Multiple Load Paths Research Articles

INVESTIGATION OF OVER OBSTACLE PERFORMANCE ANALYSIS OF AUXETIC AIRLESS TYRES

Advancing technologies are leading to the development of airless tire designs that can perform well on challenging road conditions. These designs include lattice structures, mesh structures, and periodic structures, among others. In this study, three different tire designs were analyzed using finite element analysis (FEA) to evaluate their strength and dynamic behavior. Dynamic analyses were conducted on two commercial designs and one original design with re-entrant lattice structures. The study found that these structures are versatile as they provide multiple load paths to resist deformation and failure, and they can be modified to produce different properties like stiffness and strength. The original design with re-entrant structures demonstrated mechanical properties that were twice as good as other commercial tires. Moreover, a spline-lined structure was developed, and it was discovered that a two-stage tire design could enhance strength. The analyses were conducted at specific and controlled speeds with a designated bump size. The new design demonstrated at least 66% higher impact absorption energy performance than other car tyres examined. In total, nine analyses were performed, making a significant contribution to the development of airless tire design.

Measurements of elastic properties and their dependencies within a damage mechanics workflow

Experimental rock mechanics testing provides a controlled and effective method for measuring physical properties, their dependencies, and their evolution due to the addition of localized microcracks. To understand the contributions of microcracks to first order changes in compliance, the behavior of initial undamaged properties of a material should be comprehensively investigated as a function of stress, load path, and load history. We perform a comprehensive study of elastic properties and their dependence on a variety of materials exhibiting nonlinearity, and varying levels of anisotropy in elastic stiffnesses. We programmatically perturb the testing environment of the specimens under triaxial stresses. Elastic moduli are measured within each test, and along multiple discrete loading paths for multistage tests as a function of stress, focusing on a set launch point. Four single stage triaxial tests per rock type are performed to calculate Mohr-Coulomb failure criteria, and ultrasonic velocities are captured during compression for establishing the upper bound of elastic behavior. Shear wave velocity for granite experiences a maximum value at a lower differential stress than maximum volumetric strain. Sandstone displays a similar trend at the highest confining pressure, while these two maxima converge under the lowest confining pressure.

An empirical study on stress-based fail-safe topology optimization and multiple load path design

Explicitly considering fail-safety within design optimization is computationally very expensive, since every possible failure has to be considered. This requires solving one finite element model per failure and iteration. In topology optimization, one cannot identify potentially failing structural members at the beginning of the optimization. Hence, a generic failure shape is applied to every possible location inside the design domain. In the current paper, the maximum stress is considered as optimization objective to be minimized, since failure is typically driven by the occurring stresses and thus of more practical relevance than the compliance. Due to the local nature of stresses, it is presumed that the optimization is more sensitive to the choice of the failure shape than compliance-based optimization. Therefore, various failure shapes, sizes and different numbers of failure cases are investigated and compared on the basis of a general load-path-based evaluation scheme. Instead of explicitly considering fail-safety, redundant structures are obtained at much less computational cost by controlling the maximum length scale. A common and easy to implement maximum length scale approach is employed and fail-safe properties are determined and compared against the explicit fail-safe approach.

Multiple load path damage detection with optical fiber Bragg grating sensors

In this article, a new damage indicator is presented that can detect a (partial) load path failure for a multiple load path structure, based on variable amplitude strain response measurements by fiber optic Bragg grating sensors. Many (aircraft) structures have multiple load paths where after a (partial) failure of a load path the remaining structure can carry the limit load without catastrophic failure or too severe impact on the operational characteristics of the whole structure, until the structure is repaired, replaced, or modified. The damage indicator is defined as a ratio of the strain response summation of the current strain time variation measured at fiber Bragg grating (FBG) sensors and a reference strain time variation measured at the same FBGs. For application in real structures with varying loads and environmental conditions, it should be insensitive for the load time variation as well as temperature. The FBG strain response due to a load variation can be easily computed by means of a finite element analyses. In this way, an optimal number, location and orientation of strain sensors can be derived for complex structures. A test was performed on a box-shaped structure representative of a typical aircraft structure to validate the damage indicator, showing that the damage indicator is able to detect a damaged load path at an early stage of failure with few sensors per load path. From finite element analyses, the damage size can even be determined from the damage indicator value for a known damage scenario, making it a level 3 structure health monitoring system.

