Semi-analytical solution for nonlinear vibration of laminated FGM plates with geometric imperfections

This paper investigates the nonlinear vibration of imperfect shear deformable laminated rectangular plates comprising a homogeneous substrate and two layers of functionally graded materials (FGMs). A theoretical formulation based on Reddy's higher-order shear deformation plate theory is presented in terms of deflection, mid-plane rotations, and the stress function. A semi-analytical method, which makes use of the one-dimensional differential quadrature method, the Galerkin technique, and an iteration process, is used to obtain the vibration frequencies for plates with various boundary conditions. Material properties are assumed to be temperature-dependent. Special attention is given to the effects of sine type imperfection, localized imperfection, and global imperfection on linear and nonlinear vibration behavior. Numerical results are presented in both dimensionless tabular and graphical forms for laminated plates with graded silicon nitride/stainless steel layers. It is shown that the vibration frequencies are very much dependent on the vibration amplitude and the imperfection mode and its magnitude. While most of the imperfect laminated plates show the well-known hard-spring vibration, those with free edges can display soft-spring vibration behavior at certain imperfection levels. The influences of material composition, temperature-dependence of material properties and side-to-thickness ratio are also discussed. (C) 2004 Elsevier Ltd. All rights reserved.

Non-linear analysis of the thermo-electro-mechanical behaviour of shear deformable FGM plates with piezoelectric actuators

This paper investigates the non-linear bending behaviour of functionally graded plates that are bonded with piezoelectric actuator layers and subjected to transverse loads and a temperature gradient based on Reddy's higher-order shear deformation plate theory. The von Karman-type geometric non-linearity, piezoelectric and thermal effects are included in mathematical formulations. The temperature change is due to a steady-state heat conduction through the plate thickness. The material properties are assumed to be graded in the thickness direction according to a power-law distribution in terms of the volume fractions of the constituents. The plate is clamped at two opposite edges, while the remaining edges can be free, simply supported or clamped. Differential quadrature approximation in the X-axis is employed to convert the partial differential governing equations and the associated boundary conditions into a set of ordinary differential equations. By choosing the appropriate functions as the displacement and stress functions on each nodal line and then applying the Galerkin procedure, a system of non-linear algebraic equations is obtained, from which the non-linear bending response of the plate is determined through a Picard iteration scheme. Numerical results for zirconia/aluminium rectangular plates are given in dimensionless graphical form. The effects of the applied actuator voltage, the volume fraction exponent, the temperature gradient, as well as the characteristics of the boundary conditions are also studied in detail. Copyright (C) 2004 John Wiley Sons, Ltd.

Analysis of the thermal stress behaviour of functionally graded hollow circular cylinders

This paper presents an analysis of the thermomechanical behavior of hollow circular cylinders of functionally graded material (FGM). The solutions are obtained by a novel limiting process that employs the solutions of homogeneous hollow circular cylinders, with no recourse to the basic theory or the equations of non-homogeneous thermoclasticity. Several numerical cases are studied, and conclusions are drawn regarding the general properties of thermal stresses in the FGM cylinder. We conclude that thermal stresses necessarily occur in the FGM cylinder, except in the trivial case of zero temperature. While heat resistance may be improved by sagaciously designing the material composition, careful attention must be paid to the fact that thermal stresses in the FGM cylinder are governed by more factors than are its homogeneous counterparts. The results that are presented here will serve as benchmarks for future related work. (C) 2003 Elsevier Science Ltd. All rights reserved.

Random vibration of the functionally graded laminates in thermal environments

This work deals with the random free vibration of functionally graded laminates with general boundary conditions and subjected to a temperature change, taking into account the randomness in a number of independent input variables such as Young's modulus, Poisson's ratio and thermal expansion coefficient of each constituent material. Based on third-order shear deformation theory, the mixed-type formulation and a semi-analytical approach are employed to derive the standard eigenvalue problem in terms of deflection, mid-plane rotations and stress function. A mean-centered first-order perturbation technique is adopted to obtain the second-order statistics of vibration frequencies. A detailed parametric study is conducted, and extensive numerical results are presented in both tabular and graphical forms for laminated plates that contain functionally graded material which is made of aluminum and zirconia, showing the effects of scattering in thermo-clastic material constants, temperature change, edge support condition, side-to-thickness ratio, and plate aspect ratio on the stochastic characteristics of natural frequencies. (c) 2005 Elsevier B.V. All rights reserved.

