Static Load Cases Research Articles

Unique Approach of Modern Automotive Exhaust System Mountings Design for NVH Improvement

<div>Minimizing vibration transmitted from the exhaust system to the vehicle’s passenger compartment is the primary goal of this article. With the introduction of regulatory norms on NVH behavior and emissions targets, it has become necessary to address these issues scientifically. Stringent emissions regulations increased the complexity of the exhaust system resulting in increased size and weight. Exhaust system vibration attenuation is essential not only from the vehicle NVH aspects but also for the optimized functionality of the subsystems installed on it. Based on earlier studies, this work adopts a more thorough strategy to reduce vehicle vibration caused by the exhaust system by adjusting it to actual operating conditions.</div> <div>To achieve this, a complete vehicle model of 22 DOF is considered, which consists of a powertrain, exhaust system, chassis frame, and suspension system. A method for evaluating static and dynamic vibration response is proposed. Through the use of the vehicle’s rigid body modes and actual field events, design indicators are carefully analyzed and validated. Based on actual operating conditions, the two main load cases that are taken into consideration are idling and the sweet spot operating zone. To define the sweet spot zone of the dominant vehicle/engine-operating scenario, the vehicle duty cycle is monitored experimentally.</div> <div>The baseline 22 DOF model results show a degradation in exhaust vibration performance in both load cases as its yaw and bounce modes are falling into the resonance region of the idle and sweet spot operating zone load cases, respectively. The acceleration reduction of nearly 10–20 dB in static events, and nearly 10 dB in dynamic events can be evident in the proposed model. The proposed system’s outcomes demonstrate an improvement in the eigenvalues of the yaw and bounce modes, which in turn enhances the vehicle’s overall NVH performance in both static and dynamic load cases. Thus, the study suggests that designers should consider the real field events’ load cases for modern exhaust system-mounting optimization to achieve improvement in NVH behavior, fuel efficiency, emissions performance, and durability aspects of the vehicle.</div>

Evaluation of the Modal Parameters of a Unidirectional Carbon-Based Composite Structure Using the Influential Factor of Static Loading.

Static loading can significantly alter the dynamics of unidirectional carbon-based composites (UCBCs), with modal parameters varying depending on the orientation of the carbon fibers. In this study, the sensitivity of modal parameters of UCBC structures under uniaxial static loading was investigated. The theoretical static load influential factor was derived from a linearized UCBC model and corresponded to the transformed decoupled response over the mass-normalized static load. Three rectangular UCBC specimens (carbon fiber orientation of 0°, 45°, and 90°) were prepared under fixed-fixed boundary conditions using a jig fixture. Uniaxial static loads between 0 N and 1000 N were applied, and the first three modes of the UCBC specimens were analyzed. An isotropic SUS304 specimen was used as a reference. The linearization assumption about the UCBC structure was preliminarily validated with the Modal Assurance Criterion (MAC). A high influential factor was found for the UCBC specimen when carbon fibers were aligned with the static load direction at the first two resonance frequencies. Therefore, the proposed influential factor is an efficient indicator for determining the sensitivity of the dynamic response of a UCBC structure over a static load case. The variations in the influential factors for the UCBC specimens were more pronounced than for the isotropic specimens.

Investigation of additively manufactured lattice structures for refractive optical systems based on auxetic properties

This paper reports on a novel concept of thermally stable lattice structures for next-generation refractive optical systems. The aim is to develop a metallic mount for optical lenses based on auxetic structures fabricated by additive manufacturing. Auxetic structures exhibit an effective negative Poisson ratio at the macroscopic level. This property is used to develop a mounting structure that compensates for thermal defocus between refractive optical elements. Numerical and experimental studies of the mechanical behavior of additively manufactured body-centered cubic cells provide the basis for the development of this application-specific mounting structure. Several static load cases are analyzed and deviations between numerical and experimental data are examined to quantify differences in dependence of element type, element size, and manufacturing-related geometrical inaccuracies. These results are used to compare the numerical analysis of the Poisson ratio of an auxetic unit cell with the analytical descriptions. This comparison is then applied to two-dimensional auxetic unit cell compounds. These studies provide the basis for the further development process of an auxetic mounting structure.

