No description available.

Sandwich constructions are the most commonly used structures in aircraft and navy industries, traditionally. These structures are made up of the face sheets and the core, where the face sheets will be taking the load and is connected to other structural members, while the soft core material, will be used to absorb energy during impact like situation. Thus, sandwich constructions are mainly employed in light weight structures where the high energy absorption capability is required. Generally the face sheets will be thin, made up of either metallic or composite material with high stiffness and strength, while the core is light in weight, made up of soft material. Cores generally play very crucial role in achieving the desired properties of sandwich structures, either through geometric arrangement or material properties or both. Foams are in extensive use nowadays as core material due to the ease in manufacturing and their low cost. They are extensively used in automotive and industrial field applications as the desired foam density can be fabricated by adjusting the mixing, curing and heat sink processes. Modeling of sandwich beams play a crucial role in their design with suitable finite elements for face sheets and core, to ensure the compatibility between degrees of freedom at the interfaces. Unless the mathematical model simulates the physics of the model in terms of kinematics, boundary and loading conditions, results predicted will not be accurate. Accurate models helps in obtaining an efficient design of sandwich beams. In Structural Health Monitoring studies, the responses under the impact loading will be captured by carrying out the wave propagation analysis. The loads applied will be for a shorter duration (in the orders of micro seconds), where higher frequency modes will be excited. Wavelengths at such high frequencies are very small and hence, in such cases, very fine mesh generally is employed matching the wavelength requirement of the propagating wave. Traditional Finite element softwares takes enormous time and computational e ort to provide the solution. Various possible models and modeling aspects using the existing Finite element tools for wave propagation analysis are studied in the present work. There exists a huge demand for an accurate, efficient and rapidly convergent finite elements for the analysis of sandwich beams. E orts are made in the present work to address these issues and provide a solution to the sandwich user community. Super convergent and Spectral Finite sandwich Beam Elements with metallic or composite face sheets and soft core are developed. As a philosophy, the sandwich beam finite element is constructed with the combination of two beams representing the face sheets (top and bottom) at their neutral axis. The core effects are captured at the interface boundaries in terms of shear stress and normal transverse stress. In the case of wave propagation analysis, the equations are coupled in time domain and spatial domain and solving them directly is a difficult task. In Spectral Finite Element Method(SFEM), the displacement functions are derived by solving the transformed governing equations in the frequency domain. By transforming them and forces from time domain to frequency domain, the coupled partial differential equations will become coupled ordinary differential equations. These equations in frequency domain, can be solved exactly as they are normally ordinary differential equation with constant coefficients with frequency entering as a parameter. These solutions will be used as interpolating functions for spectral element formulation and in this respect it differs from conventional FE method wherein mostly polynomials are used as interpolating functions. In addition, SFEM solutions are expressed in terms of forward and backward moving waves for all the degrees of freedom involved in the formulations and hence, SFEM provides faster and efficient solutions for wave propagation analysis. In the present work, strong form of the governing differential equations are derived for a given system using Hamilton's principle. Super Convergent elements are developed by solving the static part of the governing differential equations exactly and hence the stiffness matrix derived is exact for point static loads. For wave propagation analysis, as the mass is not exactly represented, these elements are required in the optimal numbers for getting good results. The number of these elements required are generally much lesser than the number of elements required using traditional finite elements since the stiffness distribution is exact. Spectral elements are developed by solving the governing equations exactly in the frequency domain and hence the dynamic stiffness matrix derived is exact for the dynamic loads. Hence, one element between any two joints is enough to solve the whole system under impact loads for simple structures. Developing FE for sandwich beams is quiet challenging. Due to small thickness, the face sheets can be modeled using 1D idealization, while modeling of large core requires 2-D idealization. Hence, most finite or spectral elements requires stitching of these two idealizations into 1-D idealization, which can be accomplished in a variety of ways, some of which are highlighted in this thesis. Variety of finite and spectral finite elements are developed considering Euler and Timoshenko beam theories for modeling the sandwich beams. Simple element models are built with rigid core in both the theories. Models are also developed considering the flexible core with the