Extending lagrange interpolation to develop a 4-node quadrilateral element

Today finite element method is a well established tool in engineering analysis and design. Though there axe many two and three dimensional finite elements available, it is rare that a single element performs satisfactorily in majority of practical problems. The present work deals with the development of 4-node quadrilateral element using extended Lagrange interpolation functions. The classical univariate Lagrange interpolation is well developed for 1-D and is used for obtaining shape functions. We propose a new approach to extend the Lagrange interpolation to several variables. When variables axe more than one the method also gives the set of feasible bubble functions. We use the two to generate shape function for the 4-node arbitrary quadrilateral. It will require the incorporation of the condition of rigid body motion, constant strain and Navier equation by imposing necessary constraints. The procedure obviates the need for isoparametric transformation since interpolation functions are generated for arbitrary quadrilateral shapes. While generating the element stiffness matrix, integration can be carried out to the accuracy desired by dividing the quadrilateral into triangles. To validate the performance of the element which we call EXLQUAD4, we conduct several pathological tests available in the literature. EXLQUAD4 predicts both stresses and displacements accurately at every point in the element in all the constant stress fields. In tests involving higher order stress fields the element is assured to converge in the limit of discretisation. A method thus becomes available to generate shape functions directly for arbitrary quadrilateral. The method is applicable also for hexahedra. The approach should find use for development of finite elements for use with other field equations also.

Virgin wasps develop ovaries on par with mated females, but lay fewer eggs

In the primitively eusocial wasp Ropalidia marginata, mating is not necessary for a female wasp to develop her ovaries, lay eggs, and even to become the sole egg layer of her colony despite the presence of other mated nestmates. Here, we show that virgin wasps do not differ from their mated counterparts in the extent and rapidity of their ovarian development, in the proportion of individuals that build a nest and laid eggs, and in the time taken to do so. However, a significantly larger proportion of virgin females showed resorbing oocytes, and laid fewer eggs as compared to mated individuals. Thus, virgin females have the ability to develop ovaries and lay eggs but also to refrain from necessarily laying all mature eggs produced, before mating opportunities arise. This dual ability would be adaptive in haplodiploid, tropical species with perennial nesting cycles and frequent opportunities for workers to become replacement queens or solitary nest foundresses throughout the year.

Combinatorial Approach to Develop Tailored Biodegradable Poly(xylitol dicarboxylate) Polyesters

The objective of this work was to develop a versatile strategy for preparing biodegradable polymers with tunable properties for biomedical applications. A family of xylitol-based cross-linked polyesters was synthesized by melt condensation. The effect of systematic variation of chain length of the diacid, stoichiometric ratio, and postpolymerization curing time on the physicochemical properties was characterized. The degradation rate decreased as the chain length of the diacid increased. The polyesters synthesized by this approach possess a diverse spectrum of degradation (ranging from similar to 4 to 100% degradation in 7 days), mechanical strength (from 0.5 to similar to 15 MPa) and controlled release properties. The degradation was a first-order process and the rate constant of degradation decreased linearly as the hydrophobicity of the polyester increased. In controlled release studies, the order of diffusion increased with chain length and curing time. The polymers were found to be cytocompatible and are thus suitable for possible use as biodegradable polymers. This work demonstrates that this particular combinatorial approach to polymer synthesis can be used to prepare biomaterials with independently tunable properties.

An efficient strategy to develop microwave shielding materials with enhanced attenuation constant

A mutually miscible homopolymer (here polymethyl methacrylate; PMMA) was employed to tailor the interfacial properties of immiscible polycarbonate/styrene acrylonitrile (PC/SAN) blends. In order to design materials that can shield microwave radiation, one of the key properties i.e. electrical conductivity was targeted here using a conducting inclusion; multiwall carbon nanotubes (MWNTs). Owing to higher polarity, MWNTs prefer PC over SAN which though enhance the electrical conductivity of the blends, they don't improve the interfacial properties and results in poor mechanical properties. Hence, an efficient strategy has been adopted here to simultaneously enhance the mechanical, electrical and microwave attenuation properties. Herein, the MWNTs were wrapped by PMMA via in situ polymerization of MMA (methyl methacrylate). This strategy resulted in the migration of PMMA modified MWNTs towards the blend's interface and resulted in an effective stress transfer across the interface leading to improved mechanical and dynamic mechanical properties. Interestingly, the bulk electrical conductivity of the blends was also enhanced, manifesting the improved dispersion of the MWNTs. The state of dispersion of the MWNTs and the phase morphology were assessed using scanning electron microscopy. The microwave attenuation properties were evaluated using a vector network analyzer (VNA) in the X and K-u-band frequencies. The blends with PMMA wrapped MWNTs manifested a -21 dB of shielding effectiveness which suggests attenuation of more than 99% of the incoming microwave radiation. More interestingly, the attenuation constant could be tuned here employing this unique strategy. This study clearly opens a new tool box in designing materials that show improved mechanical, dynamic mechanical, electrical conductivity and microwave shielding properties.