Ultra-Wide Bandgap in Two-Dimensional Metamaterial Embedded with Acoustic Black Hole Structures

This paper reports a type of metamaterial plate enabling in-plane ultra-wide vibration isolation in engineering equipment development. It is composed of periodic hexagonal lattice structures. The acoustic black hole (ABH) structures are embedded in each cell wall of the conventional hexagonal lattice, which results in the reduction of local stiffness in the cell wall and the local mass in the hexagonal corner. The lattice can be simplified as the form of lumped masses vibrating on springs, and two types of eigenstates can be obtained: the rotational eigenstates and the transverse eigenstates. The geometric nonlinearity of the ABH structure leads to unevenly distributed vibration modes, resulting in the ultra-wide bandgap. Experimental results prove the effective attenuation capacity. Compared with the traditional hexagonal lattice, the proposed design provides greater advantages in practical application.

A Data-driven Minimum Stiffness Prediction Method for Machining Regions of Aircraft Structural Parts

Large thin-walled structural parts have been widely used in aircrafts for the purpose of weight reduction. These parts usually contain various thin-walled complex structures with weak local stiffness, which are easy to deform during machining if improper cutting parameters are selected. Thus, local stiffness has to be seriously considered during the machining parameter planning. Existing stiffness calculation methods mainly include mechanics calculation methods, empirical formula methods, finite element methods, and surrogate-based methods. However, due to the structural complexity, these methods are either inaccurate or time consuming. To address this issue, this paper proposes a data-driven method for stiffness prediction of aircraft structural parts. First, machining regions of aircraft structural part finishing are classified into bottom, sidewall, rib and corner to further define the minimum stiffness of machining regions. Then, by representing the part geometry with attribute graph as the input feature, while computing the minimum stiffness using FEM as the output label, stiffness prediction is turned to a graph learning task. Thus, a graph neural network (GNN) is designed and trained to map the attribute graph of a machining region to its minimum stiffness. In the case study, a dataset of aircraft structural parts is used to train four GNN models to predict the minimum stiffness of the defined four types of machining regions. Compared with FEM results, the average percentage errors on the test set are 6.717%, 7.367%, 7.432% and 5.962% respectively. In addition, the data driven model once trained, can greatly reduce the time in predicting the stiffness of a new part compared with FEM, which indicates that the proposed method can meet the engineering requirements in both accuracy and computational efficiency.

Stress calculation on bevel gears with FEM influence vectors

In order to be able to carry out an optimal gear design with the aim of cost reduction and the careful handling of resources, load capacity is an important criterion for the evaluation of a gear. For the calculation of the flank and root load capacity, a precise loaded tooth contact analysis (LTCA) is necessary. With LTCA software like BECAL, influence numbers are used to calculate the deformation of the gear. These influence numbers are calculated with a BEM-module and considered for calculating the local root stress. This method simplifies the coupling stiffness in tooth width direction with a decay function and neglects the influence of local differences in tooth stiffness. In this publication, this simplification shall be questioned and evaluated.Therefore, a new method for calculating stress with FEM influence vectors is presented. This method enables the calculation of full stress tensors at any desired location in the gear with the efficiency of the influence number method. Additionally, the influence of local stiffness variations in the gear is taken into account. Various gear examples show the influence of material connections at the pinion root and the influence of the rim thickness of a wheel on the root stress. To validate the accuracy and the time efficiency of the new calculation method and to compare the results to current state-of-the-art simulations, a well-documented series of tests from the literature is recalculated and evaluated.

The effect of substrate stiffness on tensile force transduction in the epithelial monolayers