Static and dynamic analysis of a new offshore wind turbine system supported with outriggers

This article presents an innovative structural system for offshore wind turbines supported on monopiles. The novelty of this system lies in its enhancement of the lateral stiffness of the tubular tower through the incorporation of an outrigger system, widely employed in high-rise buildings. This novel system is modeled as a Timoshenko beam-column element under both static and dynamic loading scenarios, incorporating geometric nonlinearity and accounting for the effect of soil-structure interaction. A comprehensive numerical analysis was conducted to evaluate the system’s behavior under various static and dynamic load cases, utilizing soil data from the Red Sea region of Egypt. A modal analysis is also incorporated to investigate the eigenmodes of the proposed system. This study offers valuable insights for designers and researchers, providing guidelines and diagrams for the implementation of the proposed system.

A Method for Determination of Moment Contribution Ratio under Foundation Rotation in Shear Wall-Frame Systems

In shear wall-frame systems, the foundation rotation that may occur under the shear walls changes the displacements and interstory drift ratios and changes the internal force distribution. This study investigates the effect of foundation rotations under shear walls on internal force distribution in shear-frame systems. The originality of the study lies in considering parabolic loads and dynamic analysis (first mode), in addition to static uniform or triangular distributed loads, when determining the shear wall moment contribution ratio under the influence of foundation rotation. The shear wall contribution ratio, a key parameter in many earthquake codes, is defined as the ratio of the sum of bending moments taken by the shear walls at the base to the overturning moment. It plays a crucial role in determining the building’s behavior. Depending on this ratio, the load-reduction coefficient is changed. This study investigates the effect of foundation rotation on the moment distribution at the base for three different static load cases and the first mode in the dynamic analysis. The multi-story building is modeled as an equivalent sandwich beam. The moment contribution ratio (MCR) was calculated with the help of analytical solutions of the differential equations written for three different load cases in static conditions, and graphs were created for practical use directly calculating the MCR. In the methodology of the study, the initial step involves the calculation of the equivalent sandwich beam stiffness parameters and the foundational rotational spring. Subsequent to these calculations, the MCR values can be directly obtained with the help of graphs. This approach facilitates the rapid and practical determination of the MCR and can be used in the preliminary sizing phase to eliminate possible errors in the data entry of software that performs detailed analysis. In addition, in the presented study, it has been shown that taking a single mode into account is sufficient when calculating MCR values in dynamic analysis.

A form-finding method for adaptive truss structures subject to multiple static load cases

Form-finding is an essential task in the design of efficient lightweight structures. It is based on the crucial assumption of one single shape-determining load case, usually represented by self-weight. Adaptive components integrated into the structure open a way to even more efficient lightweight designs, as such structures can adapt their shapes to varying external loads and redistribute internal forces. This article presents a method for form-finding of adaptive truss structures subject to multiple, independently acting load cases, also incorporating possible design constraints. To ensure the consistency of the manufacturing lengths of passive elements in all load cases, special constraints are considered. The method enables to reduce sensitivity of the structural shape with respect to various different loads by means of actuation to meet design and serviceability requirements with a lower structural mass compared to conventional design strategies. This is demonstrated within a replaced real-world-like setting of an adaptive suspension truss bridge.

