Appl. Mech., Volume 4, Issue 4 (December 2023) – 13 articles

The attractiveness of the boundary element method—the reduction in the problem dimension by one—is lost when solving nonlinear solid mechanics problems. The point collocation method applied to strong-form differential equations is appealing because it is easy to implement. The method becomes inaccurate in the presence of traction boundary conditions, which are inevitable in solid mechanics. A judicious combination of the point collocation and the boundary integral formulation of Navier’s equation allows a pure boundary element method to be obtained for the solution of nonlinear elasticity problems. The potential of the approach is investigated in some simple examples considering isotropic and anisotropic material models in the total Lagrangian framework. Full article

This study aims to develop an integrated approach for 3D lumbar vertebral biomodel design and analysis, specifically targeting unilevel disc degeneration and the replacement of lumbar artificial discs. Key objectives include improving existing design methods through 3D techniques, inverse modeling, and an engineering biomodel preparation protocol. Additionally, the study evaluates mechanical properties in the implantation area and between disc components to gauge the effectiveness of artificial discs in restoring functional movement within the studied biological model. The construction of a biological model representing the L3–L4 functional spinal unit was based on measurements from radiographic images and computed tomography data obtained from the study sample. The 3D finite element method in Ansys software (v. 19.2, ANSYS, Inc., Canonsburg, PA, USA) was used to monitor the distribution of equivalent stress values within the core of the two artificial discs and the behavior of vertebral bone components in the model. This approach enabled the creation of personalized digital models tailored to the specific implantation requirements of each patient. Stress analysis identified critical areas within the disc cores, suggesting potential design modifications to optimize artificial disc performance, such as selectively increasing core thickness in specific regions and considering adjustments during implantation. For example, preserving part of the lateral annulus fibrosus from the degenerative disc and maintaining the anterior and posterior longitudinal ligaments may play a crucial role in balancing the forces and moments experienced by the lumbar section. This study provides valuable insights into the development of patient-specific solutions for lumbar disc degeneration cases, with the potential for enhancing artificial disc design and implantation techniques for improved functional outcomes. Full article

De-coring is an essential process in the casting process chain, determining the quality and cost of production. In this study, a coupled multibody system (MBS) and finite element modeling (FEM) technique is presented to study the mechanical loads during the de-coring process. The removal of cast-in sand cores from the inner regions of the cast part by de-coring or knocking out is a complex process with dynamic loads. Currently, the process relies upon empirical knowledge and tests. Inorganic sand cores pose additional challenges in the success of the de-coring process. Increasing complexity in geometry and stringent environmental regulations compel a predictive process in the earlier stages of design. Predicting the process’ success is challenged by the dynamic non-linearities of the system. The dynamic characteristics and the interaction between hammer and casting were studied here for the first time using an industrial-based test rig, and a novel modeling approach was formulated. The results of the developed model are in good compliance with the experiments. The methodology presented in this study can be used to include a varying number of hammers and loads. The proposed approach presents the possibility to discretize the process and qualitatively assess the process parameters for optimization. Full article

Service loads repeatedly stress components on a regular basis and lead to fatigue damage in the material. In the case of components made of short fibre-reinforced thermoplastics, which are also crash-relevant in addition to only bearing service loads, however, a significant deterioration in mechanical properties can be observed after fatigue damage has been introduced. This is where the approach presented in this paper comes in: in order to enable a realistic simulation of such components in their used conditions, the material data are assigned depending on previously determined damage. The approach, which combines the domains of highly dynamic and cyclic experiments as well as different types of numerical simulations, is tested for its performance in the present paper. For this purpose, component tests are carried out on cross-rib beams, which serve to validate the method. The novelty and uniqueness of this paper lies in the linking of fatigue life and crashworthiness considerations for short fibre-reinforced thermoplastics, which, in this case, is raised to a new level by considering the component level for the first time. Full article

