CAPES / Materiais compósitos laminados são utilizados em diversos setores da indústria, principalmente nas áreas automobilística de competição e aeroespacial, pois apresentam relações resistência-peso e rigidez-peso muito superiores aos materiais metálicos em geral. Estruturas fabricadas a partir desses materiais são normalmente finas e, consequentemente, estão sujeitas à flambagem. Requisitos tradicionais de projeto normalmente levam em conta a flambagem mas, para alguns casos, o projeto é conservador, visto que a estrutura pode ainda ser funcional no regime de pósflambagem. Entretanto, o comportamento nesse regime é não-linear, além da dificuldade de se estimar quando ocorre a falha da estrutura, o que torna a análise mais complexa e onerosa em relação à uma análise de flambagem linear. Nesse contexto está inserido o presente trabalho, que visa encontrar as orientações das fibras que maximizam as cargas de flambagem e de pós-flambagem de estruturas compósitas, usando no processo de otimização metamodelos para aliviar o custo computacional. Duas técnicas de metamodelagem são utilizadas e testadas: redes neurais artificiais e regressão de vetores de suporte, com ênfase para a última. Em combinação com os metamodelos são empregadas duas metaheurísticas de otimização desenvolvidas recentemente: o algoritmo harmony search e o algoritmo de vaga-lumes. Vários problemas com diferentes níveis de dificuldade são apresentados e discutidos. Os melhores resultados de otimização foram obtidos com o algoritmo de vaga-lumes associado ao metamodelo de regressão de vetores de suporte, mostrando que tais técnicas são promissoras na solução dessa classe de problemas. Como uma das principais contribuições desta tese tem-se a adaptação/implementação da técnica de regressão de vetores de suporte para problemas de empilhamento de lâminas em estruturas compósitas, particularmente na otimização em flambagem e pósflambagem. Além disso, foram realizados avanços na modelagem do comportamento e da otimização em pós-flambagem com a utilização de critérios de falha e de dano para compósitos. / Laminated composite materials are applied in many industrial sectors, particularly in competition automotive and aerospace fields, since they have strength-to-weight and stiffness-to-weight ratios much higher than the metals in general. Structures made by these materials are usually thin and hence they are subject to buckling. Traditional design requirements usually take into account the buckling, but in some cases the design is conservative since the structure can still be functional in the postbuckling regime. However, the behavior in this regime is nonlinear, in addition of being difficult to evaluate when the failure of the structure takes place, which makes the analysis more complex and computational expensive if compared to a linear buckling analysis. Within this context this work is inserted, which aims to find the orientations of the fibers that maximize the buckling and postbuckling load of composite structures using metamodels in the optimization process to alleviate the computational cost. Two metamodeling techniques are used and tested: artificial neural networks and support vector regression, with emphasis on the latter. In combination with the metamodels, two recently developed metaheuristics, the harmony search algorithm and the firefly algorithm, are employed. Several problems, with different levels of difficulty, are presented and discussed. The best optimization results were obtained with the firefly algorithm associated with the support vector regression metamodel, showing that these techniques are promising to solve this class of problems. One of the main contributions of this thesis is the adaptation/implementation of support vector regression for layup orientation sequence problems of composite structures, in particular for buckling and postbuckling optimizations. Moreover, advances were made in the modeling of the behavior and optimization in postbuckling regime using failure and damage criteria for composites.

