis.

Compression behaviors of 3D printed pyramidal lattice truss composite structures

The lattice truss structure is a porous lightweight periodic structure with high specific stiffness and specific strength. In this research, pyramid lattice truss structures were designed and manufactured by three-dimensional (3D) printing technology through horizontal printing and vertical printing manners, respectively. Quasi-static axial compression tests were conducted to study the mechanical properties and energy absorption of the pyramidal lattice truss structures. These two types of printed lattice truss materials had close strength and rigidity. However, the vertically printed lattice truss structures had excellent ductility and their struts never broken off during compression. Three post failure styles of the vertically printed lattice truss structures were observed, including strain-hardening, stable deforming and softening and depending on the slenderness ratio of the strut. Theoretic analysis and finite element method (FEM) were performed to investigate the compression behaviors of the vertically printed lattice truss materials. Appropriate printing method and relative density could make the 3D printed pyramidal structures achieve excellent specific energy absorption.

Modeling and reliability of insert in composite pyramidal lattice truss core sandwich panels

Valid configuration of inserts is commonly used for assembly in sandwich structures. Inherently, various uncertainty results in variability in mechanical characteristics of inserts, and need to be addressed adequately. This study explores the reliability of inserts in composite pyramidal lattice truss core sandwich panels. Finite element method is utilized to analyze the sources and sensitivity of uncertainty in mechanical properties of constituent materials and geometry of sub-components. To quantify the reliability of the insert structure in the presence of uncertainty, machine learning technology is used to investigate the uncertainty propagation by a statistical description. Failure probability is observed and the insert structure shows outstanding stability under pull-out loading. The thickness of face-sheets and the properties of the bonding interface play large roles in stiffness and strength, respectively. Suitable process controls should be implemented to maintain the both critical parameters at a high and stable level.

Life prediction model of creep-rupture and creep-buckling of a pyramidal lattice truss panel structure by analytical and finite element study

The creep failure lives of a pyramidal lattice truss panel structure at compressive and tensile loads have been investigated by theoretical and finite element methods. Two analytical models are derived to calculate the life of creep-rupture and creep-buckling. The results reveal that the creep-rupture life is highly sensitive to the geometry dimensions. With the decreases of the stamping angle, cutting angle, truss length and the increases of the truss width and thickness, the creep-rupture life decreases significantly. The creep-buckling model presents that the creep-buckling life can be improved by increasing the width and thickness of truss and decreasing the length of truss. A synthetically analytical model combines the creep-rupture and creep-buckling is proposed to predict the creep failure time accurately. The transition mechanism from creep-buckling to creep-rupture is also extensively studied. Creep-buckling is the dominant failure mechanism as the applied stress approaches the critical stress. The solid truss is inclined to creep-rupture when the compressive stress is smaller than the critical stress.

Mechanical response of pyramidal lattice truss core sandwich structures by additive manufacturing

ABSTRACTIn this study, metallic pyramidal lattice truss core sandwich structures, including single-layered as well as multi-layered ones, are fabricated from EOS Aluminium AlSi10 Mg, utilizing additive manufacturing method. Out-of-plane and in-plane compression as well as shear tests were carried out in order to measure the stiffness and strength properties of the structures. The out-of-plane compressive strength is determined by buckling of struts, and specimens fail in plastic yielding of face sheets for in-plane tests. And for the shear performance of the specimens, the strength is dominated by the node failure. In addition to experimental testing, finite element models have been developed for simulating the stiffness and strength properties and the numerical results agree well with experimental performance.

Experimental study on dynamic compressive behaviour of sandwich panel with shear thickening fluid filled pyramidal lattice truss core

The dynamic compressive behaviour of sandwich panels with shear thickening fluid (STF) filled pyramidal lattice truss cores at high strain rates is studied and compared with that of pure STF as well as the sandwich panels with empty and water filled pyramidal lattice truss cores by modified split Hopkinson pressure bar (SHPB) apparatus. The dynamic compressive strengths of the sandwich panels while filled with STF increase significantly when compared to the strengths of the sandwich panels with empty pyramidal lattice truss cores. It is interesting to note that the sandwich panel with the STF filled pyramidal lattice truss core shows “1 + 1 >> 2” dynamic energy absorption behaviour. The excellent energy absorption behaviour of the sandwich panel with STF filled truss core is interpreted by the transformation of deformation modes of core beams from non-symmetry to symmetry after filled with the STF through strong interaction between the buckling behaviour of pyramidal lattice truss core and the shear thickening behaviour of the filled STF material.