Influence lines are indispensable tools for visualizing and analyzing the dynamic variations in force factors induced by external loads within structural systems. Among these methods, the energetic approach stands as a widely employed technique, rooted in the fundamental principle of work done by changing forces. It enables engineers to transform intricate structural analysis problems into manageable ones by exploring the first derivatives of the radius vector, which represent infinitesimal velocity or displacement. This methodology seamlessly interweaves concepts such as carrier motion, relative motion, and the construction of mechanisms, bringing fresh perspectives to the analysis of influence lines. In this article, we explore the nuances of these novel methods within the domain of mechanism theory. Through comprehensive elaboration and analysis, we elucidate the underlying principles and practical applications of Jacobian contours. Crucially, we introduce a straightforward, rapid, and programmable approach, promising to revolutionize influence line determination in structural engineering. This method bridges the gap between theory and practice, offering the potential to elevate the accuracy, efficiency, and adaptability of influence line analysis. As such, it represents a significant advancement in the field of structural and applied mechanics, with broad-reaching implications for engineering practice. Full article

The augmented finite element method (AFEM) embeds cracks within solid elements. These cracks are modelled without additional degrees of freedom thanks to a dedicated static condensation process. However, static condensation can induce a lack of constraint problem, resulting in singular stiffness matrices. To address this issue, we propose a new method called the stabilised augmented finite element method (SAFEM), which produces non-singular stiffness matrices. We conducted 2D experiments involving stationary traction-free cracks and propagating cohesive discontinuities to compare the performance of the SAFEM with the AFEM. The SAFEM outperforms the AFEM in modelling traction-free cracks. Full article

When a vehicle leaves the road, crash barriers stop it and prevent significant damage to the vehicle, its environment, and the occupants. Typically, such protection systems are made of simple steel, but fiber-reinforced composites can efficiently absorb and dissipate the impact energy at high-risk locations. In order to design such protective systems, material parameters under dynamic loading are necessary. Here, split Hopkinson pressure bar tests with unidirectional glass-fiber-reinforced epoxy of 58% glass fiber content are performed. The elastic response at strain rates between 300/s and 700/s in the loading direction parallel and perpendicular to the fiber is determined. From the measured data, a model of the time dependence of the elastic modulus is derived to enable the design engineer to lay out protective systems made of such GFRPs. Full article

A new method to evaluate the maximum seismic story velocities for steel buildings is examined here. It is well known that story velocities are vital parameters for the design of steel structures with supplementary dampers. It has been recognized that nonlinear time history analysis is required to achieve an accurate evaluation of actual velocities, but this approach seems to be complicated and time-consuming for practical engineers. For this reason, this paper investigates the inelastic velocity ratio, which can be defined as the ratio of the maximum inelastic velocity to the maximum elastic one for steel buildings. The knowledge of this ratio, a unique factor for the whole structure, can be used to evaluate the maximum inelastic story velocities directly from the elastic counterparts. The proposed study is general and can be used in both ordinary steel structures as well as steel structures with supplemental damping devices. Widespread parametric studies are executed to achieve simple yet effective expressions for inelastic velocity ratios. Full article

The main objective of this paper is to study the free vibration of a Timoshenko–Ehrenfest single-walled carbon nanotube based on the nonlocal theory and taking surface effects into account. To model these effects on frequency response of nanotubes, we use Eringen’s nonlocal elastic theory and surface elastic theory proposed by Gurtin and Murdoch to modify the governing equation. A modified version of Timoshenko nonlocal elasticity theory—known as the nonlocal truncated Timoshenko beam theory—is put forth to investigate the free vibration behavior of single-walled carbon nanotubes (SWCNTs). Using Hamilton’s principle, the governing equations and the corresponding boundary conditions are derived. Finally, to check the accuracy and validity of the proposed method, some numerical examples are carried out. The impacts of the nonlocal coefficient, surface effects, and nanotube length on the free vibration of single-walled carbon nanotubes (SWCNTs) are evaluated, and the results are compared with those found in the literature. The findings indicate that the length of the nanotube, the nonlocal parameter, and the surface effect all play important roles and should not be disregarded in the vibrational analysis of nanotubes. Finally, the results show how effective and successful the current formulation is at explaining the behavior of nanobeams. Full article

