The results of a numerical study of interlaminar stresses within unsymmetrically laminated plates is presented. The focus of the study is upon the linear thermoelastic response of thin square laminated composite plates subjected to extensional, compressive, or thermal loading. Symmetric and unsymmetric 0/90, +45/-45, and 0/+45 laminate stacking sequences are examined to determine the effects of mismatch between adjacent layers in Poisson’s ratio, coefficient of mutual influence, and coefficients of thermal expansion. Since the out-of-plane (transverse) deflections of unsymmetric laminates are typically large, a geometrically nonlinear kinematic description is used to account for the large displacements and rotations. The geometrically nonlinear three-dimensional boundary value problems are formulated from nonlinear elasticity theory and approximate solutions are determined using the finite element method. A total Lagrangian, displacement-based, incremental finite element formulation is implemented using Newton’s method. Geometrically nonlinear global/local finite element analysis is used to obtain improved free edge stress predictions. For laminates subjected to external loading, the mismatch in material properties between adjacent layers causes interlaminar stresses to arise near the free edges. For unsymmetric laminates under external loading, the mismatch in material properties about the geometric midplane causes out-of-plane deflections. For the laminates and loading conditions considered, the results of this study show that the out-of- plane deflections of unsymmetric laminates reduce interlaminar shear stresses. In addition, the out-of-plane deflections reduce interlaminar normal stresses for some laminates and increase these stresses for others. For the two-layer unsymmetric laminates considered, the effect of out-of-plane deflections upon interlaminar normal stress was shown to be dependent upon the type of in-plane strain mismatch (i.e., normal and/or shear) caused by the dissimilar material properties. The results also show that as the out-of-plane deflections become large, the effects of geometric nonlinearity upon this stress-deformational response become important. These conclusions apply to extensional, compressive (prior to a change in mode shape), and thermal loading. The numerical results include interlaminar stresses for laminated plates which have buckled as a wide column under compressive loading. / Ph. D.

In this study, an analytical procedure to predict the strength and failure of laminated composite structures under monotonically increasing static loads is presented. A degenerated 3-D shell finite element that includes linear elastic and plastic material behavior with full geometric nonlinearity is used to determine stresses at selected points (Gauss quadrature points in each element) of the structure. Material stiffness (constitutive) matrices are evaluated at each Gauss point, in each lamina and in each element, and when the computed stress state violates a user selected failure criterion, the material stiffness matrix at the failed Gauss point is reduced. The reduction procedure involves setting the material stiffnesses to unity. Examples of isotropic, orthotropic, anisotropic and composite laminates are presented to illustrate the validity of the procedure developed and to evaluate various failure theories. Maximum stress, modified Hills (Mathers), Tsai-Wu (F₁₂ = 0), and Hashin's failure criteria are included. The results indicate that for large length-to-thickness ratios, the geometric nonlinear effect should be incorporated for both isotropic and anisotropic structures. The nonlinear material model influences the behavior of isotropic structures with small length-to-thickness ratios, while having nearly no effect at all on laminated anisotropic structures. Of the four failure theories compared, each predicts failure at nearly the same load levels and locations. Hashin's criterion is particularly noteworthy in that the mode is also predicted. / Ph. D.

Composite laminates are prone to delamination at free edges, straight edges or at holes, due to the mismatch at interfaces where two adjacent plies have different fiber orientations and/or different material properties. The linear analysis of the mismatch at the edge results in a mathematical singularity. That phenomenon occurs in a boundary layer and has to be treated mathematically and physically as such. In the literature it is called the "Boundary Layer Effect" or simply the "Edge Effect". It is of great importance to recognize and be able to predict delamination locations at edges prone to such events. The goal of this research was to create a model capable of providing such a prediction. In an effort to generalize the model, the more complicated case of a free edge at holes in the composite laminate was chosen rather than the case of a straight free edge. A sequel of three major efforts was completed: 1) Development of the analysis of the free-edge effect at a hole in a composite laminate, 2) Performance of an extensive experimental program to provide data for the creation of the prediction model, and 3) On the basis of the analysis, establishment of the model, and comparison with the experimental results. The prediction model consists of two major products of the analysis, the order of the singularity and the strain energy release rate. Both are useful in locating the interface most prone to delaminate and the point along the hole circumference where it initiates. Two material systems (AS4/3501-6 and AS4/1808) and two stacking sequences [(0/45/0/-45)_s)₄] and [ (0/45/90/-45)_s)₄]s , quasi-orthotropic and quasi-isotropic respectively, were quasi-statically tested under tension and compression. The specimens were X-rayed after each loading stage in order to locate the initiation of delaminations. The fact that both materials consisted of the same type of fibers, was an excellent opportunity to examine the performance of the matrix and its influence on the process of delamination. Matrix dependent behavior was successfully examined and studied through the experiments and the prediction model. Results showed good correlation and high sensitivity to the type of matrix material involved. / Ph. D.