Comparison of human alveolar osteoblasts cultured on polymer-ceramic composite scaffolds and tissue culture plates

The effects of medical grade polycaprolactone–tricalcium phosphate (mPCL–TCP) (80:20) scaffolds on primary human alveolar osteoblasts (AOs) were compared with standard tissue-culture plates. Of the seeded AOs, 70% adhered to and proliferated on the scaffold surface and within open and interconnected pores; they formed multi-layered sheets and collagen fibers with uniform distribution within 28 days. Elevation of alkaline phosphatase activity occurred in scaffold–cell constructs independent of osteogenic induction. AO proliferation rate increased and significant decrease in calcium concentration of the medium for both scaffolds and plates under induction conditions were seen. mPCL–TCP scaffolds significantly influenced the AO expression pattern of osterix and osteocalcin (OCN). Osteogenic induction down-regulated OCN at both RNA and protein level on scaffolds (3D) by day 7, and up-regulated OCN in cell-culture plates (2D) by day 14, but OCN levels on scaffolds were higher than on cell-culture plates. Immunocytochemical signals for type I collagen, osteopontin and osteocalcin were detected at the outer parts of scaffold–cell constructs. More mineral nodules were found in induced than in non-induced constructs. Only induced 2D cultures showed nodule formation. mPCL–TCP scaffolds appear to stimulate osteogenesis in vitro by activating a cellular response in AO's to form mineralized tissue. There is a fundamental difference between culturing AOs on 2D and 3D environments that should be considered when studying osteogenesis in vitro.

Damage localisation in beams and plates using vibration characteristics

Dynamic computer simulation techniques are used to develop and apply a multi-criteria procedure, incorporating changes in natural frequencies, modal flexibility and the modal strain energy, for damage localisation in beams and plates. Numerically simulated modal data obtained through finite element analyses are used to develop algorithms based on changes of modal flexibility and modal strain energy before and after damage and used as the indices for assessment of the state of structural health. The proposed procedure is illustrated through its application to flexural members under different damage scenarios and the results confirm its feasibility for damage assessment.

Sensitivity of Dot-ELISA on Nitrocellulose Membranes in Comparison with ELISA on Polystyrene Plates for the Detection of Four Plant Viruses

ABSTR.4CT Senitivity of dot-immunobindinding ELf SA on nitrocellulose membrane (DotELISA)was compared with double-antibody sandwich ELISA (DAS-ELlSA) on polystyrene plates for the detection of bean yellow mosaic virus (BYMV), broad bean stain virus (WMV-2). Dot-ELISA was 2 and 1O times more sensitive than DAS-ELISA for the detection of BBSV and WMV-2, respectively, whereas DAS-ELISA was more sensitive than Dot-ELiSA for {he detection of BYMV. Both techniques were equally sensitive for the detection of BYDV. Using one day instead uf the two-day procedure, the four viruses were still detectable and the ralative sensitivity of both techniques remained the same.

Interfacial debonding behavior of composite beam/plates with PZT patch

This paper studies interfacial debonding behavior of composite beams which include piezoelectric materials, adhesive and host beam. The focus is put on crack initiation and growth of the piezoelectric adhesive interface. Closed-form solutions of interface stresses and energy release rates are obtained for adhesive layer in the piezoelectric composite beams. Finite element analyses have been carried out to study the initiation and growth of interfaces crack for piezoelectric beams with interface element by ANSYS, in which the interface element of FE model is based on the cohesive zone models to characterize the fracture behavior of the interfacial debonding. The results have been compared with analystical solution, and the influence of different geometry and material parameters on the interfacial behavior of piezoelectric composite beams have been discussed.

