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The present study investigates the global buckling behavior of sandwich beams with graded lattice cores. The continuous equivalent theory is utilized to construct a discrete graded lattice core sandwich beam for a continuously varying gradient beam, whose material properties vary with position. A theoretical model of sandwich beams with graded lattice cores is established using the energy method. Finite element models are developed in ABAQUS to validate the theoretical results. Furthermore, four sets of specimens were manufactured and tested to validate the theoretical analysis methods used. The effects of the graded parameters and geometric parameters on the critical buckling load of sandwich beams with graded lattice cores are discussed. The graded lattice sandwich beams exhibit global buckling when the graded parameter is small, with the influence on buckling performance being minor. However, as the graded parameter increases, the graded lattice sandwich beams experience local buckling, and their buckling resistance weakens. Therefore, graded parameters that are too large and cause local buckling should be avoided in gradient design. [ABSTRACT FROM AUTHOR]

• Knee implants with different anterior lip heights have a similar wear rate during different daily activities. • The location of maximum wear depth was similar among the three tibial inserts tested with different lip heights. • The tibial insert with the highest lip showed slight anterior wear scaring due to anterior contact during swing phase. A high anterior lip on a total knee prosthesis is an effective way of reducing anterior translation, but the effect on joint wear is unclear. Using finite element analysis (FEA), this study quantitatively compared wear rates and anterior contact stresses in three posterior stabilized knee prostheses with different heights for the anterior lip during six daily activities (walking, stair ascent, stair descent, sit-to-stand, pivot turn and crossover turn). The wear rate and location of maximum wear depth were similar for the three lip heights tested, but the knee with the highest anterior lip also showed slight anterior wear scaring due to articular contact stress during swing phase, which was highly dependent on the shape of the contact interface. This study illustrates that tibial inserts with a high anterior lip maintain a wear rate similar to moderate and low lip posterior stabilized designs. [ABSTRACT FROM AUTHOR]

Abstract Background The wear properties of knee implants need to be thoroughly evaluated prior to clinical use to ensure implant longevity. ISO 14243-1:2009 and ASTM F3141-17 are the two standards typically used for evaluating wear, with the ISO standard being more common; ASTM F3141-17 was first released in 2015. The aim of this study is to compare differences between these two standards in terms of wearing on a knee prosthesis. Methods Using finite element analysis based on Archard's law, this study evaluated anterior-posterior and internal-external motion, contact area, contact force, contact stress, volumetric wear rate, wear depth, and wear distribution on the knee prosthesis. Findings The results show that simulations performed according to ASTM F3141 produced knee kinematics that were more similar to human gait. The maximum wear depth occurred on the medial side of the tibia. However, the region of peak contact stress did not always correspond with the region of the maximum wear depth, indicating that considering the contact stress alone is not sufficient for evaluating wear as the sliding distance also plays an important role. The resulting wear region from the ASTM F3141 simulation was smaller but deeper than the wear region from the simulation per ISO 14243-1. However, the volumetric wear rates were very similar, with 13.48–55.26 mm3/million for ASTM F3141 and 13.64–54.9 mm3/million for ISO 14243-1. Interpretation The resulting rate of wear is almost identical between ISO 14243-1 and ASTM F3141. However, there are differences in wear contours and wear depth. Highlights • This study compared differences between ASTM F3141 and ISO 14243-1. • ASTM F3141 produced knee kinematics that were more similar to human gait. • Simulations according to ASTM F3141 and ISO 14243-1 produce similar volumetric wear rates. • The wear region from the ASTM F3141 was smaller but deeper than ISO 14243-1. [ABSTRACT FROM AUTHOR]

It is difficult to simulate the explosive detonation of multi-lighter points and describe the assembling energy of detonation waves with the existent finite element methods. Particularly, computational efficiency and precision of the finite element methods are limited due to mesh distortion. Therefore, the explosive detonation of 2 lighters and even more lighters was numerically simulated with the material point method based on the explicit integration algorithm, to give results fitting the theoretical solution well. The proposed method not only avoids the remeshing procedure for distorted elements, but also makes an effective way to the numerical simulation of the explosive detonation. [ABSTRACT FROM AUTHOR]

A typical power series analytic solution of quasi-Laplace equation in the infinitesimal angle domain around the singular point of the square cells is provided in this article. Toward the singular point, the gradient of the potential variable will tend to infinity, which is described by the first term of the power series solution. Based on this analytic solution, three finite analytic numerical methods are proposed. These methods are analogous and are constructed, respectively, when considering different numbers of the terms or using different schemes to determine the relevant parameters in the power series. Numerical examples show that all of the three finite analytic numerical methods proposed can provide rather accurate solutions than the traditional numerical methods. In contrast, when using the traditional numerical schemes to solve the quasi-Laplace equation in a strong heterogeneous medium, the refinement ratio for the grid cell needs to increase dramatically to get an accurate result. In practical applications, subdividing each origin cell into 2 × 2 or 3 × 3 subcells is enough for the finite analytical numerical methods to get relatively accurate results. The finite analytical numerical methods are also convenient to construct the flux field with high accuracy.© 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 1755-1769, 2014 [ABSTRACT FROM AUTHOR]

Understanding fluid flows in heterogeneous porous media is fundamental to applied geosciences. The wide connectivity variations in the natural aquifer or oil reservoirs make the equivalent permeability have strong spatial variations. When performing the simulations for subsurface flows, the permeabilities may have strong discontinuities across the interfaces between different grid cells. Utilizing the traditional numerical schemes to simulate flows in strong heterogeneous media, the refinement ratio for the grid cell needs to increase dramatically to get an accurate result. Recently, we proposed a finite analytic numerical scheme to solve the two-dimensional fluid flows in heterogeneous porous media. With only 2 × 2 or 3 × 3 subdivisions, this scheme can provide rather accurate solutions. In this paper, we develop the finite analytic numerical method for solving the three-dimensional fluid flows in heterogeneous porous media. For the rectangular grid system, it is generally proposed that the pressure gradient in a plane normal to the edge joining different permeability regions will tend to infinite as approaching the edge according to a typical power-law solution and the tangential derivate of the pressure along the edge must be of limited value due to the pressure continuity. Consequently, the three-dimensional flow will reduce to the two-dimensional one in the neighborhood around each edge. Such quasi-two-dimensional behavior is then applied to construct a finite analytic numerical scheme. Numerical examples show that the proposed scheme can provide rather accurate solutions with only 2 × 2 × 2 or 3 × 3 × 3 subdivisions and the convergent speed is independent of the permeability heterogeneity. Due to its high calculation efficiency, the proposed scheme is utilized to test the well known LLM (Landau, Lifshitz and Matheron) conjecture, which provides k eq / k G = exp ⁡ ( 1 6 σ ln ⁡ k 2 ) for the isotropic log-normal porous medium. The numerical results do not support this conjecture for large σ ln ⁡ k , but strongly suggest the linear relation k eq / k G = 1 + 1 6 σ ln ⁡ k 2 . [ABSTRACT FROM AUTHOR]