Numerical Simulation of Crack Propagation and Branching Behaviors in Heterogeneous Rock-like Materials

The characterization and understanding of crack evolution in non-uniform geological structures are crucial for predicting the mechanical response of rock-like materials or structures under varying loading conditions. In this study, an improved Peridynamic model with a degree of heterogeneity characterized by random pre-breaking “bonds” coefficients is introduced to capture the intricacies of crack initiation, propagation, and branching behaviors in heterogeneous rock-like materials. MATLAB discrete programs for heterogeneous material models and PD simulation programs based on the FORTRAN language were developed. The effectiveness of the heterogeneous PD model in simulating crack propagation and branching patterns in heterogeneous materials has been verified through dynamic and static (quasi-static) loading cases with pre-notch. The different levels of heterogeneity not only affect the direction of crack propagation but also determine the crack deflection direction and branching patterns. The crack propagation path appears to possess obvious asymmetry in the crack propagation direction. As the load applied continues to increase, the asymmetric multi-crack branching phenomenon will occur. The higher the level of heterogeneity, the more complex the behaviors of crack propagation and branching become. This research provides valuable insights into the interplay of material heterogeneity and crack evolution, offering a foundation for improved numerical simulations and contributing to the broader field of geomechanics.

Optimisation of bonded and hybrid step lap joints of thick carbon fibre/epoxy panels used in aircraft structures

The use of composite materials is widely spread across the Aerospace sector. Scarf and step lap joints are amongst the most commonly used methods for flush joint repairs; they restore original stiffness and nearly original strength. Prior investigations conducted by the authors have shown that bonded and hybrid step lap joints have superior static strength capabilities than bolted joints. Hybrid step lap joints have shown the highest fatigue resistance than its bolted and bonded counterparts. This investigation aims at optimising the previous step lap joint design containing five steps with a 90 mm long overlap length in order to improve joint efficiency. Four new step lap joint configurations are considered based on a parametric study conducted using Abaqus; two of which contain seven steps and a 130 mm long overlap (bonded and hybrid) whilst the other two contain six steps and a 105 mm long overlap (bonded and hybrid) with a tapered outer step region. Experimental tests right through to numerical modelling using three-dimensional (3D) finite element (FE) models have been investigated. Adhesive non-linear material properties, fastener contacts and friction forces were all included in the 3D FE models. The Multicontinuum Theory (MCT) is used to simulate the progressive failure process and determine the stress states in the four configurations. Overall the FE models are able to accurately predict the bonded and hybrid joint strengths and highlights the importance of not only optimising the number of steps and their lengths but also the individual step heights. This is a parameter which has often been overlooked by fellow researchers. Experimental results showed that all four step lap joint configurations have significant improvement under static and fatigue load cases; the greatest improvement is seen in the two bonded step lap joint configurations. Overall the hybrid joint configuration consistently outperformed the bonded joint configurations. The presence of fasteners supress crack propagation, minimise peak peeling stresses at the ends of the overlap and increase the durability of the joint. This enables early crack detection which can assist composite joint repair certification.

Topology optimization of periodic structures for crash and static load cases using the evolutionary level set method

Assembly complexity and manufacturing costs of engineering structures can be significantly reduced by using periodic mechanical components, which are defined by combining multiple identical unit cells into a global topology. Additionally, the superior energy-absorbing properties of lattice-based periodic structures can potentially enhance the overall performance in crash-related applications. Recent research developments in periodic topology optimization (PTO) have shown its efficacy for tackling new design problems and finding advanced novel structures. However, most of these methods rely on gradient information in the optimization process, which poses difficulties for crash problems where analytical sensitivities are usually not directly applicable. In this paper, we present an effective periodic evolutionary level set method (P-EA-LSM) for the optimization of periodic structures. P-EA-LSM uses a low-dimensional level-set representation based on moving morphable components to parametrize a single unit cell, which is replicated in the design domain according to a predefined pattern. The unit cell is optimized using an evolutionary algorithm and the structural responses are calculated for the entire system. We initially assess the performance of P-EA-LSM using three 2D minimum compliance test cases with varying periodicities. Our results demonstrate that our approach produces solutions comparable to other state-of-the-art methods for PTO while keeping a low dimensionality of the optimization problem. Subsequently, we effectively evaluate the capabilities of P-EA-LSM in a crashworthiness scenario. This particular application highlights the significant potential of the method, which does not rely on analytical sensitivities.