Maximum length scale requirement in a topology optimisation method based on NURBS hyper-surfaces

This paper deals with a new method for handling manufacturing and geometrical requirements in the framework of a general Topology Optimisation (TO) strategy. In particular, the maximum length scale constraint (MLSC) implementation is addressed in order to obtain multiple load paths or to locally limit the size of the component. The classic formulation of the MLSC is revisited in the framework of a density-based TO algorithm wherein the pseudo-density field is represented through a NURBS hyper-surface. The NURBS hyper-surface properties are exploited to effectively formulate the MLSC. The effectiveness of the proposed approach is proven on a meaningful 3D benchmark.

A New Triaxial Apparatus Imposing Nonuniform Shearing for Deep Learning of Soil Behavior

Abstract Soil behavior is commonly characterized based on laboratory tests with imposed or assumed uniform stress and strain distribution within a given soil specimen for convenient data reduction. This uniformity assumption limits the interpretation of each test to a single stress-strain path, and therefore, extensive laboratory testing is required to represent field soil behavior under a broad range of loading paths. This article presents the development of a modified, next-generation, triaxial device (NG-TX) to generate multiple loading paths in a single test that can be interpreted using an evolutionary deep-learning inverse analysis. This device inherits all features of a conventional triaxial test and adds lateral restraint clamps to increase nonuniformity in specimen deformation, combined with a digital photogrammetry system to measure the 3-D deformed shape of the specimen. The design of the restraint clamps was optimized using numerical simulations, which showed that the sheared specimen includes shear modes that cannot currently be mobilized with available testing devices. By coupling SelfSim, a deep-learning algorithm, with the modified triaxial device (NG-TX), the shear behavior of Ottawa sand was extracted. The SelfSim-extracted Neural Network material models were able to successfully capture the global behavior of each test and extract the nonuniform stress-strain behavior from within the specimens. The interpreted stress paths cover broad portions of stress space that current laboratory tests cannot cover. The stress-strain behavior is interpreted in terms of the mobilized secant friction angle using 2-D and 3-D failure criteria. The mobilized secant friction angle interpretation shows better agreement with empirically developed envelopes when computed along the octahedral plane accounting for the influence of intermediate principal stress.

Damage Tolerance Evaluation of Rotorcraft Horizontal Tail Under Variable Amplitude Service Loading Conditions

To ensure the safe operation of the helicopter throughout its lifetime, the primary structure has to be designed taking into account damage tolerance criteria. This has been considered in the design process, for example, by using multiple load paths as well as by taking into account the presence of certain structural defects like impacts or manufacturing defects in composite parts when performing the dimensioning and lifetime calculations. This paper describes and presents an effort performed for damage tolerance (DT) aspects of rotorcraft horizontal tail (HT) through multi-scale (MS) modeling computational approach to assess the growth rate of damages from fatigue under spectrum loading from rotorcraft mission profile and consideration of the effects of material variability to assess structural advantages. Main emphasis was laid on the design of the cyclic loaded components in order to achieve unlimited life with high flaw tolerance. A micromechanics-based multi-scale progressive failure analysis (MS-PFA) approach that detects damage and fracture evolution is carried out to assess the durability and damage tolerance (DD (2) fiber waviness exhibited in thick sections; and (3) void shape, size, distribution. Fatigue life is estimated under service spectrum block loading conditions in critical mission by determining the material stiffness and strength degradation, failure load and cycles.