Steel–concrete–steel (SCS) sandwich structures have gained increasing interest in new constructions. The external steel plates increase the stiffness, the sustainability, and the strength of the structures under some extreme solicitations. Moreover, the use of these plates as lost prefabricated formwork makes SCS structures modular, enabling higher construction rates. However, for a better understanding of the complex behavior of these structures up to failure, refined numerical simulations are needed to consider various local phenomena, such as concrete crushing in compression and interface interactions. Indeed, the highly non-linear steel–concrete interaction around the dowels is the key point of the composite action. In this contribution, a refined methodology is first proposed and applied on a push-out test. It is especially demonstrated that a regularization technique in compression is needed for the concrete model. Interface elements are also developed and associated with a nonlinear constitutive law between steel connectors and external plates. From this refined methodology, simplified numerical modeling is then deduced and validated. Directly applied to an SCS wall-to-wall junction, this simplified strategy enables the reproduction of the overall behavior, including the elastic phase, the degradation of the system, and the failure mode. The response of each component is particularly analyzed, and the key points of the behavior are highlighted. Full article

Advanced Driver Assistance Systems (ADASs) attract constantly growing attention from academics and industry as more and more vehicles are equipped with such technology. Level-3 ADASs, like the DRIVE PILOT from Mercedes-Benz AG, are expected to appear more and more on the market in the next few years. However, automated driving raises new challenges for the system validation required for series approval. The replacement of a human driver as control instance expands the range of variants to be validated and verified. The scenario-based validation approach meets these challenges by simulating only specific safety-critical driving scenarios using software-in-the-loop simulation. According to the current state of the art, various safety-relevant driving scenarios are parameterized as idealized maneuvers which, however, requires a great modeling effort, and at the same time, such simplifications may bias the safety assessment. Therefore, a novel approach using artificial intelligence methods is taken here to generate more realistic driving scenarios. Namely, a generative model based on a variational autoencoder is trained with real-world data and then used to generate trajectories for a specific driving maneuver. Through a comprehensive analysis of the synthetic trajectories, it becomes clear that the generative model can learn and replicate relevant properties of real driving data as well as their probabilistics much better than the mathematical models used so far. Furthermore, it is proven that both the statistical properties and the time characteristics are almost equal to those of the input data. Full article

Mechanical structural systems are subject to multiple dynamic disturbances during service. While several possible scenarios can be examined to determine their design loading conditions, only a relatively small set of such scenarios is considered critical. Therefore, only such particular deterministic set of critical load cases is commonly employed for the structural design and optimization. Nevertheless, during the design and optimization stages, the mass and stiffness distributions of such assemblies vary, and, in consequence, their dynamic response also varies. Thus, it is important to consider the variations in the dynamic loading conditions during the design-and-optimization cycles. This paper studies the modal participation factors at length and proposes an alternative to the current point-wise treatment of the dynamic equations of motion of flexible bodies during design optimization. First, the most relevant-to-structural-dynamics definitions available in the literature are reviewed in depth. Second, the analysis of those definitions that have the potential to be adopted as point-wise constraint equations during structural optimization is extended. Finally, a proof of concept is presented to demonstrate the usability of each definition, followed by a case study in which the potential advantages of the proposed extended analysis are shown. Full article

Based on elasticity theory, this paper discusses the static analysis of a cracked double-beam system in the presence of a Winkler-type medium. It is further assumed that the double-beam system is constrained at both ends by elastically flexible springs with transverse and rotational stiffness. Using a variational formulation, the governing static equations are derived and solved using analytical and numerical approaches. In the first approach, closed-form solutions for the displacement functions are obtained based on the Euler–Bernoulli beam theory. In the second approach, the Cell Discretisation Method (CDM) is performed, whereby the two beams are reduced to a set of rigid bars connected by elastic constraints, in which the flexural stiffness of the bars is concentrated. The resulting stiffness matrix is easily deduced, and the governing equations of the static problem can be immediately solved. A comparative analysis is performed to verify the accuracy and validity of the proposed method. The study focuses on the effect of various parameters, including crack depth and position, boundary conditions, elastic medium and slenderness. The validity of the proposed analysis is confirmed by comparing the current results with those obtained from other approaches. In particular, the results obtained by closed-form solution and CDM are compared with the Finite Element Method (FEM). The accuracy of the results was assessed by making comparisons with results found in the literature and reported in the bibliography. It was shown that the proposed algorithm provides a simple and powerful tool for dealing with the static analysis of a double-beam system. Finally, some concluding remarks are made. Full article