Fully Comprehensive Geometrically Non-Linear Dynamic Analysis of Multi-Body Beam Systems with Elastic Couplings

This paper is concerned with the dynamic analysis of flexible,non-linear multi-body beam systems. The focus is on problems where the strains within each elastic body (beam) remain small. Based on geometrically non-linear elasticity theory, the non-linear 3-D beam problem splits into either a linear or non-linear 2-D analysis of the beam cross-section and a non-linear 1-D analysis along the beam reference line. The splitting of the three-dimensional beam problem into two- and one-dimensional parts, called dimensional reduction,results in a tremendous savings of computational effort relative to the cost of three-dimensional finite element analysis,the only alternative for realistic beams. The analysis of beam-like structures made of laminated composite materials requires a much more complicated methodology. Hence, the analysis procedure based on Variational Asymptotic Method (VAM), a tool to carry out the dimensional reduction, is used here.The analysis methodology can be viewed as a 3-step procedure. First, the sectional properties of beams made of composite materials are determined either based on an asymptotic procedure that involves a 2-D finite element nonlinear analysis of the beam cross-section to capture trapeze effect or using strip-like beam analysis, starting from Classical Laminated Shell Theory (CLST). Second, the dynamic response of non-linear, flexible multi-body beam systems is simulated within the framework of energy-preserving and energy-decaying time integration schemes that provide unconditional stability for non-linear beam systems. Finally,local 3-D responses in the beams are recovered, based on the 1-D responses predicted in the second step. Numerical examples are presented and results from this analysis are compared with those available in the literature.

Synthesis, Structure, Negative Thermal Expansion, and Photocatalytic Property of Mo Doped ZrV(2)O(7)

A new series of compounds identified in the phase diagram of ZrO(2)-V(2)O(8)-MoO(3) have been synthesized via the solution combustion method. Single crystals of one of the compounds in the series, ZrV(1.50)Mo(0.50)O(7.25), were grown by the melt-cool technique from the starting materials with double the MoO(3) quantity. The room temperature average crystal structure of the grown crystals was solved using the single crystal X-ray diffraction technique. The crystals belong to the cubic crystal system, space group Pa (3) over bar (No. 205) with a = 8.8969 (4) angstrom, V = 704.24 (6) angstrom(3), and Z = 4. The final R(1) value of 0.0213 was achieved for 288 independent reflections during the structure refinement. The Zr(4+) occupies the special position (4a) whereas V(5+) and Mo(6+) occupy two unique (8c) Wyckoff positions. Two fully occupied O atoms, (24d) and (4b), one partially occupied 0 atom (8c) have been identified for this molybdovanadate, which is a unique feature for these crystals. The structure is related to both ZrV(2)O(7) and cubic ZrMo(2)O(8). The temperature dependent single crystal studies show negative thermal expansion above 370 K. The compounds have been characterized by powder X-ray diffraction, solid-state UV-vis diffuse reflectance spectra, scanning electron microscopy (SEM), and transmission electron microscopy (TEM). The photocatalytic activity of these compounds has been investigated for the degradation of various dyes, and these compounds show specificity toward the degradation of non-azoic dyes.