The computer algebra system MACSYMA is used to derive the nonlinear expression for the Lagrangian and the nonlinear equations of motion of composite plates undergoing large deformations by using a higher-order shear-deformation theory. When computer algebra is not used, the derivation of these equations is very involved and time consuming. A time-averaged-Lagrangian technique is developed for the nonlinear analysis of the response of a wide variety of physical systems. It is a perturbation method that produces accurate second-order approximate solutions in the neighborhoods of different resonances. As an application of the technique, the nonlinear response of a fluid-relief valve is discussed in detail. The different resonances are studied, and in each case the responses are compared to those obtained by using the Galerkin procedure. The shortcomings of the latter procedure are pointed out. The time-averaged-Lagrangian technique is implemented in a MACSYMA code that produces second-order perturbation solutions. The effects of the quadratic nonlinearities are incorporated into the solution and different cases of resonances are fully investigated. First-order differential equations are derived for the evolution of the amplitudes and phases for the following resonances: primary resonance, subharmonic resonance of order one-half, and superharmonic resonance of order two. The evolution equations are used to determine the fixed point or constant solutions and the results are then used to obtain representative frequency-response and force-response curves for each case. The stability of the fixed points is investigated. The results show that stable and unstable solutions may coexist when multi-valued solutions are possible, the initial conditions determine which describes the response. The multi-valuedness of the solutions lead to the jump phenomenon. The results show that subharmonic resonances of order one-half cannot be activated unless the excitation amplitude exceeds a threshold value. Lastly, a numerical-perturbation approach is used to study modal interactions in the response of the surface of a liquid in a cylindrical container to a principal parametric resonant excitation in the presence of a two-to-one internal (autoparametric) resonance. The force-response curves exhibit saturation, jumps, and Hopf bifurcations. They also show that the response does not start until a certain threshold level of excitation is exceeded. The frequency-response curves exhibit jumps, pitchfork bifurcations, and Hopf bifurcations. For certain parameters and excitation frequencies between the Hopf bifurcation values, limit-cycle solutions of the modulation equations are found. As the excitation frequency changes, the limit-cycles deform and lose their stability through either pitchfork or cyclic-fold (saddie-node) bifurcations. Some of these saddle-node bifurcations cause a transition to chaos. The pitchfork bifurcations break the symmetry of the limit cycles. Period-three motions are observed over a narrow range of excitation frequencies. / Ph. D.

Compressive loads can cause local buckling in composite laminates that have a near-surface delamination. This buckling causes load redistribution and secondary loads, which in turn cause interlaminer stresses and delamination growth. The goal of this research effort was to enhance the understanding of this instability-related delamination growth in laminates containing either an embedded or an edge delamination. There were three primary tasks: 1) development of a geometrically nonlinear finite element analysis named NONLIN3D; 2) performance of a parametric analytical study to determine the effects of strain, delamination shape, and delamination size on the distribution of the strain energy release rate components along the delamination front; and 3) performance of a combined experimental and analytical study of instability-related delamination growth (IRDG). Two material systems (AS4/PEEK and IM7/8551-7) and two stacking sequences (0/90/90/0)₆ and (90/0/0/90)₆ were examined. The laminates were fabricated with Kapton inserts between the fourth and fifth plies from the top surface to give an initial delamination. The analysis predicted a large variation of G_I and G_II along the delamination front. The G_III component was always small. The location of maximum G_I and G_II depended on the delamination shape and applied strain. In general, the strain-energy release rates were small except in a small region. Hence, delamination growth was expected to occur over only a small portion of the delamination front. Experiments corroborated this prediction. The laminate stacking sequence had a large effect on the shape of the deformed region, the direction of delamination growth, and the strain at which delamination growth occurred. These effects were predicted by the analysis. The G_I component appeared to govern initial delamination growth in the IM7/8551-7 laminates. Matrix ply cracking generally accompanied delamination growth. In some cases fiber micro-buckling also occurred shortly after delamination growth occurred. / Ph. D.

