Summary Among numerous finite element techniques, few models can perfectly (without any numerical problems) break through MacNeal's theorem: any 4‐node, 8‐DOF membrane element will either lock in in‐plane bending or fail to pass a C0 patch test when the element's shape is an isosceles trapezoid. In this paper, a 4‐node plane quadrilateral membrane element is developed following the unsymmetric formulation concept, which means two different sets of interpolation functions for displacement fields are simultaneously used. The first set employs the shape functions of the traditional 4‐node bilinear isoparametric element, while the second set adopts a novel composite coordinate interpolation scheme with analytical trail function method, in which the Cartesian coordinates (x,y) and the second form of quadrilateral area coordinates (QACM‐II) (S,T) are applied together. The resulting element US‐ATFQ4 exhibits amazing performance in rigorous numerical tests. It is insensitive to various serious mesh distortions, free of trapezoidal locking, and can satisfy both the classical first‐order patch test and the second‐order patch test for pure bending. Furthermore, because of usage of the second form of quadrilateral area coordinates (QACM‐II), the new element provides the invariance for the coordinate rotation. It seems that the behaviors of the present model are beyond the well‐known contradiction defined by MacNeal's theorem. Copyright © 2015 John Wiley & Sons, Ltd.

SUMMARYAmong all 3D 8-node hexahedral solid elements in current finite element library, the 'best' one can produce good results for bending problems using coarse regular meshes. However, once the mesh is distorted, the accuracy will drop dramatically. And how to solve this problem is still a challenge that remains outstanding. This paper develops an 8-node, 24-DOF (three conventional DOFs per node) hexahedral element based on the virtual work principle, in which two different sets of displacement fields are employed simultaneously to formulate an unsymmetric element stiffness matrix. The first set simply utilizes the formulations of the traditional 8-node tri-linear isoparametric element, while the second set mainly employs the analytical trial functions in terms of 3D oblique coordinates (R, S, T). The resulting element, denoted by US-ATFH8, contains no adjustable factor, and can be used for both isotropic and anisotropic cases. Numerical examples show it can strictly pass both the first-order (constant stress/strain) patch test and the second-order patch test for pure bending, remove the volume locking, and provide the

Superpave gyratory compaction (SGC) and Marshall compaction methods are essentially designed according to volumetric properties. In spite of the similarity, the optimum asphalt contents (OAC) of the two methods are greatly affected by the laboratory compaction process, which would further influence their performance. This study aims to evaluate the performance of styrene-butadiene-styrene (SBS)-modified stone mastic asphalt (SMA) with basalt fiber by using SGC and Marshall compaction methods. Basalt fiber was proved to improve and strength the basic properties of SBS-asphalt according to test results of asphalt binder. The effects of SGC and Marshall compaction methods on OAC and volumetric properties, i.e., density, air voids (VA), voids in mineral aggregates (VMA), and voids filled with asphalt (VFA), were evaluated in detail. Finally, the pavement performance of asphalt mixture prepared by SGC and Marshall compaction methods were compared in order to analyze the high-temperature creep, low-temperature splitting, and moisture stability performance. Results showed that the OAC of SGC (~5.70%) was slightly lower than that of Marshall method (5.80%). Furthermore, the pavement performance of SGC specimens were improved to a certain extent compared with Marshall specimens, indicating that SGC has a better compaction effect and mechanical performance.

This study focuses on improving the performance of asphalt mixture at low- and high- temperature and analyzing the effect of diatomite and basalt fiber on the performance of the asphalt mixture. Based on the L16(45) orthogonal experimental design (OED), the content of diatomite (D) and basalt fiber (B) and the asphalt-aggregate (A) ratio were selected as contributing factors, and each contributing factor corresponded to four levels. Bulk volume density (γf), volume of air voids (VV), voids filled with asphalt (VFA), Marshall stability (MS) and splitting strength at −10 °C (Sb) were taken as the evaluation indexes. According to the results of the orthogonal experiment, the range analysis and variance analysis were used to study the effect of the diatomite content, basalt fiber content and asphalt-aggregate ratio on the performance of the asphalt mixture, and the grey correlation grade analysis (GCGA) was used to obtain the optimal mixing scheme. Furthermore, the performance tests were conducted to evaluate the performance improvement of asphalt mixtures with diatomite and basalt fibers, and the scanning electron microscopy (SEM) tests were carried out to analyze the mechanism of diatomite and basalt fibers in asphalt mixtures. The results revealed that the addition of diatomite and basalt fiber can significantly increase the VV of asphalt mixture, and reduce γf and VFA; the optimal performance of the asphalt mixture at high- and low-temperature are achieved with 14% diatomite, 0.32% basalt fibers and 5.45% asphalt-aggregate ratio. Moreover, the porous structure of diatomite and the overlapping network of basalt fibers are the main reasons for improving the performance of asphalt mixture.

A novel plane quadratic shape-free hybrid stress-function (HS-F) polygonal element is developed by employing the principle of minimum complementary energy and the fundamental analytical solutions of the Airy stress function. Without construction of displacement interpolation function, the formulations of the new model are much simpler than those of the displacement-based polygonal elements and can be degenerated into triangular or quadrilateral elements directly. In particular, it is quite insensitive to various mesh distortions and even can keep precision when element shape is concave. Furthermore, the element does not show any spurious zero energy modes. Numerical examples show the excellent performance of the new element, denoted by HSF-AP-19β, in both displacement and stress solutions.

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That airborne particulate matter (PM) in the air has received increasing attention due to its serious environmental pollution and huge health risk for humans. Here we demonstrate the synthesis of...