An exact solution for the bending of thin rectangular plates with uniform, linear, and quadratic thickness variations

In this paper, the analysis of the titled problem is based on classical thin-plate theory, and its numerical solution is carried out by using the small parameter method and Lévy-type approach. The thin rectangular plate considered herein is simply supported on two opposite edges. The boundary conditions at the other two edges may be quite general, and between these two edges the plate may have varying thickness. Closed-form solutions have been developed for the static response of isotropic rectangular plates with non-uniform thickness variation and subjected to arbitrary loading. The accuracy of the present model is demonstrated via problems for which the exact solutions and numerical results are available, and results are also compared with those obtained by using the finite-difference method.     

An exact approach for free vibration analysis of rectangular plates with line-concentrated mass and elastic line-support

An exact approach for free vibration of an isotropic rectangular plate carrying a line-concentrated mass and with a line-translational spring support or carrying a line-spring-mass system is presented in this paper. The mode shape function of vibration of such a plate is expressed in terms of the four fundamental solutions derived in this paper. The main advantage of the proposed method is that the resulted frequency equation for such a rectangular plate can be conveniently obtained from a second-order determinant. The proposed method is thus computationally efficient due to the significant decrease in the determinant order as compared with previously developed procedures which usually led to an eighth-order determinant for solving the title problem. Two numerical examples are given to illustrate the efficiency of the proposed method and to investigate the effects of the location and the magnitude of a line-concentrated mass and elastic line-support as well as the influence of the aspect ratio on the natural frequencies of a rectangular plate.     

Transverse stress profiles reconstruction for finite element analysis of laminated plates

The present work focuses on a posteriori, equilibrium based, reconstruction of transverse stress profiles in the finite element analysis of FSDT laminated plates. The accuracy of this reconstruction depends on accuracy of the first and second-order derivatives of the plate stress resultants, which is not guaranteed by most available low-order plate finite elements. To cure this trouble, two different strategies, based on the Recovery by Compatibility in Patches procedure, are here proposed and compared. Numerical results of typical reconstructed transverse stress profiles are presented showing the effectiveness of the proposed approach.     

Development of open-cathode polymer electrolyte fuel cells using printed circuit board flow-field plates: Flow geometry characterisation

Open-cathode air-breathing fuel cells have the advantage of reduced system complexity and simplified operation, as oxygen is taken directly from ambient air without the need for blowers/compressors. In this study, printed circuit boards (PCBs) are used as flow-field plates. The use of PCBs offers the potential for significant cost reduction due to their well-established manufacturing processing and low materials cost. This study investigates the effect of varying the cathode geometry (parallel and circular) and opening ratios (43%, 53% and 63%) on fuel cell performance using polarisation curves, electrochemical impedance spectroscopy (EIS) and thermal imaging. The results obtained indicate that circular openings afford lower Ohmic resistance than parallel flow-field designs, which helps improve contact between the gas diffusion layer and flow-field plate. However, flow-field plates with circular openings suffer from greater mass transport limitation effects. Likewise, greater opening ratios offer better mass transport but increased Ohmic resistance as a result of the reduced area of lands/ribs. The thermal imaging results reveal lower temperature in the middle of the fuel cell due to “bowing” of the printed circuit board flow field plates which reduces the local current density. A trade-off between these factors results in a design with a maximum area specific power density of 250 mW cm⁻².     

Local–global mode interaction in stringer-stiffened plates

A recently developed nonlinear analytical model for axially loaded thin-walled stringer-stiffened plates based on variational principles is extended to include local buckling of the main plate. Interaction between the weakly stable global buckling mode and the strongly stable local buckling mode is highlighted. Highly unstable post-buckling behaviour and a progressively changing wavelength in the local buckling mode profile are observed under increasing compressive deformation. The analytical model is compared against both physical experiments from the literature and finite element analysis conducted in the commercial code Abaqus; excellent agreement is found both in terms of the mechanical response and the predicted deflections.     

Micro-roll forming of stainless steel bipolar plates for fuel cells

Stainless steel bipolar plates for use in proton exchange membrane (PEM) fuel cells have been identified as a lighter and cheaper alternative to graphite plates. Current manufacturing of metal bipolar plates by hydroforming or micro-stamping leads to excessive stretching of the material and therefore limits the channel depths that can be formed. Low channel depths for the bipolar plates will result in low overall fuel cell efficiency. In comparison, the bending-dominated deformation mode present in roll forming provides the potential to form metal bipolar plates with less thinning and to greater channel depths. In this work, the roll forming process is employed for the first time to form thin stainless steel sheets to micro-scale channel sections of the kind required for bipolar plates. This paper describes the process and machine design as well as the establishment of the forming methodology. Experimental trials are performed and the final part quality is evaluated in terms of material thinning, longitudinal bow and cross-sectional shape. The process was numerically analysed to understand the causes of the forming problems and shape defects observed in the experimental trials. The results of this work show that roll forming of micro-scale corrugated bipolar sheets is feasible. Furthermore, the findings provide a summary of both the practical difficulties and the possible advantages of using micro-roll forming to manufacture improved thin metal micro-corrugations for bipolar plates.     