Low frequency Lamb waves in composite laminates were investigated theoretically and experimentally. To have a general solution for Lamb wave propagation in multilayered composite laminates is not practical due to a large number of boundary conditions needed to be satisfied at the interlaminar interfaces. Various approximate theories have been proposed to model low frequency Lamb wave propagation in composite laminates. In the present study, an approximate solution was derived from an elementary shear deformation plate theory and was shown to work well in the low frequency, long wavelength region. A simple method, similar in configuration to the acousto-ultrasonic technique, was used to measure Lamb wave phase velocities. Low frequency Lamb waves, usually in the range of 10 kHz to 1 MHz, were generated. Dispersion curves of the lowest symmetric Lamb mode and the lowest antisymmetric Lamb mode were obtained. The experimental data were compared with the results obtained from the approximate solution for the lowest Lamb modes in the low frequency, long wavelength region for a unidirectional laminate, a symmetric cross-ply laminate, a symmetric quasi-isotropic laminate and an aluminum plate. There is good correlation between the data and the results obtained from the approximate solution, which suggests that the lowest Lamb modes are modeled adequately by the present theory in these cases. This experimental procedure of measuring phase velocities can be used to characterize laminated composite plates with and without damage since each material and stacking sequence gives distinct lowest symmetric and antisymmetric curves. Stiffness reduction of composite laminates caused by damage can be related to the change in Lamb wave propagation speed. Damage in the form of transverse cracks in the 90° plies of a [90/90/90/0], graphite/epoxy laminate reduced the phase velocities of the Lamb modes. The lowest antisymmetric mode is sensitive to stiffness reduction in composite plates. Consequently, axial stiffness reduction in [0/45/0/45/0/45], and [0]₁₂ woven graphite/polyimide composite laminates was monitored by the lowest antisymmetric Lamb mode. / Ph. D.

Free vibration, buckling and postbuckling analyses of laminated composite plates with multiple delaminations are presented. A fInite element method based on a layer-wise laminated composite plate theory is developed to formulate the problem. Geometric nonlinearity in the sense of von Karman and the imperfection in the plate in the form of initial global deflection and initial delamination openings are included. A simple contact algorithm which precludes the physically inadmissible overlapping between delaminated surfaces is proposed and incorporated in the analysis. A sublaminate concept is adopted in the analysis to reduce the computational efforts, and found to be efficient. Numerical results are obtained for through-the-width, circular and rectangular delaminations addressing the effects of the number of delaminations, their lengths and through-the-thickness and axial locations on the critical buckling load and buckling mode shapes as well as free vibration frequency and modes. Postbuckling responses are investigated with respect to different magnitudes and directions of initial imperfections. The effects of material anisotropy and contact condition between delaminated surfaces are also considered. It is found that the proposed approach is very efficient and powerful for solving the above mentioned problems. / Ph. D.

In this work, a finite element formulation and associated computer program is developed for the transient large deformation analysis of laminated composite plate/shell structures. In order to satisfy the plate/shell surface traction boundary conditions and to have accurate stress description while maintaining the low cost of the analysis, a newly assumed displacement field theory is formulated by adding higher-order terms to the transverse displacement component of the first-order shear deformation theory. The laminated shell theory is formulated using the Updated Lagrangian description of a general continuum-based theory with assumptions on thickness deformation. The transverse deflection is approximated through the thickness by a quartic polynomial of the thickness coordinate. As a result both the plate/shell surface tractions (including nonzero tangential tractions and nonzero normal pressure) and the interlaminar shear stress continuity conditions at interfaces are satisfied simultaneously. Furthermore, the rotational degree of freedoms become layer dependent quantities and the laminate possesses a transverse deformation capability (i.e. the normal strain is no longer zero). Analytical integration through the thickness direction is performed for both the linear analysis and the nonlinear analysis. Resultants of the stress integrations are expressed in terms of the laminate stacking sequence. Consequently, the laminate characteristics in the normal direction can be evaluated precisely and the cost of the overall analysis is reduced. The standard Newmark method and the modified Newton Raphson method are used for the solution of the nonlinear dynamic equilibrium equations. Finally, a variety of numerical examples are presented to demonstrate the validity and efficiency of the finite element program developed herein. / Ph. D.

Guadua angustifolia Kunth (Guadua) is a bamboo species native to South and Central America that has been widely used for structural applications in small and large-scale buildings, bridges and temporary structures. Currently, its structural use is regulated within seismic resistant building codes in countries such as Peru and Colombia. Nevertheless, Guadua remains a material for vernacular construction associated with high levels of manual labour and structural unpredictability. Guadua buildings are limited to two storeys due to the overall flexibility of the slender and hollow culms and its connection systems. Its axial specific stiffness is comparable to that of steel and hardwoods, but unlike wood, Guadua’s hollow structure and lack of ray cells render it prone to buckling along the grain and to transverse crushing. As a result, Guadua’s mainstream use in construction and transformation into standard sizes or engineered Guadua products is scarce. Therefore, this work focussed on the development of standardised flat industrial structural products from Guadua devising replicable manufacturing technologies and engineering methods to measure and predict their mechanical behaviour. Cross-laminated Guadua panels were developed using thermohydro-mechanically modified and laminated flat Guadua strips glued with a high performance resin. Guadua was subjected to thermo-hydro-mechanical (THM) treatments that modified its microstructure and mechanical properties. THM treatment was applied to Guadua with the aim of tackling the difficulties in the fabrication of standardised construction materials and to gain a uniform fibre content profile that facilitated prediction of mechanical properties for structural design. Densified homogenous flat Guadua strips (FGS) were obtained. Elastic properties of FGS were determined in tension, compression and shear using small-clear specimens. These properties were used to predict the structural behaviour of G-XLam panels comprised of three and five layers (G-XLam3 and G-XLam5) by numerical methods. The panels were assumed as multi-layered systems composed of contiguous lamellas with orthotropic axes orientated at 0º and 90º. A finite element (FE) model was developed, and successfully simulated the response of G-XLam3 & 5 panels virtually loaded with the same boundary conditions as the following experimental tests on full-scale panels. G-XLam3 and G-XLam5 were manufactured and their mechanical properties evaluated by testing large specimens in compression, shear and bending. Results from numerical, FE predictions and mechanical testing demonstrated comparable results. Finally, design and manufacturing aspects of the G-XLam panels were discussed and examples of their architectural and structural use in construction applications such as mid-rise buildings, grid shells and vaults are presented. Overall, this research studies THM treatments applied to Guadua in order to produce standardised engineered Guadua products (EGP), and provides guidelines for manufacturing, testing, and for the structural analysis and design with G-XLam panels. These factors are of key importance for the use of Guadua as a mainstream material in construction.