CAPES / Materiais compósitos laminados são utilizados em diversos setores da indústria, principalmente nas áreas automobilística de competição e aeroespacial, pois apresentam relações resistência-peso e rigidez-peso muito superiores aos materiais metálicos em geral. Estruturas fabricadas a partir desses materiais são normalmente finas e, consequentemente, estão sujeitas à flambagem. Requisitos tradicionais de projeto normalmente levam em conta a flambagem mas, para alguns casos, o projeto é conservador, visto que a estrutura pode ainda ser funcional no regime de pósflambagem. Entretanto, o comportamento nesse regime é não-linear, além da dificuldade de se estimar quando ocorre a falha da estrutura, o que torna a análise mais complexa e onerosa em relação à uma análise de flambagem linear. Nesse contexto está inserido o presente trabalho, que visa encontrar as orientações das fibras que maximizam as cargas de flambagem e de pós-flambagem de estruturas compósitas, usando no processo de otimização metamodelos para aliviar o custo computacional. Duas técnicas de metamodelagem são utilizadas e testadas: redes neurais artificiais e regressão de vetores de suporte, com ênfase para a última. Em combinação com os metamodelos são empregadas duas metaheurísticas de otimização desenvolvidas recentemente: o algoritmo harmony search e o algoritmo de vaga-lumes. Vários problemas com diferentes níveis de dificuldade são apresentados e discutidos. Os melhores resultados de otimização foram obtidos com o algoritmo de vaga-lumes associado ao metamodelo de regressão de vetores de suporte, mostrando que tais técnicas são promissoras na solução dessa classe de problemas. Como uma das principais contribuições desta tese tem-se a adaptação/implementação da técnica de regressão de vetores de suporte para problemas de empilhamento de lâminas em estruturas compósitas, particularmente na otimização em flambagem e pósflambagem. Além disso, foram realizados avanços na modelagem do comportamento e da otimização em pós-flambagem com a utilização de critérios de falha e de dano para compósitos. / Laminated composite materials are applied in many industrial sectors, particularly in competition automotive and aerospace fields, since they have strength-to-weight and stiffness-to-weight ratios much higher than the metals in general. Structures made by these materials are usually thin and hence they are subject to buckling. Traditional design requirements usually take into account the buckling, but in some cases the design is conservative since the structure can still be functional in the postbuckling regime. However, the behavior in this regime is nonlinear, in addition of being difficult to evaluate when the failure of the structure takes place, which makes the analysis more complex and computational expensive if compared to a linear buckling analysis. Within this context this work is inserted, which aims to find the orientations of the fibers that maximize the buckling and postbuckling load of composite structures using metamodels in the optimization process to alleviate the computational cost. Two metamodeling techniques are used and tested: artificial neural networks and support vector regression, with emphasis on the latter. In combination with the metamodels, two recently developed metaheuristics, the harmony search algorithm and the firefly algorithm, are employed. Several problems, with different levels of difficulty, are presented and discussed. The best optimization results were obtained with the firefly algorithm associated with the support vector regression metamodel, showing that these techniques are promising to solve this class of problems. One of the main contributions of this thesis is the adaptation/implementation of support vector regression for layup orientation sequence problems of composite structures, in particular for buckling and postbuckling optimizations. Moreover, advances were made in the modeling of the behavior and optimization in postbuckling regime using failure and damage criteria for composites.

Orientador: Marco Lúcio Bittencourt / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecânica / Made available in DSpace on 2018-08-24T09:08:40Z (GMT). No. of bitstreams: 1 LimaeSilva_RafaelAugustode_M.pdf: 10555723 bytes, checksum: 1d037ebafbabc24e214c06ad76c5f54a (MD5) Previous issue date: 2013 / Resumo: O trabalho descreve o projeto mecânico convencional de uma biela automotiva de motor de combustão interna e apresenta uma metodologia alternativa baseada em métodos de otimização estrutural com o objetivo de reduzir a massa do componente. Para tal, é feita a descrição de todos os parâmetros de projeto assim como a definição de critérios de projeto. Em virtude da criticidade da aplicação selecionada, motor de ciclo Diesel utilizado em caminhões de trabalho pesado com picos de pressão de combustão de até 240 bar, a biela foi projetada sem bucha utilizando-se extensivamente os métodos numéricos. O Método dos Elementos Finitos foi aplicado para cálculo de tensões, deslocamentos, pressões de contato, flambagem, fadiga e para a síntese modal de componentes utilizados na análise dinâmica de multicorpos com mancais elasto-hidrodinâmicos. Dois modelos de fadiga dos materiais foram estudados: o modelo americano baseado no diagrama de Goodman e tensões principais e o modelo alemão baseado no diagrama de Haigh e efeito do gradiente de tensões multiaxiais; dos quais concluiu-se que o modelo americano é suficiente para o projeto da biela ao passo que o modelo alemão traz oportunidades adicionais de redução de massa. A otimização topológica, otimização de forma e análise de sensibilidade permitiram a obtenção de uma biela 210g (3\%) mais leve e com melhor desempenho dos mancais hidrodinâmicos. Finalmente, concluiu-se que o Método da