variation of transverse displacements across depth of the core. This has direct influence on shear stress variation and also transverse normal stress in the core. Simple to higher order models are developed considering different variations in shear stress and transverse normal stress across depth of the core. Development of super convergent finite Euler Bernoulli beam elements Eul4d (4 dof element), Eul10d (10 dof element) are explained along with their results in Chapter 2. Development of different super convergent finite Timoshenko beam elements namely Tim4d (4 dof), Tim7d (7 dof), Tim10d (10 dof) are explained in Chapter 3. Validation of Euler Bernoulli and Timoshenko elements developed in the present work is carried out with test cases available in the open literature for displacements and free vibration frequencies are presented in Chapter 2 and Chapter 3. The results indicates that all developed elements are performing exceedingly well for static loads and free vibration. Super convergence performance for the elements developed is demonstrated with related examples. Spectral elements based on Timoshenko theory STim7d, STim6d, STim6dF are developed and the wave propagation characteristics studies are presented in Chapter 4. Euler spectral elements are derived from Timoshenko spectral elements by enforcing in finite shear rigidity, designated as SEul7d, SEul6d, SEul6dF and are presented. E orts were made in this present work to model the horizontal cracks in top or bottom face sheets using the spectral elements and the methodology is presented in Chapter 4. Wave propagation analysis using general purpose software N AST RAN and the super convergent as well as spectral elements developed in this work, are discussed in detail in Chapter 5. Modeling aspects of sandwich beam in N AST RAN using various combination of elements available and the performance of four possible models simulated were studied. Validation of all four models in N AST RAN, Super convergent Euler, Timoshenko and Spectral Timoshenko finite elements was carried out by simulating a homogenous I beam by comparing the longitudinal and transverse responses. Studies were carried out to find out the response predictions of a sandwich beam with soft core and all the predictions were compared and discussed. The responses in case of cracks in top or bottom face sheets under the longitudinal and transverse loading were studied in this chapter. In Chapter 6, Parametric studies were carried out for bringing out the sensitiveness of the important specific parameters in overall behaviour and performance of a sandwich beam, using Super convergent and Spectral elements developed. This chapter clearly brings out the various aspects of design of sandwich beam such as material selection of core, geometrical configuration of overall beam and core. Effects of shear modulus, mass density on wave propagation characteristics, effects of thick or thin cores with reference to the face sheets and dynamic effects of core are highlighted. Wave propagation characteristics studies includes the study of wave numbers, group speeds, cut off frequencies for a given configuration and identification of frequency zone of operations. The recommendations for improvement in design of sandwich beams based on the parametric studies are made at the end of chapter. The entire thesis, written in seven Chapters, presents a unified treatment of sandwich beam analysis that will be very useful for designers working in the area.

Composite structures provide opportunities for weight reduction, material tailoring and integrating control surfaces with embedded transducers, which are not possible in conventional metallic structures. As a result there is a substantial increase in the use of composite materials in aerospace and other major industries, which has necessitated the need for structural health monitoring(SHM) of aerospace structures. In the context of SHM of aircraft structures, there are many areas, which are still not explored and need deep investigation. Among these, one of the major areas is the development of efficient damage models for complex composite structures, like stiffened structures, box-type structures, which are the building blocks of an aircraft wing structure. Quantification of the defect due to porosity and especially the methods for identifying the porous regions in a composite structure is another such area, which demands extensive research. In aircraft structures, it is not advisable for the structures, to have high porosity content, since it can initiate common defects in composites such as, delamination, matrix cracks etc.. In fact, there is need for a high frequency analysis to detect defects in such complex structures and also to detect damages, where the change in the stiffness due to the damage is very small. Lamb wave propagation based method is one of the efficient high frequency wave based method for damage detection and are extensively used for detecting small damages, which is essentially needed in aircraft industry. However, in order, to develop an efficient Lamb wave based SHM system, we also need an efficient computational wave propagation model. Developing an efficient computational wave propagation model for complex structures is still a challenging area. One of the major difficulty is its computational expense, when the analysis is performed using conventional FEM. However, for 1D And 2D composite structures, frequency domain spectral finite element method (SFEM), which are very effective in sensing small stiffness changes due to a defect in a structure, is one of the