Experimental study of twisted thin-walled box components in single-layer domes

In recent years, the demand for thin-walled structures has dramatically increased in civil, mechanical, and aerospace engineering fields. Numerous new structural components were introduced due to the upsurge trend. Thus a deep understanding of their performance is necessary. One of these components is a twisted thin-walled box component, a concept that derives from the members of a single-layer dome. Hence, static experiments on twisted thin-walled box components under four load cases were carried out to test their mechanical behavior in this study. The stress and deformation were obtained at several essential measuring points of the structure. Then, finite element analysis was conducted, and the correctness of the finite element model was verified by comparing it with the experimental results. The results demonstrate that all measuring points remain elastic under the considered static load cases. For the overload case, the structure would be destroyed at 4.4 times the load case magnitude, from which the twisting and denting were identified as the main failure mode. Therefore, the structure displays high safety reserves and good potential in high-load-resisting systems.

Integrated hydrostatic and hydrodynamic analysis of flexible floating structures

This study presents an effective numerical solution procedure to integrate hydrostatic and hydrodynamic analyses for flexible floating structures. Unlike conventional analyses, a single integrated mesh model is adopted to seamlessly perform both analyses. A complete integrated formulation is derived. A floating structure is modeled using the finite element method and the external fluid is modeled using the boundary element method. An integrated mesh model is used for both hydrostatic and hydrodynamic analyses, in which a waterline matching mesh is unnecessary. After hydrostatic analysis, hydroelastic analysis including rigid body hydrodynamic analysis can be performed without remeshing, even when various static loading cases are considered. The effectiveness of the proposed method is demonstrated through several numerical examples.

Similarity-Driven Topology Optimization for Statics and Crash via Energy Scaling Method

Abstract Topology optimization (TO) is used in the initial design phase to optimize certain objective functions under given boundary conditions by finding suitable material distributions in a specified design domain. Currently available methods in the industry work very efficiently to get topologically optimized design concepts under static and dynamic load cases. However, conventional methods do not address the designer’s preferences about the final material layout in the optimized design. In practice, the final design might be required to have a certain degree of local or global structural similarity with an already present good reference design because of economic, manufacturing, and assembly limitations or the desire to re-use parts in different systems. In this article, a heuristic energy scaling method (ESM) for similarity-driven TO under static as well as dynamic loading conditions is presented and thoroughly evaluated. A 2D cantilever beam under static point load is used to show that the proposed method can be coupled with gradient-based and also heuristic, nongradient methods to get designs of varying similarity with respect to a reference design. Further testing of the proposed method for similarity-driven TO on a 2D crash test case and a large-scale 3D hood model of a car body indicates the effectiveness of the method for a wide range of problems in the industry. Finally, the application of similarity-driven TO is further extended to show that ESM also has the potential for sensitivity analysis of performance with respect to the extension of design domain.

Optimization of Curvilinear Stiffener Beam Structures Simulated by Beam Finite Elements with Coupled Bending-Torsion Formulation.

This research presents the application of a beam finite element, specifically derived for simulating bending-torsion coupling in equivalent box-beam structures with curvilinear stiffeners. The stiffener path was simulated and optimized to obtain an expected coupling effect with respect to four typical static load cases, including geometric constraints related to the additive manufacturing production method. The selected load condition was applied to the centroid of the beam section, and the structure performance was consequently determined. A variation in load position up to one-fourth of the beam width was considered for investigating the stiffener path variation corresponding to a minimum bending-torsion coupling effect. The results demonstrated the capability of such a beam finite element to correctly represent the static behavior of beam structures with curvilinear stiffeners and show the possibility to uncouple its bending-torsion behavior using a specific stiffener orientation. The simulation of a laser powder bed fusion process showed new opportunities for the application of this technology to stiffened panel manufacturing.

