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.

Failure modes for sandwich beams of GFRP laminate skins and Nomex honeycomb core are investigated. Theoretical models using honeycomb mechanics and classical beam theory are described. A failure mode map for loading under 3-point bending, is constructed, showing the dependence of failure mode and load on the ratio of skin thickness to span length and honeycomb relative density. Beam specimens are tested in 3-point bending. The effect of honeycomb direction is also examined. The experimental data agree satisfactorily with the theoretical predictions. The results reveal the important role of core shear in a sandwich beam's bending behaviour and the need for a better understanding of indentation failure mechanism. High order sandwich beam theory (HOSBT) is implemented to extract useful information about the way that sandwich beams respond to localised loads under 3-point bending. 'High-order' or localised effects relate to the non-linear patterns of the in-plane and vertical displacements fields of the core through its height resulting from the unequal deformations in the loaded and unloaded skins. The localised effects are examined experimentally by Surface Displacement Analysis of video images recorded during 3-point bending tests. A new parameter based on the intrinsic material and geometric properties of a sandwich beam is introduced to characterise its susceptibility to localised effects. Skin flexural rigidity is shown to play a key role in determining the way that the top skin allows the external load to pass over the core. Furthermore, the contact stress distribution in the interface between the central roller and the top skin, and its importance to an indentation stress analysis, are investigated. To better model the failure in the core under the vicinity of localised loads, an Arcan- type test rig is used to test honeycomb cores under simultaneous compression and shear loading. The experimental measurements show a linear relationship between the out-of-plane compression and shear in honeycomb cores. This is used to derive a failure criterion for applied shear and compression, which is combined with the high order sandwich beam theory to predict failure caused by localised loads in sandwich beams made of GFRP laminate skins and Nomex honeycomb under 3-point bending loading. Short beam tests with three different indenter's size are performed on appropriately prepared specimens. Experiments validate the theoretical approach and reveal the nature of pre- and post-failure behaviour of these sandwich beams. HOSBT is used as a compact computational tool to reconstruct failure mode maps for sandwich panels. Superposition of weight and stiffness contours on these failure maps provide carpet plots for design optimisation procedures.

Byggbranschens utsläpp av växthusgaser utgör en stor andel av Sveriges totala utsläpp. För att minska de byggrelaterade utsläppen är det på många fronter som byggbranschen behöver förändras och effektiviseras. De senaste åren har en succesiv ökning av byggandet i trä skett vilket är gynnsamt då trä alternativet är mer klimatvänligt än stål och betong. De tuffa klimatmålen vi nu står framför innebär dock att mer behöver göras än att endast öka andelen träbyggnader. Pappersmassaindustrin är lätt att bortse ifrån, då den hittills inte varit relevant för byggbranschen och för att återanvändning är relativt framträdande inom den branschen. Ifrån sågverken som sönderdelar trästockar till virke fraktas flis som blir över till pappersbruk. Av flisen görs sedan bland annat diverse pappförpackningar som går att återvinna. Problemet är att dessa förpackningar endast går att återvinna ett visst antal gånger innan fibrerna blir obrukbara och istället används som biobränsle. Om byggmaterial skulle gå att producera baserat på dessa fibrer, skulle detta innebära en mer långlivad användning av dem. Ett byggmaterial som uppfunnits, gjort på fibrer från pappersmassabruk är core-materialet ”Greenwood”. Eftersom materialet är nytt och egenskaperna till stor del är okända krävs det att diverse studier görs som undersöker materialets olika egenskaper som är relevanta för en eventuell tillämpning inom byggbranschen. Denna studie avser att undersöka skjuvstyvhet, böjstyvhet och bärförmåga hos sandwichelement uppbyggda av core-materialet Greenwood och ytskikt av papp. Detta genom att först  dynamiskt och statiskt testa de ingående materialens egenskaper, följt av böjprovning av nio sandwichbalkar med varierande tjocklek på ytskikten. Samtliga balkar testades även dynamiskt. Core-materialet Greenwood som ingick i sandwichelementen var endast den begränsande faktorn en gång av tio böjprov. När core-materialets skjuvstyvhet togs fram både dynamiskt och statiskt och när den omvandlades till en skjuvmodul visade det sig att Greenwood har en mer än dubbelt så stor styvhet som EPS-cellplast vid liknande densitet. Detta är intressant då denna cellplast ofta agerar som ett core-material i sandwichelement ute i byggbranschen. Testerna visar även på att balkarna har en relativt liten spridning vilket innebär att resultaten har god tillförlitlighet. Slutligen, kan det konstateras att dessa sandwichelement uppvisar sega egenskaper med en viss kvarvarande lastkapacitet även efter brott. Samtliga nämnda egenskaper ovan talar för en viss potential för tillämpning av dessa sandwichelement inom byggbranschen. Fortsatta studier av fukt- och krypegenskaper vid långtidsbelastning rekommenderas, vilket är viktigt för användning inom byggandet. De omfattande resultaten från föreliggande studie utgör dock ett bra underlag för fortsatta undersökningar och värdering av möjliga tillämpningar. / The construction industry`s greenhouse emissions, makes up for a large portion of Sweden’s total emissions. In order to reduce construction related emissions, a fair amount of fronts within the construction industry needs to be changed and streamlined. In the last couple of years, there has been a successive increase in the number of structures that are built from wood amongst other things, which is beneficial because the wood alternative is more climate friendly than steel and concrete. The current tough climate goals entails that more has to be done than just increasing the amount of wood constructions. The pulp industry is easy to write off because so far, it has not been relevant to the construction industry and because recycling is relatively prominent within that industry. From the sawmills that dismember wooden logs to lumber, leftover wood chips are transported to paper mills. Among other things, different cardboard packages that can be recycled are then made from those wood chips. The problem with these packages is that they can only be recycled a certain number of times before the fibers become unusable and instead, are used as biofuel. If building materials were to be able to be produced with these fibers, that would be a more long-lived use of them. A building material, recently invented, made of fiber from paper mills is the core-material “Greenwood”. Because the material is new and its properties for the most part are unknown, this requires that various studies are conducted that examines the different properties the material possesses that are relevant for a contingent enforcement within the construction industry. This study intends to examine the shear rigidity, flexural rigidity and maximum capacity for sandwich panels made from the core-material Greenwood and faces of paperboard. This was achieved by first dynamically and statically test the properties of the two different materials, followed by flexure testing nine sandwich beams with varying face thicknesses. Every beam was also tested dynamically. The core-material Greenwood which was a part of the sandwich panels, was only the limiting factor 1 time out of 10 flexure tests. When the shear rigidity of the core-material was calculated both statically and dynamically and when it was converted to a shear modulus it was shown that Greenwood has a rigidity of more than double that of EPS cellular plastic at similar density. This is interesting because this type of cellular plastic often acts as a core-material in sandwich structures found in the construction industry. The tests also show that the beams have a relatively small spread which means that the results have good reliability. Finally, it can be concluded that these  sandwich panels exhibit ductile properties with a certain lasting load capacity even after ultimate load has been reached. Every property mentioned above indicates that there is a certain potential for applicability of these sandwich panels within the construction industry. Continued studies of moisture properties and creep properties during long-term loading is recommended, which is important for a possible use within construction. The extensive results from this study constitutes a good basis for continued research and assessment of possible applications.