Experimental study and numerical simulation on the structural and mechanical properties of Typha leaves through multimodal microscopy approaches

The Typha leaf, with special multi-level structure, low density and excellent mechanical properties, is an ideal bionic prototype utilized for lightweight design. In order to further study the relationship between the structure and mechanical properties, the three-dimensional macroscopic morphology of Typha leaves was characterized by micro computed tomography (Micro-CT) and its internal microstructure was observed by scanning electron microscopy (SEM). The combination of experimental and computational research was carried out in this paper, to reveal and verify the effect of multi-level structure on the mechanical properties. A universal testing machine and a self-developed mechanical testing apparatus with high precision and low load were used to measure the mechanical properties of the axial compression and lateral bending of the leaves, respectively. Three models with different internal structures were established based on the above-mentioned three-dimensional morphologies. The result demonstrated that the structure of partitions and diaphragms within the Typha leaf could form a reinforcement ribs structure which could provide multiple load paths and make the process of compression and bending difficult. The further nonlinear finite element analysis through LS-DYNA proved that internal structure could improve the ability of the models to resist compression and deformation. The investigation can be the reference for lightweight thin-walled structure design and inspire the application of the bionic structural materials.

Automated local line rolling forming and simplified deformation simulation method for complex curvature plate of ships

Abstract. Local line rolling forming is a common forming approach for the complex curvature plate of ships. However, the processing mode based on artificial experience is still applied at present, because it is difficult to integrally determine relational data for the forming shape, processing path, and process parameters used to drive automation equipment. Numerical simulation is currently the major approach for generating such complex relational data. Therefore, a highly precise and effective numerical computation method becomes crucial in the development of the automated local line rolling forming system for producing complex curvature plates used in ships. In this study, a three-dimensional elastoplastic finite element method was first employed to perform numerical computations for local line rolling forming, and the corresponding deformation and strain distribution features were acquired. In addition, according to the characteristics of strain distributions, a simplified deformation simulation method, based on the deformation obtained by applying strain was presented. Compared to the results of the three-dimensional elastoplastic finite element method, this simplified deformation simulation method was verified to provide high computational accuracy, and this could result in a substantial reduction in calculation time. Thus, the application of the simplified deformation simulation method was further explored in the case of multiple rolling loading paths. Moreover, it was also utilized to calculate the local line rolling forming for the typical complex curvature plate of ships. Research findings indicated that the simplified deformation simulation method was an effective tool for rapidly obtaining relationships between the forming shape, processing path, and process parameters.

Compressive ratcheting effect of expanded PTFE considering multiple load paths

Uniaxial stress-controlled ratcheting behaviors of expanded PTFE (ePTFE) under cyclic compressive loads were tested. The effects of temperature, stress rate and mean stress on the ratcheting behaviors of ePTFE considering multiple load paths were discussed in detail. Results present that the steady ratcheting strain is rate-independent when the stress rate is less than about 0.1 MPa/s, while it approximately linearly decreases with increasing the stress rate for greater stress rate. Additionally, the steady ratcheting is temperature-independent when the temperature is greater than about 150 °C, but it nearly linearly increases with enhancing the temperature for lower temperature. Especially, the stress rate almost has little effect on the ratcheting strain of ePTFE at 200 °C. Moreover, the accumulated ratcheting strain enhances rapidly in about the first 80 cycles, and subsequently tends to shakedown in the subsequent cycles for each load path. Furthermore, if a higher stress is used in the prior cycling, the greater ratcheting strain may be produced, and a negative ratcheting strain rate can be obtained in the subsequent cycling with lower mean stress due to the greater strain hardening and deformation resistance produced by the previous higher stress.

Damage tolerance in parallel systems

Damage tolerance is a fundamental prerequisite for the safety and robustness of large complex systems. Here we analyze the response of a system of parallel rods under a damage event. The approach is based on the presence of multiple load paths in a complex structure, that is, various ways to perform a task. We found that, as much as the complexity increases, the presence of effective ways of carrying the load becomes crucial for the robustness of the structural system under a damage process acting at random on the structure. In addition, the size of the system plays an important role: although tendentially more fragile, large systems are able to redistribute and absorb the effects of damage even with low complexity. The results, here discussed with reference to mechanical systems, can be exported to other disciplines.