Otimização Topológica apresenta oportunidades interessantes aos projetistas na fase de conceituação de produtos como alternativa aos desenhos convencionais, no entanto, demanda esforço adicional para o atendimento de todos os critérios de projeto do componente / Abstract: The present work consists of the conventional mechanical design description of an internal combustion engine connecting rod and also the proposal of an alternative methodology based on optimization methods with the objective of reducing the component mass. Therefore, it is performed a detailed view of all design parameters as well as the definition of design criteria. Because of the critical application selected, Diesel engine of heavy duty truck with combustion pressure reaching up to 240bar, the connecting rod was designed without bushing and with extensive use of numerical methods. The Finite Element Method was applied to assess stresses, displacements, contact pressures, buckling, fatigue and to perform the Component Modal Synthesis for multi-body dynamics simulation with elasto-hydrodynamic bearings. Two fatigue models were studied: the American model based on Goodman's diagram and principal stresses and the German model based on Haigh's diagram and multiaxial stress gradient effect; from which it was concluded that the American model is enough to design the connecting rod, while the German model presents additional weight reduction opportunities. The topology optimization, shape optimization and sensitivity analysis enabled a 210g (3\%) lighter connecting rod with improved bearings performance. Finally, it was concluded that the Topology Optimization Method presents good opportunities for the design engineers in the conceptual phases of product development with alternatives to the conventional designs. However, additional effort is necessary to fit the concept into all design criteria / Mestrado / Mecanica dos Sólidos e Projeto Mecanico / Mestre em Engenharia Mecânica

The collapse of the I-35W Bridge in Minneapolis, MN on August 1, 2007 brought into question the design and inspection of gusset plates in steel truss bridges. The experimental tests performed in this research study the sway-buckling strength and behavior of large-scale steel gusset plates in an isolated truss connection. Parameters studied include plate thickness,combination member loading, initial out-of-plane imperfection, diagonal compression member out-of-plane flexural stiffness, corrosion, and alternative retrofits to increase lateral stiffness. The flexural stiffness of the diagonal compression member and retrofit designs were unique to the testing program. The variables monitored during testing include gusset plate surface stresses and strains, member axial strains, out-of-plane displacement of the gusset plate free edge, and buckling capacity. The results were compared with previously established design models for predicting buckling capacity of gusset plates which include the Whitmore effective width, the Modified-Thornton method, and the FHWA Load Rating Guidelines. A parametric finite element model was developed to determine the lateral stiffness of the gusset plate connection and the additional stiffness provided by the alternative retrofit options. The results showed interaction between the diagonal compression member and gusset plate occurs, which affects sway-buckling capacity. Combination of member loads showed evidence of detrimental effects on sway-buckling capacity. Corrosion of the gusset plates along the top edge of the bottom chord did not lead to significant reduction in sway-buckling capacity. The two retrofit designs showed increases in both lateral stiffness and buckling capacity as well as economic benefits over traditional retrofit methods. Comparison of the results to the current design guidelines showed that the current methods are conservative and do not accurately represent the true behavior of gusset plate connections. The research concludes with two proposed models for future use in design and retrofit of gusset plates. The first is a member-gusset plate interaction model based on a stepped column analogy that takes into account the effects of member flexural stiffness and gusset plate stiffness. The second is a general design guideline developed for retrofit of gusset plate connections dominated by sway-buckling behavior which uses a stiffness based approach to increase the capacity of gusset plate connections. / Graduation date: 2012

The discovery of carbon nanotubes (CNTs) in 1991 by Iijima revealed the possibility of ultra-strong materials exploiting the properties of materials at smaller length scales. The superior strength, stiffness, and ability to perform under extreme conditions motivated researchers to investigate further on CNTs and similar materials at nanoscale. This resulted in discovery of various nanostructures such boron nitride nanotubes (BNNTs), graphene, hexagonal boron nitride sheets etc. Many of such nanostructures exhibited superior strength and stiffness comparable to that of CNTs. Out of these nanotubes, BNNTs have recently attracted attention from researchers due to their excellent mechanical properties similar to that of CNTs along with better chemical and thermal stability. Thus, BNNTs can be used for varieties of applications such as protective shield for nanomaterials, optoelectronics, bio-medical, nano spintronics, field-emission tips in scanning tunneling and atomic force microscope, and as reinforcement in composites. BNNTs are also used in other applications such as water cleansing, hydrogen storage, and gas accumulators. To exploit these ultra-strong materials, the mechanics of materials under different conditions of loading and failure need to be studied and understood. Also, to make use of the material in