Vibration of L-shaped plates under a deterministic force or moment excitation : a case of statistical energy analysis application

Analytical and closed form solutions are presented in this paper for the vibration response of an L-shaped plate under a point force or a moment excitation. Inter-relationships between wave components of the source and the receiving plates are clearly defined. Explicit expressions are given for the quadratic quantities such as input power, energy flow and kinetic energy distributions of the L-shaped plate. Applications of statistical energy analysis (SEA) formulation in the prediction of the vibration response of finite coupled plate structures under a single deterministic forcing are examined and quantified. It is found that the SEA method can be employed to predict the frequency averaged vibration response and energy flow of coupled plate structures under a deterministic force or moment excitation when the structural system satisfies the following conditions: (1) the coupling loss factors of the coupled subsystems are known; (2) the source location is more than a quarter of the plate bending wavelength away from the source plate edges in the point force excitation case, or is more than a quarter wavelength away from the pair of source plate edges perpendicular to the moment axis in the moment excitation case due to the directional characteristic of moment excitations. SEA overestimates the response of the L-shaped plate when the source location is less than a quarter bending wavelength away from the respective plate edges owing to wave coherence effect at the plate boundary

Bond characteristics between CFRP and steel plates in double strap joints

This paper describes a series of double strap shear tests loaded in tension to investigate the bond between CFRP sheets and steel plates. Both normal modulus (240 GPa) and high modulus (640 GPa) CFRPs were used in the test program. Strain gauges were mounted to capture the strain distribution along the CFRP length. Different failure modes were observed for joints with normal modulus CFRP and those with high modulus CFRP. The strain distribution along the CFRP length was found to be similar for the two cases. A shorter effective bond length was obtained for joints with high modulus CFRP whereas larger ultimate load carrying capacity can be achieved for joints with normal modulus CFRP when the bond length is long enough. The Hart-Smith Model was modified to predict the effective bond length and ultimate load carrying capacity of joints between the normal modulus CFRP and steel plates. The Multilayer Distribution Model developed by the authors was modified to predict the load carrying capacity of joints between the high modulus CFRP and steel plates. The predicted values agreed well with experimental ones.

Experimental and finite element analysis of a double strap joint between steel plates and normal modulus CFRP

Strengthening of steel structures using externally-bonded carbon fibre reinforced polymers ‘CFRP’ is a rapidly developing technique. This paper describes the behaviour of axially loaded flat steel plates strengthened using carbon fibre reinforced polymer sheets. Two steel plates were joined together with adhesive and followed by the application of carbon fibre sheet double strap joint with different bond lengths. The behaviour of the specimens was further investigated by using nonlinear finite element analysis to predict the failure modes and load capacity. In this study, bond failure is the dominant failure mode for normal modulus (240 GPa) CFRP bonding which closely matched the results of finite elements. The predicted ultimate loads from the FE analysis are found to be in good agreement with experimental values.

Biomaterials in orthopedic bone plates : a review

This paper aims to review biomaterials used in manufacturing bone plates including advances in recent years and prospect in the future. It has found among all biomaterials, currently titanium and stainless steel alloys are the most common in production of bone plates. Other biomaterials such as Mg alloys, Ta alloys, SMAs, carbon fiber composites and bioceramics are potentially suitable for bone plates because of their advantages in biocompatibility, bioactivity and biodegradability. However, today either they are not used in bone plates or have limited applications in only some flexible small-size implants. This problem is mainly related to their poor mechanical properties. Additionally, production processes play an effective role. Therefore, in the future, further studies should be conducted to solve these problems and make them feasible for heavy-duty bone plates.

Orthopedic bone plates : evolution in structure implementation technique and biomaterial

With many important developments over the last century, nowadays orthopedic bone plate now excels over other types of internal fixators in bone fracture fixation. The developments involve the design, material and implementation techniques of the plates. This paper aims to review the evolution in implementation technique and biomaterial of the orthopedic bone plates. Plates were initially used to fix the underlying bones firmly. Accordingly, Compression plate (CP), Dynamic compression plate (DCP), Limited contact dynamic compression plate (LC-DCP) and Point contact fixator (PC-Fix) were developed. Later, the implementation approach was changed to locking, and the Less Invasive Stabilization System (LISS) plate was introduced as a result. Finally, a combination of both of these approaches has been used by introducing the Locking Compression Plate (LCP). Currently, precontoured LCPs are mainly used for bone fracture fixation. In parallel with structure and implementation techniques, numerous advances have occurred in biomaterials of the plates. Titanium and stainless steel alloys are now the most common biomaterials in production of orthopedic bone plates. However, regarding the biocompatibility, bioactivity and biodegradability characteristics of Mg alloys, Ta alloys, SMAs, carbon fiber composites and bioceramics, these materials are considered as potentially suitable for plates. However, due to poor mechanical properties, they have very limited applications. Therefore, further studies are required in future to solve these problems and make them feasible for heavy-duty bone plates.