Painéis de Cross Laminated Timber (CLT) consistem em um elemento construtivo relativamente novo no cenário da construção civil internacional. No Brasil, a fabricação desta tecnologia iniciou-se há cerca de seis anos. Em razão de sua incipiente utilização em território nacional, não se formou ainda bibliografia consistente a seu respeito, suscitando questionamentos sobre o desempenho dos painéis ao longo da vida útil da edificação. Deve-se ressaltar também que o elemento construtivo estudado consiste em uma inovação, associada à pré-fabricação e a técnicas de fabricação digital, diferenciando-se das tecnologias convencionais com as quais arquitetos e projetistas estão acostumados a projetar. Consequentemente, observam-se frequentes dúvidas não apenas sobre o desempenho dos painéis, mas também associadas a como projetar, de forma eficaz e apropriada, um edifício em CLT. Logo, surge o interesse em aprofundar os estudos acerca da tecnologia, com o intuito de propor, ao final da pesquisa, recomendações para projetos arquitetônicos que visem incorporar painéis de CLT de produção brasileira. Dessa forma, estudou-se tanto o desempenho do elemento construtivo, no que diz respeito à segurança estrutural e à durabilidade, conforme a ABNT NBR 15575:2013, quanto o processo construtivo de edificações em CLT. Para a análise de desempenho mencionada foram realizados os seguintes ensaios laboratoriais: retenção e penetração do produto preservativo na matéria-prima utilizada para a fabricação dos painéis nacionais; impacto de corpo mole, impacto de corpo duro e determinação da resistência do painel às solicitações de peças suspensas; estanqueidade à água; verificação do comportamento do painel exposto à ação de calor e choque térmico; ensaios de delaminação. Ao final, em vista de inconformidades apontadas em alguns ensaios, constatou-se a necessidade de assegurar a qualidade no tratamento da matéria-prima e na colagem das lamelas, de modo a garantir a devida vida útil da edificação. Concluiu-se, também, que o CLT se apresenta, de fato, como uma alternativa extremamente promissora na construção civil. Contudo, seu emprego, deve ser planejado de maneira a se compreender e respeitar a intrínseca relação existente entre suas etapas construtivas e as soluções técnicas e arquitetônicas, para que se garanta adequado desempenho da edificação em uso. / Cross Laminated Timber (CLT) panels are a relatively new building component to the international construction sector. Their production in Brazil started around six years ago. Since its use is still scarce in the country, academic and technical references are still rare and there are uncertainties about the performance of the panels during the life of the building. In addition, CLT can be considered as an innovation, which is associated to pre-fabrication and digital technologies, being consequently different from usual building techniques. Therefore, the doubts concern not only the panels performance but also the appropriate design of the CLT building. In order to provide recommendations for architectural designs which will use Brazilian CLT panels, this research aims to extend the investigation of CLT in Brazil. The study focuses on structural performance and durability of CLT panels, according to the Brazilian regulation ABNT NBR 15575, and on the construction process of CLT buildings. The performance analysis is based on the following laboratory tests: retention and penetration of the wood preservatives used in the panels manufacture; soft body impact and hard body impact tests and suspended pieces loading tests; water tightness; heat and thermal shock test; delamination tests. Some of the tests results showed nonconformities. This indicates the importance of a quality control process of the wood preservation treatment and bonding of CLT layers, to ensure the proper performance of the building. In conclusion, CLT panels are indeed a promising alternative to the construction sector. However, its use must respect the intrinsic relation between construction steps, as well as technical and architectural solutions, in order to guarantee adequate performance of the CLT building.