Final-State Structural Behavior of the Long-Span Kömürhan Cable-Stayed Bridge under Torsional and Bending Loadings

Final-state field load testing is an effective method for understanding the real behavior of a bridge before it opens to traffic. The paper presents the procedure and the results of final-state static field tests on the new long span Kömürhan cable-stayed bridge with a single pylon and back span anchorage block under torsional and bending loadings. A total of six static loading cases were conducted to investigate real structural behavior of the bridge having a back span anchorage block and main span deck connected to the pylon with 42 tensioned cables in the deck center. Measured results have been obtained from the surveys and sensors while theoretical results have been calculated from the three-dimensional finite element model of the bridge final-state geometry. The results of final-state static load tests include the main span deck deflections, pylon horizontal displacements, the strains of the main span deck and the pylon, and the cable forces. A good agreement has been achieved between the experimental and theoretical results. Both experimental and theoretical results have shown that the real bridge behavior is in the elastic state under the planned test loads and supplies the design requirements. It is also observed that the results from the torsional and bending load cases positioned in the same sections are close to each other.

A composite resin core with a new zirconia tube reduces the surface strain at the cervical area of a mandibular molar: A model tooth study.

This study aimed to evaluate the surface strain at the cervical area of endodontically treated molars with a large pulp chamber restored using a composite resin core with three different types of core build-up systems. Reproduction models of human mandibular molars with prepared post spaces were used in this study. Roots duplicated with a composite resin were used as the experimental teeth. Three types of core build-up systems were used: composite resin core(RC), composite resin core with fiber posts (FC), and composite resin core with a prefabricated zirconia tube (ZC). Each group comprised eight specimens. Crowns made of yttria partially stabilized zirconia were cemented with dual-cure resin cement. Four strain gauges were attached to the surfaces of each specimen: the cervical area of the root and crown, on the buccal and lingual sides. The surface strain at each cervical area was measured using a static loading test and statistically analyzed. In the case of static loading to the buccal cusp inner slope, ZC showed a significantly lower strain than RC in the crown on the buccal side and in the root and FC in the root. In the central fossa, ZC showed a significantly lower strain than FC in the root on the lingual side. The prefabricated zirconia tube reduced the surface strain at the cervical area of the buccal/lingual root in molars; however, the effect was small in the cervical area of the crown.

Mode II- delamination modeling in multi-directional laminates using cohesive zone methodology under static and dynamic loading

Most of the ply-by-ply laminated composite structures are constrained by delamination type of failure under different loadings. There were attempts to develop modeling methods for delamination under static and dynamic loads in the past. Most of the earlier attempts are focused on the unidirectional laminates because of complexity involved in the multi-directional laminates. However, in the real life, many time multi-directional laminates are used. This paper is an effort to create such modeling methodology for multi-directional carbon composite laminates (with 0–0, 45–45 and 90–90 interfaces) under static and dynamic loads. For modeling the static load case, Ansys software is used with the in-built contact based cohesive zone material model. The mode II experiments were conducted on multi-directional carbon composite coupons as per ASTM standards and the load displacement behavior is verified using the finite element analysis (FEA) cohesive zone models (CZM). Mode II test coupons are modeled in 3D, and the delamination is captured in the analysis simulation. For dynamic loading, LS-Dyna is used with the in-built tiebreak contact-Dycoss-Option 9 capabilities which are almost similar to the cohesive zone elements. The results indicate that cohesive zone models can predict the delamination in the kind of materials under static and dynamic loading conditions. The modeling methods will be further improvised for both situations to make it more robust and ready for applications to aircraft engine components in consideration of delamination.

Optimization of the Polarization Profile of Conical-Shaped Shells Piezoelectric Sensors.

