Exact solutions for static bending of symmetric laminated orthotropic plates with different Lévy-type boundary conditions are developed. The shear deformation plate theories of Mindlin-Reissner and Reddy as well as the three-dimensional elasticity theory are employed. Using the minimum total potential energy principle, governing equilibrium equations of laminated orthotropic plates and pertaining boundary conditions are derived. Closed-form Lévy-type solutions are obtained for the governing equations of both theories using separation of variables method and different types of classical boundary conditions, namely simply-supported, clamped and free edge, are exactly satisfied. Thereafter, 3-D elasto-static equations for orthotropic materials are solved for bending analysis of laminated plates using two different approaches. First, the method of separation of variables is utilized and an exact closed-from solution is achieved for simply-supported laminated orthotropic plates. Next, a combined Fourier-Differential Quadrature (DQ) approach is employed to present a semi-numerical solution for bending of laminated orthotropic plates with Lévy-type boundary conditions based on the three-dimensional elasticity theory. High accuracy of the presented solutions are proven and comprehensive comparative numerical results are provided and discussed. Presented comparative numerical results can serve as benchmark for investigating the correctness of new solution methods which may be established in the future.
The elasticity in bending of European oak (Quercus robur L.) and Norway spruce (Picea abies (L.) Karst.) timber was evaluated before and after thermal modificationand related to the changes in chemical composition of the wood as a result of the modification. A new software was developed (MATESS) and used to identify characteristic points on the force-deformation diagram. The modulus of elasticity(MOE), stress at the limit of proportionality (LOP) and elastic potential (PE) were used to describe the wood properties. Extractives, lignin, cellulose, holocellulose, and hemicelluloses were analysed to reveal the patterns that occur during the loading of the specimens. Thermal modification lowers the mechanical properties (MOE, LOP and PE) of oak and spruce wood, and the reduction increases with increasing modification temperature. Changes in chemical composition of thermally modified wood show a strong relationship to the reduction in elasticity properties for bot species.
In this article, a new exact closed-form procedure is presented to solve freevibration analysis of functionallygradedrectangularthickplates based on the Reddy’s third-order shear deformation plate theory while the plate has two opposite edges simply supported (i.e., Lévy-type rectangularplates). The elasticity modulus and mass density of the plate are assumed to vary according to a power-law distribution in terms of the volume fractions of the constituents whereas Poisson’s ratio is constant. Based on the present solution, five governing complicated partial differential equations of motion were exactly solved by introducing the auxiliary and potential functions and using the method of separation of variables. The validity and high accuracy of the present solutions are investigated by comparing some of the present results with their counterparts reported in literature and the 3-D finite element analysis. It is obvious that the present exact solution can accurately predict not only the out of plane, but also the in-plane modes of FG plate. Furthermore, a new eigenfrequency parameter is defined having its special own characteristics. Finally, the effects of boundary conditions, thickness to length ratio, aspect ratio and the power law index on the frequency parameter of the plate are presented
A 3D computational homogenization method based on X-ray microcomputed tomography (μCT) was proposed and implemented to investigate how the fiber weight fraction, orthotropy and orientation distribution affect the effective elastic properties of regenerated cellulose fiber-polylactic acid (PLA) biocomposites. Three-dimensional microstructures reconstructed by means of the X-ray μCT were used as the representative volume elements (RVEs) and incorporated into the finite element solver within the computational homogenization framework. The present method used Euclidean bipartite matching technique so as to eliminate the generation of artificial periodic boundaries and use the in-situ solution domains. In addition, a reconstruction algorithm enabled finding the volume and surface descriptions for each individual fiber in a semi-automatic manner, aiming at reducing the time and labor required for fiber labeling. A case study was presented, through which the method was compared and validated with the experimental investigations. The present study is thus believed to give a precise picture of microstructural heterogeneities for biocomposites of complex fiber networks and to provide an insight into the influences of the individual fibers and their networks on the effective elastic properties.
The increasing use of Fiber Reinforced Polymers (FRP) to repair, strengthen or upgrade reinforced concrete (RC) structural elements means that there is a need to develop analytical methods for analyzing the behavior of strengthened members under fatigue loading. This paper describes an analytical model for simulating the fatigue behavior of RC beams strengthened with Carbon Fiber Reinforced Polymer (CFRP). Fatigue calculations are performed using a lamellar model that considers the fatigue behavior of the RC and CFRP strengthening materials during loading. The model’s output is compared to experimental data for four CFRP-strengthened beams, showing that the new model accurately predicted the deflection and strain of each one. In addition, various models for predicting the fatigue life of CFRP-strengthened RC beams were tested and a model capable of providing conservative fatigue life estimates was identified.
This study examines the effect of manufacturing induced voids on failure of adhesive joints. A single lap joint with preexisting crack between the adherend and the adhesive is considered and the crack growth behavior is studied in the presence of a void in the adhesive. The analysis conducted is numerical using finite elements and a revised virtual crack closure technique for calculating the energy release rate of the interface crack. After verifying the numerical model for a case where analytical solution exists, it is used to gain insight into the failure of the adhesive joint by conducting a parametric study where the size, shape and location of the void with respect to the crack tip are varied. The case of two preexisting cracks on opposite interfaces in the presence of a void is also examined.