a nanocomposite or other applications, the material properties should be evaluated. The present work is focused on the computational study of the mechanics of nanotubes with special reference to BNNTs and CNTs. Note that the attention is not given to the material but to the nanostructure and mechanics. Hence depending on the state-of-the-art, BNNTs and CNTs are used wherever it is appropriate along with justifications. The chapter-wise outline of the present work is given below. The first chapter is an introduction along with a state-of-the-art literature review. The second chapter introduces the molecular simulation methodology in brief. The chapters from the third to the seventh present the work in detail and describe the major contributions. The final chapter summarizes the work along with a few possible directions to extend the present work. Chapter 1 In this chapter, the importance of computational techniques to study the mechanics at the nanoscale is outlined. A brief introduction to various nanostructures and nanotubes are also given. A detailed literature review on the mechanics of nanotubes with special attention to elastic properties, buckling, tensile failure, and as reinforcement in nanocomposites is presented. Chapter 2 In this chapter, the molecular simulation technique is outlined. The molecular dynamics (MD) simulation is one of the most common simulation techniques used to study materials at the nanoscale. A few interatomic potentials that are used in an MD simulation are explained. Theories linking continuum mechanics with the molecular dynamics are also explained here. Chapter 3 In this chapter, the elastic behavior of single-walled BNNTs under axial and torsional loading is studied. Molecular dynamics (MD) simulation is carried out with a tersoff potential for modeling the interatomic interactions. Different chiral configurations with similar diameter are considered to study the effect of chirality on the elastic and shear moduli. Furthermore, the effects of tube length on elastic modulus are also studied by considering different aspects ratios. It is observed that both elastic and shear moduli depend on the chirality of a nanotube. For aspect ratios less than 15, the elastic modulus reduces monotonically with an increase in the chiral angle. For chiral nanotubes the torsional response shows a dependence on the direction of loading. The difference between the shear moduli against and along the chiral twist directions is maximum for a chiral angle of 15◦, and zero for zigzag (0◦) and armchair (30◦) configurations. Chapter 4 Buckling of nanotubes have been studied using many methods such as MD, molecular mechanics, and continuum based shell theories. In MD, motion of the individual atoms are tracked under an applied temperature and pressure, ensuring a reliable estimate of the material response. The response thus simulated varies for individual nanotubes and is only as accurate as the force field used to model the atomic interactions. On the other hand, there exists a rich literature on the understanding of continuum mechanics based shell theories. Based on the observations on the behavior of nanotubes, there have been a number of shell-theory-based approaches to study the buckling of nanotubes. Although some of these methods yield a reasonable estimate of the buckling stress, investigation and comparison of buckled mode shapes obtained from continuum analysis and MD are sparse. Previous studies show that a direct application of shell theories to study nanotube buckling often leads to erroneous results. In this chapter, the nonlocal effect on the mechanics of nanostructures is studied using Eringen’s nonlocal elasticity. The buckling of carbon nanotubes is considered as an example to demonstrate and understand the nonlocal effect in the nanotubes. Single-walled armchair nanotubes with the radius varying from 3.4nm to 17.7nm are considered and their critical buckling stresses are predicted based on multiscale modeling techniques including classical and nonlocal continuum mechanics theories and MD simulation. Fitting nonlocal mechanics models to MD simulation yields a radius-dependent length-scale parameter, which increases approximately linearly with the radius of carbon nanotube. In addition, the nonlocal shell model is found to be a better continuum model than the nonlocal beam model due to its ability to include the circumferential nonlocal effect. Chapter 5 In this chapter, the effects of geometrical imperfections on the buckling of nanotubes are studied. The present study reveals that a major source of the error in continuum shell theories in calculating the buckling stress can be attributed to the geometrical imperfections. Here, geometrical imperfections refer to the departure of the shape of the nanotube from a perfect cylindrical shell. Analogous to the shell buckling in the macro-scale, in this work the nanotube is modeled as a thin-shell with initial imperfection. Then a nonlinear buckling analysis is carried out using the Riks method. It is observed that this proposed approach yields significantly improved estimate of the buckling stress and mode shapes. It is also shown that the present method can account for the variation of buckling stress as a function of the temperature considered. Hence, this turn out to be a robust method for a continuum analysis of nanotubes taking in the effect of variation of temperature as well. Chapter 6 In this chapter, the effects of Stone-Wales (SW) and vacancy defects on the failure behavior of BNNTs under tension are investigated using MD simulations. The Tersoff-Brenner potential is used to model the atomic interaction and the temperature is maintained close to 300 K. The effect of a SW defect is studied by determining the failure strength and failure