efficient tool for developing computationally efficient and accurate wave based damage models. In this work, we extend the efficiency of SFEM in developing damage models, for detecting damages in built-up composite structures and porous composite structure. Finally, in reality, the nature of variability of the material properties in a composite structure, created a variety of structural problems, in which the uncertainties in different parameters play a major part. Uncertainties can be due to the lack of good knowledge of material properties or due to the change in the load and support condition with the change in environmental variables such as temperature, humidity and pressure. The modeling technique is also one of the major sources of uncertainty, in the analysis of composites. In fact, when the variations are large, we can find in the literatures available that the probabilistic models are advantageous than the deterministic ones. Further, without performing a proper uncertain wave propagation analysis, to characterize the effect of uncertainty in different parameters, it is difficult to maintain the reliability of the results predicted by SFEM based damage models. Hence, in this work, we also study the effect of uncertainty in different structural parameters on the performance of the damage models, based on the models developed in the present work. First, two SFEM based models, one based on the method of assembling 2D spectral elements and the other based on the concept of coupling 2D and 1D spectral elements, are developed to perform high frequency wave propagation analysis of some of the commonly used built-up composite structures. The SFEM model developed using the plate-beam coupling approach is then used to model wave propagation in a multiple stiffened structure and also to model the stiffened structures with different cross sections such as T-section, I-section and hat section. Next, the wave propagation in a porous laminated composite beam is modeled using SFEM, based on the modified rule of mixture approach. Here, the material properties of the composite is obtained from the modified rule of mixture model, which are then used in SFEM to develop a new model for solving wave propagation problems in porous laminated composite beam. The influence of the porosity content on the parameters such as wave number, group speed and also the effect of variation in theses parameters on the time responses are studied first. Next, the effect of the length of the porous region (in the propagation direction) and the frequency of loading, on the time responses, is studied. The change in the time responses with the change in the porosity of the structure is used as a parameter to find the porosity content in a composite beam. The SFEM models developed in this study is then used in the context of wave based damage detection, in the next study. First ,the actual measured response from a structure and the numerically obtained response from a SFEM model for porous laminated composite beam are used for the estimation of porosity, by solving a nonlinear optimization problem. The damage force indicator (DFI) technique is used to locate the porous region in a beam and also to find its length, using the measured wave propagation responses. DFI is derived from the dynamic stiffness matrix of the healthy structure along with the nodal displacements of the damaged structure. Next, a wave propagation based method is developed for modeling damage in stiffened composite structures, using SFEM, to locate and quantify the damage due to a crack and skin-stiffener debonding. The method of wave scattering and DFI technique are used to quantify the damage in the stiffened structure. In the uncertain wave propagation analysis, a study on the uncertainty in material parameters on the wave propagation responses in a healthy metallic beam structure is performed first. Both modulus of elasticity and density are considered uncertain and the analysis is performed using Monte-Carlo simulation (MCS) under the environment of SFEM. The randomness in the material properties are characterized by three different distributions namely normal, Weibul and extreme value distribution and their effect on wave propagation, in beam is investigated. Even a study is performed on the usage of different beam theories and their uncertain responses due to dynamic impulse load. A study is also conducted to analyze the wave propagation response In a composite structure in an uncertain environment using Neumann expansion blended with Monte-Carlo simulation (NE-MCS) under the environment of SFEM. Neumann expansion method accelerates the MCS, which is required for composites as there are many number of uncertain variables. The effect of the parameters like, fiber orientation, lay-up sequence, number of layers and the layer thickness on the uncertain responses due to dynamic impulse load, is thoroughly analyzed. Finally, a probabilistic sensitivity analysis is performed to estimate the sensitivity of uncertain material and fabrication parameters, on the SFEM based damage models for a porous laminated composite beam. MCS is coupled with SFEM, for the uncertain wave propagation analysis and the Kullback-Leibler relative entropy is used as the measure of sensitivity. The sensitivity of different input variables on the wave number, group speed and the values of DFI, are mainly considered in this study. The thesis, written in nine chapters, presents a unified document on wave propagation in healthy and defective composite structure subjected to both deterministic and highly uncertain environment.