Conical shell structures are frequently submitted to severe static and dynamic mechanical loads that can result in situations that affect the service of the systems that are part of, or even cause catastrophic failures. For this reason, a common solution is to design an active deformation control system, usually using piezoelectric patches strategically distributed along the surface of the shell structure. Moreover, these elements may be part of an energy recovery system. This paper details the methodology to topologically optimize the placement of piezoelectric elements through a characteristic function, analysing static and free vibration loading cases by means of the finite element method. Then, the optimal arrangement of the electrode with different polarization profiles is distributed throughout the entire structure. The nature of the loading cases studied corresponds to a general situation where static loads and dynamics vibration are considered. The objective function of the problem only depends linearly on the displacement fields, and therefore, the optimal electrode profile can be obtained for any combination of loads. As a consequence, this technique allows for maximising the electric charge obtained, which results in a greater capacity for monitoring, actuation and/or energy harvesting.

Study on Composite Column Under Monotonic and Cyclic Loading

Nowadays, composite beams and columns were used as structural members for their higher strength and rigidity for load-carrying structures. Generally, the concrete-encased composite column has a compound section formed by the steel section and the surrounding concrete will be made by a composite. Based on the studies of steel encased concrete sections based on experimental and computational analysis over static and dynamic load cases shows advantages over the conventionally use structural steel or reinforced concrete in terms of ductility and shear resistance. The structure can experience static loads as well as fatigue loads in some situations. So the behavior of structural elements under differential loading should be obtained to design them effectively. A similar shape of the column section plays a key role in resisting lateral buckling under axial compression. This paper compares the behaviour of steel concrete composite sections by varying the shape and size for both concrete infilled and encased conditions based on the earlier research works.

First Carpometacarpal Joint Motion and Proximal Migration of the First Metacarpal After Tensioning of a Suture Device Suspensionplasty Compared With Trapeziectomy: A Biomechanical Cadaver Study

The purpose of this cadaveric biomechanical experiment was to evaluate the effects of suture button suspensionplasty of the first carpometacarpal joint on thumb biomechanics and thumb position compared with an intact, arthritic specimen. Six tendons in 8 cadaver hands were loaded to simulate 6 activities of daily living and passively moved through a circumduction motion. Proximal migration of the base of the first metacarpal was measured using optical motion sensors in the intact hand, after trapeziectomy, and following insertion of a suture button suspensionplasty with nominal tightening (approximately 4.5 N) and with firm tightening (approximately 44.5 N). Removal of the trapezium caused a significant increase in the proximal migration of the first metacarpal during a simulated jar grasp, opposition, flexion, extension, and abduction (average, 9.5 mm) compared with its location with the thumb in the intact, neutral position (average, 3.8 mm). Firm tightening of the tightrope caused a near elimination of the proximal migration of the first metacarpal (average, 0.7 mm). In all 6 static loading cases with the trapezium removed, firm tightening caused a significantly smaller migration than in the absence of tightening. This biomechanical cadaver study supports the hypothesis that trapeziectomy results in proximal migration of the first metacarpal. Suture suspensionplasty mitigates against this migration while maintaining normal motion of the first metacarpal compared with the intact state. Firm tightening of the suture does not adversely affect the first metacarpal's mobility and further decreases proximal migration. However, firm tightening may cause impingement between the first and second metacarpals. Suture button suspensionplasty can be used in addition to trapeziectomy in the treatment of basal joint arthritis, and may diminish the need for ligament reconstruction or temporary K-wire insertion.

Lightweight design approach of an LFT-metal multi-material vehicle door concept

This work presents a new approach to design and validate an economical lightweight multi-material roof-integrated vehicle door concept made of long-fiber thermoplastics (LFT) and metals with the consideration of package constrain, critical static and crash loading cases. A novel “two-ring” door structure is introduced, which consists of a major load-bearing region and a minor load-bearing but highly function-integrated region. This concept design concentrates on using cost-efficient lightweight materials, such as aluminum, LFTs and uni-directional tapes (UD-Tapes), as well as corresponding mass-production methods. Using the topology and parameter optimization along with the load anisotropy analysis, the rib structure on the door concept is optimized and the effective usage of UD-Tapes is guaranteed. In comparison to the steel reference, the final LFT-metal multi-material door concept achieves 20% weight reduction with a comparable or improved mechanical performance.