In recent years, the importance of mechanical signaling and the cellular mechanical microenvironment in affecting cellular behavior has been widely accepted. Cells in epithelial monolayers are mechanically connected to each other and the underlying extracellular matrix (ECM), forming a highly connected mechanical system subjected to various mechanical cues from their environment, such as the ECM stiffness. Changes in the ECM stiffness have been linked to many pathologies, including tumor formation. However, our understanding of how ECM stiffness and its heterogeneities affect the transduction of mechanical forces in epithelial monolayers is lacking. To investigate this, we used a combination of experimental and computational methods. The experiments were conducted using epithelial cells cultured on an elastic substrate and applying a mechanical stimulus by moving a single cell by micromanipulation. To replicate our experiments computationally and quantify the forces transduced in the epithelium, we developed a new model that described the mechanics of both the cells and the substrate. Our model further enabled the simulations with local stiffness heterogeneities. We found the substrate stiffness to distinctly affect the force transduction as well as the cellular movement and deformation following an external force. Also, we found that local changes in the stiffness can alter the cells’ response to external forces over long distances. Our results suggest that this long-range signaling of the substrate stiffness depends on the cells’ ability to resist deformation. Furthermore, we found that the cell’s elasticity in the apico-basal direction provides a level of detachment between the apical cell-cell junctions and the basal focal adhesions. Our simulation results show potential for increased ECM stiffness, e.g. due to a tumor, to modulate mechanical signaling between cells also outside the stiff region. Furthermore, the developed model provides a good platform for future studies on the interactions between epithelial monolayers and elastic substrates.Author summaryCells can communicate using mechanical forces, which is especially important in epithelial tissues where the cells are highly connected. Also, the stiffness of the material under the cells, called the extracellular matrix, is known to affect cell behavior, and an increase in this stiffness is related to many diseases, including cancers. However, it remains unclear how the stiffness affects intercellular mechanical signaling. We studied this effect using epithelial cells cultured on synthetic deformable substrates and developed a computational model to quantify the results better. In our experiments and simulations, we moved one cell to observe how the substrate stiffness impacts the deformation of the neighboring cells and thus the force transduction between the cells. Our model also enabled us to study the effect of local stiffness changes on the force transduction. Our results showed that substrate stiffness has an apparent impact on the force transduction within the epithelial tissues. Furthermore, we found that the cells can communicate information on the local stiffness changes over long distances. Therefore, our results indicate that the cellular mechanical signaling could be affected by changes in the substrate stiffness which may have a role in the progression of diseases such as cancer.

Constructing Steklov-type cubature formulas for a finite element in the shape of a bipyramid

This paper reports the construction of cubature formulas for a finite element in the form of a bipyramid, which have a second algebraic order of accuracy. The proposed formulas explicitly take into consideration the parameter of bipyramid deformation, which is important when using irregular grids. The cubature formulas were constructed by applying two schemes for the location of interpolation nodes along the polyhedron axes: symmetrical and asymmetrical. The intervals of change in the elongation (compression) parameter of a bipyramid semi-axis have been determined, within which interpolation nodes of the constructed formulas belong to the integration region, while the weight coefficients are positive, which warrants the stability of calculations based on these cubature formulas. If the deformation parameter of the bipyramid is equal to unity, then both cubature formulas hold for the octahedron and have a third algebraic order of accuracy. The resulting formulas make it possible to find elements of the local stiffness matrix on a finite element in the form of a bipyramid. When calculating with a finite number of digits, a rounding error occurs, which has the same order for each of the two cubature formulas. The intervals of change in the elongation (compression) parameter of the bipyramid semi-axis have been determined, which meet the requirements, which are employed in the ANSYS software package, for deviations in the volume of the bipyramid from the volume of the octahedron. Among the constructed cubature formulas for a bipyramid, the optimal formula in terms of the accuracy of calculations has been chosen, derived from applying a symmetrical scheme of the arrangement of nodes relative to the center of the bipyramid. This formula is invariant in relation to any affinity transformations of the local bipyramid coordinate system. The constructed cubature formulas could be included in libraries of methods for approximate integration used by those software suites that implement the finite element method.

Evaluation of Geosynthetics Use in Pavement Foundation Layers and Their Effects on Design Methods

This report presents findings of a research effort aimed at reviewing and updating existing Illinois Department of Transportation (IDOT) specifications and manuals regarding the use of geosynthetic materials in pavements. The project consisted of three tasks: evaluate current IDOT practice related to the use of geosynthetics; review research and state of the practice on geosynthetics applications, available products, design methods, and specifications; and propose recommendations for geosynthetic solutions in pavements to modernize IDOT’s practices and manuals. The review of IDOT specifications revealed that geotextiles are the most used geosynthetic product in Illinois, followed by geogrids. Several of IDOT’s manuals have comprehensive guidelines to properly design and construct pavements with geosynthetics, but several knowledge gaps and potential areas for modernization and adoption of new specifications still exist. Based on the review of the available design methods and the most relevant geosynthetic properties and characterization methods linked to field performance, several updates to IDOT’s practice were proposed. Areas of improvement are listed as follows. First, establish proper mechanisms for using geogrids, geocells, and geotextiles in subgrade restraint and base stabilization applications. This includes using shear wave transducers, i.e., bender elements, to quantify local stiffness enhancements and adopting the Giroud and Han design method for subgrade restraint applications. Second, update IDOT’s Subgrade Stability Manual to include property requirements for geogrids, geotextiles, and geocells suitable for subgrade restraint applications. Third, establish proper standards on stabilization, separation, and pumping resistance for geotextiles by incorporating recent research findings on geotextile clogging and permeability criteria. Fourth, promote the use of modern geosynthetic products, such as geotextiles with enhanced lateral drainage, and fifth, elaborate on proper methods for construction/quality control measures for pavements with geosynthetics.