Fracture analysis in continuously nonhomogeneous magneto-electro-elastic solids under a thermal load by the MLPG

AbstractA meshless method based on the local Petrov–Galerkin approach is proposed, to solve initial-boundary value problems of magneto-electro-elastic solids with continuously varying material properties. Stationary and transient thermal problems are considered in this paper. The mechanical 2-D fields are described by the equations of motion with an inertial term. Nodal points are spread on the analyzed domain, and each node is surrounded by a small circle for simplicity. The spatial variation of displacements, electric and magnetic potentials is approximated by the moving least-squares (MLS) scheme. After performing the spatial integrations, one obtains a system of ordinary differential equations for certain nodal unknowns. That system is solved numerically by the Houbolt finite-difference scheme as a time stepping method

A NEW C0 THIRD-ORDER SHEAR DEFORMATION THEORY FOR THE NONLINEAR FREE VIBRATION ANALYSIS OF STIFFENED FUNCTIONALLY GRADED PLATES

Nonlinear free vibration of stiffened functionally graded plates is presented by using the finite element method based on the new C0 third-order shear deformation theory. The material properties are assumed to be graded in the thickness direction by a power-law distribution. Based on the Von Karman theory and the third-order shear deformation theory, the nonlinear governing equations of motion are derived from the Hamilton’s principle. An iterative procedure based on the Newton-Raphson method is employed in computing the natural frequencies and mode shape. The comparison between these solutions and the other available ones suggests that this procedure is characterized by accuracy and efficiency

Flexural Analysis of FRP Strengthened RCC Beams Using Meshless Local Petrov Galerkin Method (MLPG)

In this project Meshless local Petrov Galerkin (MLPG) method is utilized for the flexural analysis of simply supported RCC beams strengthened with FRP laminates. This method uses the moving least-squares (MLS) approximation with different weight functions to interpolate the field variables and uses a local symmetric weak form (LSWF). The beams under consideration are rectangular and T-beams reinforced either on tension face or on both faces as per IS 456:2000. The proposed method is first applied to unstrengthened beam to check its applicability. The computed displacements are in good accord with the displacements attained using code formula. Then, it is extended to beams strengthened with FRP laminate. A parametric study is carried out to study the effect of disparity of field nodes in the global domain, integration cells in the sub domain and young`s modulus on the displacement. The efficiency of the algorithm developed is verified

Finite Block Method and Applications in Engineering with Functional Graded Materials

PhDFracture mechanics plays an important role in understanding the performance of all types of materials including Functionally Graded Materials (FGMs). Recently, FGMs have attracted the attention of various scholars and engineers around the world since its specific material properties can smoothly vary along the geometries. In this thesis, the Finite Block Method (FBM), based on a 1D differential matrix derived from the Lagrangian Interpolation Method, has been presented for the evaluation of the mechanical properties of FGMs on both static and dynamic analysis. Additionally, the coefficient differential matrix can be determined by a normalized local domain, such as a square for 2D, a cubic for 3D. By introducing the mapping technique, a complex real domain can be divided into several blocks, and each block is possible to transform from Cartesian coordinate (xyz) to normalized coordinate ( ) with 8 seeds for two dimensions and 20 seeds for three dimensions. With the aid of coefficient differential matrix, the differential equation is possible to convert to a series of algebraic functions. The accuracy and convergence have been approved by comparison with other numerical methods or analytical results. Besides, the stress intensity factor and T-stresses are introduced to assess the fracture characteristics of FGMs. The Crack Opening displacement is applied for the calculation of the stress intensity factor with the FBM. In addition, a singular core is adopted to combine with the blocks for the simulation of T stresses. Numerical examples are introduced to verify the accuracy of the FBM, by comparing with Finite Element Methods or analytical results. Finally, the FBM is applied for wave propagation problems in two- and three-dimensional porous mediums considering their poroelasticities. To demonstrate the accuracy of the present method, a one-dimensional analytical solution has been derived for comparison

Software for evaluating probability-based integrity of reinforced concrete structures

In recent years, much research work has been carried out in order to obtain a more controlled durability and long-term performance of concrete structures in chloride containing environment. In particular, the development of new procedures for probability-based durability design has proved to give a more realistic basis for the analysis. Although there is still a lack of relevant data, this approach has been successfully applied to several new concrete structures, where requirements to a more controlled durability and service life have been specified. A probability-based durability analysis has also become an important and integral part of condition assessment of existing concrete structures in chloride containing environment. In order to facilitate the probability-based durability analysis, a software named DURACON has been developed, where the probabilistic approach is based on a Monte Carlo simulation. In the present paper, the software for the probability-based durability analysis is briefly described and used in order to demonstrate the importance of the various durability parameters affecting the durability of concrete structures in chloride containing environment

A 3D layer-wise model for the correct imposition of transverse shear/normal load conditions in FGM shells

A general elasticity 3D layer-wise shell model is proposed for the static investigation of plates and shells including functionally graded material (FGM) layers. A closed-form solution is used considering simply-supported sides and harmonic forms for displacements and loads. The partial differential equations obtained from the 3D equilibrium relations developed in curvilinear orthogonal coordinates are solved using the exponential matrix methodology. These equations have constant coefficients because an opportune number of mathematical layers has been introduced in order to calculate the parametric coefficients including the radii of curvature for the shells and the elastic coefficients that are variable through the thickness direction in the case of functionally graded materials. The main aim of the present work is to fill the gap found in the literature where the 3D elasticity theories always give solutions for FGM plates or shells in the only case of a transverse normal load positioned at the top or at the bottom surfaces. The present work proposes an exhaustive static analysis where the load boundary conditions have been appropriately rewritten in order to allow the use of several transverse normal and transverse shear loads separately or simultaneously positioned at top and/or bottom surfaces. One-layered and sandwich FGM plates, cylinders, cylindrical shells and spherical shells are analyzed changing the material laws and properties, the applied loads and the thickness ratios. The importance of the zigzag features, the interlaminar continuity in terms of compatibility and equilibrium requirements, the boundary load requirements, the considerations about the symmetry, the thickness ratio effect and the three-dimensional behavior have been opportunely discussed. Advantages connected with the use of FGM layers have also been analyzed. These new 3D exact results will allow the validation of recent advanced 2D shell models in the literature for the static investigation of FGM structures subjected to different load conditions. The proposed 3D model is general for several geometries (plates and shells) and materials (classical ones, composites and FGMs) and it allows a unique 3D exact solution for a large variety of structures

Bending and Free Vibration Analysis of Functionally Graded Plates via Optimized Non-polynomial Higher Order Theories

Optimization concept in the context of shear deformation theories was born for the development of accurate models to study the bending problem of structures. The present study seeks to extend such an approach to the dynamic analysis of plates. A compact and unified formulation with non-polynomial shear strain shape functions (SSSFs) is employed to develop a static and free vibration analysis of simply supported functionally graded plates. In this context, three new non-polynomial displacement fields are proposed using trigonometric and hyperbolic SSSFs. Then, the non-polynomial SSSFs are optimized by varying the arguments of the trigonometric and hyperbolic functions. Additionally, the Mori-Tanaka approach is used to estimate the effective properties of the functionally graded plates. The Principle of Virtual Displacement (PVD) and the Hamilton’s Principle along with the Navier closed-form solution technique are used to obtain exact results. The obtained numerical results are in a good agreement with 3D and 2D higher order shear deformation theory solutions available in the literature