A theory of one-dimensional fracture

A completely analytical theory is developed for the mixed mode partition of one-dimensional fracture in laminated composite beams and plates. Two sets of orthogonal pure modes are determined first. It is found that they are distinct from each other in Euler beam or plate theory and coincide at the Wang-Harvey set in Timoshenko beam or plate theory. After the Wang-Harvey set is proved to form a unique complete orthogonal pure mode basis within the contexts of both Euler and Timoshenko beam or plate theories, it is used to partition a mixed mode. Stealthy interactions are found between the Wang-Harvey pure mode I modes and mode II modes in Euler beam or plate theory, which alter the partitions of a mixed mode. The finite element method is developed to validate the analytical theories.     

Active screen plasma nitriding of 316 stainless steel for the application of bipolar plates in proton exchange membrane fuel cells

Proton exchange membrane fuel cell (PEMFC) has attracted considerable interest because of its superb performance, and many researches are focused on the development of high-performance, long-life bipolar plates. Stainless steel bipolar plates offer many advantages over the conventional graphite bipolar plates, such as low material and fabrication cost, excellent mechanical behaviour and ease of mass production. However, the insufficient corrosion resistance and relatively high interfacial contact resistance (ICR) become the major obstacles to the widespread use of stainless steel bipolar plates. In this work, active screen plasma nitriding (ASPN), a novel plasma nitriding technique, was used to modify the surface of 316 austenitic stainless steel. A variety of analytical techniques, including X-ray diffraction (XRD), scanning electron microscopy (SEM), glow discharge optical emission spectrometer (GDOES), were employed to characterize the nitrided samples. The results reveal that a nitrogen supersaturated S-phase layer has been successfully produced on the surface of all nitrided 316 stainless steel samples. The interfacial contact resistance (ICR) value can be decreased dramatically after ASPN treatment and the corrosion resistance can also been improved. In addition, better corrosion resistance can be achieved by active screen plasma nitriding with a stainless steel screen than with a carbon steel screen. This technique could be used to improve the performance and lifespan of bipolar plates for fuel cells.     

Mechanism investigation of welding induced buckling using inherent deformation method

Due to the increasing use of thin plates in lightweight welded structure, welding induced buckling may occur in such thin plate welded structure. In this study, welding induced buckling of thin plate welded structure is investigated using the eigenvalue analysis and elastic Finite Element (FE) analysis based on inherent deformation theory, and the mechanism of welding induced buckling is clarified.Bead-on-plate welding is first examined. Measured out-of-plane welding distortion indicates that saddle type buckling is produced after cooling. Eigenvalue analysis shows the computed lowest buckling mode is the saddle type and the corresponding critical force is less than the applied tendon force evaluated by Thermal–Elastic–Plastic (TEP) Finite Element (FE) analysis beforehand. Using elastic Finite Element (FE) analysis in which all components of inherent deformation are used and also considering initial deflection, out-of-plane welding distortion is predicted with high accuracy compared with measurement. It is also concluded that tendon force (longitudinal inherent shrinkage) is the dominant reason of buckling and it determines the buckling mode, and initial deflection and inherent bending are considered to be disturbances which trigger buckling.Later, a thin plate stiffened welded structure with fillet welded joints is examined. Although welding did not induce buckling of plate fields in bending modes in the considered thin plate stiffened welded structure, the whole stiffened welded structure buckles in a twisting mode, while plate panels remain unbuckled. Eigenvalue analysis gives the twisting buckling mode as the lowest buckling mode. However, in stiffened welded structures, not only tendon force (longitudinal inherent shrinkage) but also transverse inherent shrinkage is responsible for buckling. The good agreement between computed and measured out-of-plane welding distortion shows that the elastic Finite Element (FE) analysis using inherent deformation theory is an advantage of the computational approach to predict welding distortion in large-scale and complex welded structure with enough computational accuracy.     

Stochastic nonlinear failure analysis of laminated composite plates under compressive transverse loading

This paper present the second ordered statistics of first-ply failure response of laminated composite plate with random material properties under random loading. The basic formulation is based on higher order shear deformation plate theory (HSDT) with the geometrically nonlinearity in the von-Karman. The direct iterative based C⁰ nonlinear finite element method combined with mean centered first order perturbation technique developed by the authors are extended and successfully applied nonlinearity for failure problem with a reasonable accuracy to predict the second order statistics (standard deviation) of first-ply failure response using Tsai-Wu and Hoffman failure criterion with macroscopic analysis. Typical numerical results for various combinations of boundary conditions, plate thickness ratios, aspect ratios, laminates scheme and layers, elastic modulus ratios have been presented to illustrate the application of developed procedure. Some new results are presented and examined which clearly demonstrated the importance of the randomness in the system parameters in the failure response of the structures subjected to transverse loadings.