Predictions on the Internal Loads and Structural Deflection in a Full-scale Experimental Bearingless Rotor

In this paper, the unsteady aerodynamics and blade structural dynamics of an experimental bearingless rotor were analyzed. Due to the multiple load path and nonlinear behavior of a bearingless rotor, sophisticated structural modeling and structural-aerodynamic coupled analysis is required. To predict the internal load and deformation of an experimental bearingless rotor, trim analysis was implemented. The results showed good agreement when compared with those predicted by CAMRAD II the rotorcraft comprehensive analysis. It is possible to extend the present structural-aerodynamic combined analysis to further advanced configurations of the bearingless rotor in the future.

Fibre cables in the lacunae of Typha leaves contribute to a tensegrity structure

Cables composed of long, non-lignified fibre cells enclosed in a cover of much shorter thin-walled, crystal-containing cells traverse the air chambers (lacunae) in leaves of the taller species of Typha. The non-lignified fibre cables are anchored in diaphragms composed of stellate cells of aerenchyma tissue that segment the long air chambers into smaller compartments. Although the fibre cables are easily observed and can be pulled free from the porous-to-air diaphragms, their structure and function have been ignored or misinterpreted. Leaves of various species of Typha were dissected and fibre cables were pulled free and observed with a microscope using bright-field and polarizing optics. Maximal tensile strength of freshly removed cables was measured by hanging weights from fibre cables, and Instron analysis was used to produce curves of load versus extension until cables broke. Polarized light microscopy revealed that the cellulose microfibrils that make up the walls of the cable fibres are oriented parallel to the long axis of the fibres. This orientation ensures that the fibre cables are mechanically stiff and strong under tension. Accordingly, the measured stiffness and tensile strength of the fibre cables were in the gigapascal range. In combination with the dorsal and ventral leaf surfaces and partitions that contain lignified fibre bundles and vascular strands that are strong in compression, the very fine fibre cables that are strong under tension form a tensegrity structure. The tensegrity structure creates multiple load paths through which stresses are redistributed throughout the 1-3 m tall upright leaves of Typha angustifolia, T. latifolia, T. × glauca, T. domingensis and T. shuttleworthii. The length of the fibre cables relative to the length of the leaf blades is reduced in the last-formed leaves of flowering individuals. Fibre cables are absent in the shorter leaves of Typha minima and, if present, only extend for a few centimetres from the sheath into the leaf blade of Typha laxmannii. The advantage of the structure of the Typha leaf blade, which enables stiffness to give way to flexibility under windy conditions, is discussed for both vegetative and flowering plants.

Development of sheet metal active-pressurized hydrodynamic deep drawing system and its applications

Abstract An active-pressurized hydrodynamic deep drawing (AHDD) system applying closed-loop control to regulate cavity pressure and blank holding force (BHF) independently in real time was developed to realize various loading paths for manufacturing complex parts. The conventional passive-pressurized hydrodynamic deep drawing (PHDD) method generates pressure by compressing liquid as the punch drawing into the die cavity, which is an open-loop controlling system and provides large control error. Proposed AHDD system consists of mainframe, hydraulic control system and real-time control system based on upper and lower computers. In order to obtain higher control precision, the PID controllers with error judgment were employed. Meanwhile, the punch speed was controlled according to real-time detection of errors between desired value and measured value to restrict control errors to a limited scope. Furthermore, the process experiments were carried out on the developed AHDD system, and the effects of control strategies on the formability of the parts were investigated. The qualified parts without tears and wrinkling were manufactured integrally on the AHDD system using PID controllers possessing error detection. The results indicated that the AHDD system offers multiple loading paths of BHF and cavity pressure, which is propitious to form complicated structural components and high-strength materials, and the proposed PID control strategy can improve the formability and uniformity of wall thickness distributions of the workpieces.

Structural Analysis of a Bearingless Rotor Using an Improved Flexible Multibody Model

This paper presents an improved structural analysis for a bearingless helicopter rotor. The bearingless rotor usually features a significantly large elastic twist in the flexbeam and additional unique structural characteristics. Thus, it will require sophisticated structural analysis and relevant numerical validation procedures due to its multiple load paths, as induced by the single or multiple flexbeams and the torque tube. In this paper, an extended finite element formulation was derived to consider the multiple components as individual beam elements. A geometrically exact beam formulation was adopted to describe the nonlinear behavior of these major components in the rotor precisely. To implement the interconnecting kinematic relationship with the major components, Lagrange multipliers were used. The present static analysis was validated through comparisons with the existing multi-body dynamics analysis DYMORE. Additional results were obtained for rotating conditions in both a vacuum and a set atmosphere in a wind tunnel. Finally, an experimental full-scale bearingless rotor system was coupled with finite-state dynamic inflow aerodynamics to simulate forward flight. The present predictions of the rotor responses and aerodynamics were well correlated with those by CAMRAD II.

