The unsymmetric finite element method employs compatible test functions but incompatible trial functions. The pertinent 8-node quadrilateral and 20-node hexahedron unsymmetric elements possess exceptional immunity to mesh distortion. It was noted later that they are not invariant and the proposed remedy is to formulate the element stiffness matrix in a local frame and then transform the matrix back to the global frame. In this paper, a more efficient approach will be proposed to secure the invariance. To our best knowledge, unsymmetric 4node quadrilateral and 8-node hexahedron do not exist. They will be devised by using the Trefftz functions as the trial function. Numerical examples show that the two elements also possess exceptional immunity to mesh distortion with respect to other advanced elements of the same nodal configurations.
PrefaceLaminated composites made of continuous fibers and metal, ceramic, or polymer matrices have been used for structural applications for more than half a century. Many modern industries such as aerospace engineering or wind power energy engineering would not have advanced to their current levels if composites had not been used. Among all of the superior characteristics of composites in comparison with other more traditional, isotropic structural materials, three are the most well known. They are high-specific stiffness (stiffness to mass ratio), high-specific strength and the ability to tailor desired properties by choosing suitable fiber and matrix materials as well as the fiber architecture geometry.Determination of the composite mechanical properties has attracted the attention of scientists, researchers and engineers. From an application point of view, it would be best if all of the mechanical properties of the composites can be estimated by using their constituent fiber and matrix properties and the fiber architecture parameters, i.e., by using a micromechanical approach. For the composite stiffness, this is feasible. There are many micromechanical models for efficiently estimating the effective elastic properties of laminated composites, which have been the focus of most of the available mechanics of composite materials textbooks and monographs. A very challenging problem, however, is to estimate the composite strength as well as other inelastic behaviors micromechanically. In the current literature, there is a lack of a book systematically addressing this problem. Almost all of the monographs dealing with laminate strength follow a phenomenological philosophy. Namely, the laminate strength is estimated based on the information of lamina strengths, which must be measured on composites themselves. However, predicting laminate strength micromechanically is very important, as one of the most critical issues in designing a composite structure is to know its load carrying capacity in priori. Only when this capacity has been explicitly related to the constituent properties and geometric parameters, can an optimal design choosing proper constituent materials, fiber content and architecture, and laminate layups for the structure before fabrication, be achieved.Would it be possible to dream that any mechanical property, including the ultimate load carrying capacity of a composite made using any continuous fiber architecture subjected to arbitrary loads, would be simply available without any experiment on it but be based only on an established database containing the required constituent properties? Will this become a reality? More than a decade Preface vi ago, the first author of this book established a unified micromechanical theory, the bridging model, to describe the constitutive relationship of a composite up to the point of failure. The unique feature of this theory is that the internal stresses in the constituent fiber and matrix materials of the composite under any arbitrary load conditions, including a t...
The tuning of vertical morphology is critical and challenging for organic solar cells (OSCs). In this work, a high open-circuit voltage (V OC ) binary D18-Cl/L8-BO system is attained while maintaining the high short-circuit current (J SC ) and fill factor (FF) by employing 1,4-diiodobenzene (DIB), a volatile solid additive. It is suggested that DIB can act as a linker between donor or/and acceptor molecules, which significantly modifies the active layer morphology. The overall crystalline packing of the donor and acceptor is enhanced, and the vertical domain sizes of phase separation are significantly decreased. All these morphological changes contribute to exciton dissociation, charge transport, and collection. Therefore, the best-performing device exhibits an efficiency of 18.7% with a V OC of 0.922 V, a J SC of 26.6 mA cm −2 , and an FF of 75.6%. As far as it is known, the V OC achieved here is by far the highest among the reported OSCs with efficiencies over 17%. This work demonstrates the high competence of solid additives with two iodine atoms to tune the morphology, particularly in the vertical direction, which can become a promising direction for future optimization of OSCs.
SUMMARYIn this paper, a rotation-free triangle is formulated. Unlike the thin and degenerated shell finite element models, rotation-free triangles employ translational displacements as the only nodal DOFs. Compared with the existing rotation-free triangles, the present triangle is simple and physical yet its accuracy remains competitive. Using a corotational approach and the small strain assumption, the tangential bending stiffness matrix of the present triangle can be approximated by a constant matrix that does not have to be updated regardless of the displacement magnitude. This unique feature suggests that the triangle is a good candidate for fabric drape simulation in which fabric sheets are often flat initially and the displacement is much larger than those in conventional shell problems. Nonlinear shell and fabric drape examples are examined to demonstrate the efficacy of the formulation.
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