mechanism of nanotubes with different radii. In the case of a vacancy defect, the effect of an N-vacancy and a B-vacancy is studied separately. Nanotubes with different chirality but similar diameter are considered first to evaluate the chirality dependence. The variation of failure strength with the radius is then studied by considering nanotubes of different diameter but same chirality. It is observed that the armchair BNNTs are extremely sensitive to defects, whereas the zigzag configurations are the least sensitive. In the case of pristine BNNTs, both armchair and zigzag nanotubes undergo brittle failure, whereas in the case of defective BNNTs only the zigzag ones undergo brittle failure. An interesting defect-induced plastic behavior is observed in defective armchair BNNTs. For this nanotube, the presence of a defect triggers mechanical relaxation by bond breaking along the closest zigzag helical path, with the defect as the nucleus. This mechanism results in a plastic failure. Chapter 7 In this chapter, the utility of BNNTs as reinforcement for nanocomposites with metal matrix is studied using MD simulation. Due to the light weight, aluminium is used as the matrix. The influence of number of walls on the strength and stiffness of the nanocomposite is studied using single-and double-walled BNNTs. The three body tersoff potential is used to model the atomic interactions in BNNTs, while the embedded atom method (EAM) potential is used to model the aluminium matrix. The van der Waals interaction between different groups — the aluminium matrix with the nanotube or the between the concentric tubes in double walled BNNT — is modeled using a Lennard Jones potential. A representative volume element approach is used to model the nanocomposite. The constitutive relations for the nanocomposite is also proposed wherein the elastic constants are obtained using the MD simulation. The nanocomposite with reinforcement shows improved axial stiffness and strength. The double-walled BNNT provides more strength to the nanocomposite than the single-walled BNNT. The BNNT reinforcement can be used to design nanocomposites with varying strength depending on the direction of the applied stress. Chapter 8 The summary of the work with a broad outlook is presented in this chapter. The major conclusions of the work are reiterated and possible directions for taking the work further ahead are mentioned.

Aujourd’hui, la technologie du béton ayant fortement évolué, il est, sous certaines conditions, réaliste de construire des éléments structuraux en béton ayant à la compression une résistance de 90N/mm² voire nettement plus. En conséquence, l’ingénieur concepteur peut être amené dans le cadre du dimensionnement des colonnes à en diminuer les dimensions transversales pour des raisons esthétiques ou d’encombrement. <p><p>Inévitablement, cette diminution de la section transversale induit une augmentation de l’élancement et augmente ainsi les risques des instabilités de flambement. <p>A cette question de flambement, il faut adjoindre l’influence d’une préconception qui veut qu’une structure en béton à haute résistance soit moins ductile qu’une structure construite avec un béton normal !De ceci résulte la question à la base de ce travail :<p><p>« Peut-on arriver à diminuer la section transversale d’une colonne en utilisant des résistances de béton plus élevées tout en imposant la même valeur de capacité portante et en ne réduisant pas leur ductilité ?»<p><p>Afin de répondre à cette question, le travail s’est articulé autour de deux axes essentiels qui sont d’une part une campagne d’essais (afin d’obtenir des résultats fiables) sur 12 colonnes en béton armé à haute résistance (90N/mm²) d’élancement 74 et 82 dont l’excentricité de la charge est une variable, et d’autre part l’implémen- tation de deux programmes informa- tiques utilisant le principe de l’analyse au second ordre en vue de réaliser une étude paramétrique dont l’excentricité, la hauteur des colonnes, la proportion d’acier, la résistance du béton sont les variables.<p><p>Trop souvent encore, les ingénieurs de bureau d’études hésitent à effectuer un calcul au second ordre et placés devant la question des dimensions de section à donner à une colonne de hauteur et de capacité portante imposées, déterminent celles-ci pour se satisfaire d’un calcul au 1er ordre. Au terme de notre étude, nous avons montré que cette approche est loin d’être optimale, qu’il est possible, au prix d’un calcul au second ordre (mais il est fait à l’ordinateur), de tirer profit d’une augmentation de la résistance du béton pour réduire les dimensions des sections et aboutir en toute sécurité à un dimensionnement plus économique en consommation de matériaux (acier, béton, ciment).<p><p> / Doctorat en sciences appliquées / info:eu-repo/semantics/nonPublished

The considerable progress in the research and development of thin-walled beam structures responds to their growing use in engineering construction and to their increased need for efficiency in strength and cost. The result is a structure that exhibits large shear strains and important non uniform warping under different loadings, such as non uniform torsion, shear bending and distortion.<p><p>A unified approach is formulated in this thesis for 3D thin walled beam structures with arbitrary profile geometries, loading cases and boundary conditions. A single warping function, defined by a linear combination of longitudinal displacements at cross sectional nodes (derived from Prokic work), is enhanced and adapted in order to qualitatively and quantitatively reflect and capture the nature of a widest possible range of behaviors. Constraints are prescribed at the kinematics level in order to enable the study of arbitrary cross sections for general loading. This approach, differing from most published theories, has the advantage of enabling the study of arbitrary cross sections (closed/opened or mixed) without any restrictions or distinctions related to the geometry of the profile. It generates automatic data and characteristic computations from a kinematical discretization prescribed by the profile geometry. The amount of shear bending, torsional and distortional warping and the magnitude of the shear correction factor is computed for arbitrary profile geometries with this single formulation.