Impact damage assessment by using peridynamic theory

Abstract This study presents an application of peridynamic theory for predicting residual strength of impact damaged building components by considering a reinforced panel subjected to multiple load paths. The validity of the approach is established first by simulating a controlled experiment resulting in mixed-mode fracture of concrete. The agreement between the PD prediction and the experimentally observed behavior is remarkable especially considering the simple material model used for the concrete. Subsequently, the PD simulation concerns damage assessment and residual strength of a reinforced panel under compression after impact due to a rigid penetrator.

Alternative Load Paths in Steel through-Truss Bridges: Case Study

Conventional design and evaluation procedures usually classify steel through-truss bridges as single-load-path structures; however, their historic performance has demonstrated considerable structural resiliency. This paper presents a study of the Grand River Bridge, a Pratt through-truss bridge in Cayuga, Ontario, Canada, that systematically investigates the load paths not conventionally assumed in design and evaluation. The bridge with individual truss members removed was analyzed using nonlinear finite-element analyses to investigate the alternative load paths and associated critical members and responses. A system reliability analysis was conducted to evaluate the failure probabilities of the bridge accounting for the member resistance uncertainties. The bridge was found to be sufficient to carry its nominal dead load, even for the worst case of removal of an end post. The end bottom chord and hanger vertical were found to be the critical tension chord and web member, respectively. If multiple alternative load paths exist, the variability of the system collapse load is much less than that of the critical member resistance.

Progressive Collapse and Structural Robustness of Bridges

Structural robustness has been recognized as a fundamental property of structural systems to prevent the occurrence of disproportionate failure events and progressive collapse. Bridges are primarily horizontally aligned structures with one main axis of extension. Only a few of many modern building codes provided methods can be applied to bridges. In this paper, associated strategies to enhance collapse resistance can be addressed by controlling abnormal events, individual local element behavior and global system behavior. Various design methods towards preventing progressive collapse such as non-structural protective measures, local resistance, multiple load paths or structural segmentation are applied to bridges. The suitability depends on the type of bridge structures.

Incremental Method for Structural Analysis of Joined-Wing Aircraft

Joined-wing aircraft are characterized by statically indeterminate structures, i.e., structures with multiple load paths. A newway of analyzing these configurations is introduced. This new formulation is based on the fully intrinsic equations, which introduce neither singularities nor infinite-degree nonlinearities caused by finite rotation. The formulation makes use of an incremental form of the kinematical equations, which allows preservation of the main advantageous features of the fully intrinsic equations. Themethod is applied and verified for a joined-wing structure.

Inelastic constitutive relations for foamed materials: A statistical approach and its application to open-cell melamine

The aim of this study is to characterize the viscoelastic behavior at finite strain of a melamine foam submitted to multiple loading paths of uniaxial compression. The constitutive law is obtained by specializing a previously proposed model arising from an irreversible thermodynamic approach for several types of material (e.g. polymer, metal alloys) to include the essential microscopic features of this open-cell foam. The model is based on the central concept of relaxed state, which is defined as a thermodynamic state of metastable equilibrium including the strain history effect. In the case of the present material, it is shown that the corresponding relaxed stress may thus be formulated using the tools of statistical mechanics: namely, the Shannon entropy 〈 S〉 is extremized under adequate geometric constraints. Thus, the Lagrange multipliers associated with these requirements are defined as forces conjugated to the degrees of freedom of the geometrical transformation. By comparing the predictions from the proposed inelastic constitutive model with experimental data for uniaxial compression interrupted by loading–unloading sequences, we conclude that the constitutive relations predict the mechanical behavior of the melamine foam.