Effect of cross sectional shape of struts on the mechanical properties of aluminum based pyramidal lattice structures

Three types of cross sectional shapes of struts are designed in a pyramidal lattice truss structure including circular, semi-circular and U-type, and fabricated using pure aluminum by 3-D printing based investment casting technology. The compressive mechanical behaviors of the lattice truss structures were examined and the related mechanisms were analyzed. It is shown that, when the inclination angle was 70°, the compression strengths of semi-circular and U-type lattice truss structures were twice that of circular strut structure due to the increased area moment of inertia of struts contributing to higher buckling resistance.

Mechanical behavior of three-dimensional pyramidal aluminum lattice materials

Al based pyramidal lattice truss materials have been fabricated through 3-D printing and molten metal infiltration technology. It is shown that the designable structures with thin struts and small cells can be realized by this technology. Similar to usual porous materials, the present Al based lattice materials also exhibited three-stage compressive mechanical behavior, i.e. linear elastic, plateau and densification stages. The mechanical properties of the lattice materials showed obvious dependence on the structure parameters including the inclination angle of strut with the bottom plane, strut length and strut diameter etc, but actually all these dependences can be attributed to varied relative densities of the lattice materials. Moreover, it is found that the deformation mode of the lattice materials was different if the inclination angle was obviously changed. When the inclination angle was relatively small, the deformation uniformly took place in the form of strut buckling, while it occurred in a localized zone followed by the extending of the zone if the inclination angle was large enough.

A novel strengthening method for carbon fiber composite lattice truss structures

The composite pyramidal lattice truss core sandwich panel, in which the lattice core is strengthened by end frames between various nodes and the struts are reinforced with unidirectional fibers, is fabricated by the hot-press molding technique and interlocking method. Because all of the continuous fibers are aligned in the rod direction, the fiber’s intrinsic strength can be fully exploited; thus, the lattice truss core has the maximum load-carrying capacity. Furthermore, the composite lattice truss core (strengthened by the top and bottom aluminum connectors) has the ability to collaboratively deform under compressive and shear loading. Compressive and shear experiments were conducted to investigate the mechanical properties and failure mechanism of this new composite pyramidal lattice structure. The experimental results show that the present composite pyramidal lattice structure has some significant advantages compared with other existing composite pyramidal lattice structures.

Normal and oblique projectile impact of double-layered pyramidal lattice truss structures filled with ceramic insertions

Systematic three-dimensional finite element (FE) simulations are carried out to study the ballistic protection performance of double-layer sandwich plates having metallic pyramidal lattice truss cores filled with ceramic prism insertions and void-filling epoxy resin. Both normal and oblique projectile impacts are considered in the FE simulations that are validated against experimental measurements. The ballistic limit velocity, the energy absorbed by key constituting elements and the critical oblique angle corresponding to the transition from ballistic perforation to projectile embedment are calculated. As the oblique angle is increased, the evolution of deformation and failure in the double-layer plates as well as the underlying mechanisms are explored. It is demonstrated that the proposed double-layer sandwich plates outperform both the single-layer sandwich plates and the homogeneous (monolithic) metallic plates having equal total mass, and the top layer (the ceramic insertions in particular) of the double-layer configuration plays a more dominant role in energy absorption.

Comparison of Brazed Residual Stress and Thermal Deformation between X-Type and Pyramidal Lattice Truss Sandwich Structure: Neutron Diffraction Measurement and Simulation Study

Abstract This paper uses finite element method and neutron diffraction measurement to study the residual stress in lattice truss sandwich structure. A comparison of residual stress and thermal deformation between X-type and pyramidal lattice truss sandwich structure has been carried out. The residual stresses are concentrated in the middle joint and then decreases gradually to both the ends. The residual stresses in the X-type lattice truss sandwich structure are smaller than those in pyramidal structure. The maximum longitudinal and transverse stresses of pyramidal structure are 220 and 202 MPa, respectively, but they decrease to 190 and 145 MPa for X-type lattice truss sandwich structure, respectively. The thermal deformation for lattice truss sandwich panel structure is of wave shape. The X-type has a better resistance to thermal deformation than pyramidal lattice truss sandwich structure. The maximum wave deformation of pyramidal structure (0.02 mm) is about twice as that of X-type (0.01 mm) at the same brazing condition.