<p><p>The proposed formulation is compared to existing theories with respect to the main assumptions and restrictions. The variation of the location of the torsional center, distortional centers and distortional rotational ratio of a profile is discussed in terms of their dependency on the loading cases and on the boundary conditions.<p><p>A 3D beam finite element model is developed and validated with several numerical applications. The displacements, rotations, amount of warping, normal and shear stresses are compared with reference solutions for general loading cases involving stretching, bending, torsion and/or distortion. Some examples concern the case of beam assemblies with different shaped profiles where the connection type determines the nature of the warping transmission. Other analyses –for which the straightness assumption of Timoshenko theory is relaxed– investigate shear deformation effects on the deflection of short and thin beams by varying the aspect ratio of the beam. Further applications identify the cross sectional distortion and highlight the importance of the distortion on the stresses when compared to bending and torsion even in simple loading cases. <p><p>Finally, a non linear finite element based on the updated lagrangian formulation is developed by including torsional warping degrees of freedom. An incremental iterative method using the arc length and the Newton-Raphson methods is used to solve the non linear problem. Examples are given to study the flexural, torsional, flexural torsional and lateral torsional buckling problems for which a coupling between the variables describing the flexural and the torsional degrees of freedom occurs. The finite element results are compared to analytical solutions based on different warping functions and commonly used in linear stability for elastic structures having insufficient lateral or torsional stiffnesses that cause an out of plane buckling. <p> / Doctorat en sciences appliquées / info:eu-repo/semantics/nonPublished

Indiana University-Purdue University Indianapolis (IUPUI) / Crashworthiness design is gaining more importance in the automotive industry due to high competition and tight safety norms. Further there is a need for light weight structures in the automotive design. Structural optimization in last two decades have been widely explored to improve existing designs or conceive new designs with better crashworthiness and reduced mass. Although many gradient based and heuristic methods for topology and topometry based crashworthiness design are available these days, most of them result in stiff structures that are suitable only for a set of vehicle components in which maximizing the energy absorption or minimizing the intrusion is the main concern. However, there are some other components in a vehicle structure that should have characteristics of both stiffness and flexibility. Moreover, the load paths within the structure and potential buckle modes also play an important role in efficient functioning of such components. For example, the front bumper, side frame rails, steering column, and occupant protection devices like the knee bolster should all exhibit controlled deformation and collapse behavior. This investigation introduces a methodology to design dynamically crushed thin-walled tubular structures for crashworthiness applications. Due to their low cost, high energy absorption efficiency, and capacity to withstand long strokes, thin-walled tubular structures are extensively used in the automotive industry. Tubular structures subjected to impact loading may undergo three modes of deformation: progressive crushing/buckling, dynamic plastic buckling, and global bending or Euler-type buckling. Of these, progressive buckling is the most desirable mode of collapse because it leads to a desirable deformation characteristic, low peak reaction force, and higher energy absorption efficiency. Progressive buckling is generally observed under pure axial loading; however, during an actual crash event, tubular structures are often subjected to oblique impact loads in which Euler-type buckling is the dominating mode of deformation. This undesired behavior severely reduces the energy absorption capability of the tubular structure. The design methodology presented in this paper relies on the ability of a compliant mechanism to transfer displacement and/or force from an input to desired output port locations. The suitable output port locations are utilized to enforce desired buckle zones, mitigating the natural Euler-type buckling effect. The problem addressed in this investigation is to find the thickness distribution of a thin-walled structure and the output port locations that maximizes the energy absorption while maintaining the peak reaction force at a prescribed limit. The underlying design for thickness distribution follows a uniform mutual potential energy density under a dynamic impact event. Nonlinear explicit finite element code LS-DYNA is used to simulate tubular structures under crash loading. Biologically inspired hybrid cellular automaton (HCA) method is used to drive the design process. Results are demonstrated on long straight and S-rail tubes subject to oblique loading, achieving progressive crushing in most cases.