On the role of large cross-sectional deformations in the nonlinear analysis of composite thin-walled structures

AbstractThe geometrical nonlinear effects caused by large displacements and rotations over the cross section of composite thin-walled structures are investigated in this work. The geometrical nonlinear equations are solved within the finite element method framework, adopting the Newton–Raphson scheme and an arc-length method. Inherently, to investigate cross-sectional nonlinear kinematics, low- to higher-order theories are employed by using the Carrera unified formulation, which provides a tool to generate refined theories of structures in a systematic manner. In particular, beams and shell-like laminated composite structures are analyzed using a layerwise approach, according to which each layer has its own independent kinematics. Different stacking sequences are analyzed, to highlight the influence of the cross-ply angle on the static responses. The results show that the geometrical nonlinear effects play a crucial role, mainly when higher-order theories are utilized

On the role of large cross-sectional deformations in the nonlinear analysis of composite thin-walled structures

The geometrical nonlinear effects caused by large displacements and rotations over the cross section of composite thin-walled structures are investigated in this work. The geometrical nonlinear equations are solved within the finite element method framework, adopting the Newton–Raphson scheme and an arc-length method. Inherently, to investigate cross-sectional nonlinear kinematics, low- to higher-order theories are employed by using the Carrera unified formulation, which provides a tool to generate refined theories of structures in a systematic manner. In particular, beams and shell-like laminated composite structures are analyzed using a layerwise approach, according to which each layer has its own independent kinematics. Different stacking sequences are analyzed, to highlight the influence of the cross-ply angle on the static responses. The results show that the geometrical nonlinear effects play a crucial role, mainly when higher-order theories are utilized

Topology optimization considering geometrical nonlinear behavior

Foi realizada a validação de um programa de análise de elementos finitos não lineares já desenvolvido, PROAES_NL. Para tal, quatro exemplos encontrados na literatura foram resolvidos utilizando o programa e os resultados foram comparados com os valores apresentados em artigos publicados e também com os resultados obtidos com o software de elementos finitos ANSYS. O erro relativo entre os resultados obtidos utilizando o PROAES_NL e as duas outras fontes mencionadas anteriormente foi relativamente pequeno e o programa foi considerado validado. A teoria de cálculo de sensibilidades em estruturas com comportamento não linear desenvolvida por Santos [1] foi estudada, interpretada e traduzida para o domínio físico. As equações resultantes foram implementadas numericamente em linguagem Octave completando o código PROAES_NL usando apenas dados de pós-processamento de elementos finitos. Para validar as expressões de análise de sensibilidade utilizadas foram resolvidos cinco exemplos. Os resultados obtidos foram comparados com os valores obtidos pelo método das diferenças finitas e com os resultados apresentados por Santos [1]. O erro relativo entre o programa PROAES_NL e as fontes mencionadas anteriormente foi pequeno e as expressões de sensibilidade foram consideradas validadas. Além disso, é demonstrado que existe uma diferença entre o cálculo da análise de sensibilidades numa análise linear e numa análise não linear. As expressões de sensibilidades implementadas foram depois usadas para executar otimizações de topologia. O objetivo era verificar se haveria alguma diferença entre executar uma otimização de topologia utilizando análises lineares e não lineares. Embora alguns dos artigos estudados mostrem diferenças entre a configuração ótima obtida com análise linear e análise não linear, usando o programa PROAES_NL, a diferença foi visível em apenas um dos dois exemplos estudados. Durante a fase final deste trabalho, limitações na convergência da análise não linear resultaram em restrições na seleção dos parâmetros de otimização

Geometrical nonlinear analysis of thin-walled composite beams using finite element method based on first order shear deformation theory

Based on a seven-degree-of-freedom shear deformable beam model, a geometrical nonlinear analysis of thin-walled composite beams with arbitrary lay-ups under various types of loads is presented. This model accounts for all the structural coupling coming from both material anisotropy and geometric nonlinearity. The general nonlinear governing equations are derived and solved by means of an incremental Newton–Raphson method. A displacement-based one-dimensional finite element model that accounts for the geometric nonlinearity in the von Kármán sense is developed to solve the problem. Numerical results are obtained for thin-walled composite beam under vertical load to investigate the effects of fiber orientation, geometric nonlinearity, and shear deformation on the axial–flexural–torsional response

Stability of the human spine: a biomechanical study

The influences of curvatures and of physical properties on the mechanical stability of the spine were analysed by means of a three-dimensional, geometrical, nonlinear biomechanical model. According to the model, the initial buckling load decreases with increasing lordotic and kyphotic curvatures. When the body weight is taken into account as a load distributed along the whole spine, the calculated initial buckling load is twice the value that it is in the case of a single concentrated load acting at the top of the spine. Applying the large deflection theory, no relation is found between the increased slenderness of a spine and a ‘buckled’ configuration of a scoliotic spine

Geometrically nonlinear analysis of thin-walled composite box beams

A general geometrically nonlinear model for thin-walled composite space beams with arbitrary lay-ups under various types of loadings has been presented by using variational formulation based on the classical lamination theory. The nonlinear governing equations are derived and solved by means of an incremental Newton–Raphson method. A displacement-based one-dimensional finite element model that accounts for the geometric nonlinearity in the von Kármán sense is developed. Numerical results are obtained for thin-walled composite box beam under vertical load to investigate the effect of geometric nonlinearity and address the effects of the fiber orientation, laminate stacking sequence, load parameter on axial–flexural–torsional response

Geometrically nonlinear analysis of thin-walled open-section composite beams

A geometrically nonlinear model for general thin-walled open-section composite beams with arbitrary lay-ups under various types of loadings based on the classical lamination theory is presented. It accounts for all structural coupling coming from the material anisotropy and geometric nonlinearity. Nonlinear governing equations are derived and solved by means of an incremental Newton–Raphson method. The finite element model that accounts for the geometric nonlinearity in the von Kármán sense is developed to solve the problem. Numerical results are obtained for thin-walled composite Z-beam and I-beam to investigate effects of geometric nonlinearity, fiber orientation and warping restraint on the flexural–torsional response

Geometrically nonlinear theory of thin-walled composite box beams using shear-deformable beam theory

A general geometrically nonlinear model for thin-walled composite space beams with arbitrary lay-ups under various types of loadings is presented. This model is based on the first-order shear deformable beam theory, and accounts for all the structural coupling coming from both material anisotropy and geometric nonlinearity. The nonlinear governing equations are derived and solved by means of an incremental Newton–Raphson method. A displacement-based one-dimensional finite element model that accounts for the geometric nonlinearity in the von Kármán sense is developed. Numerical results are obtained for thin-walled composite box beams under vertical load to investigate the effects of shear deformation, geometric nonlinearity and fiber orientation on axial–flexural–torsional response

Emergence of geometrical optical nonlinearities in photonic crystal fiber nanowires

We demonstrate analytically and numerically that a subwavelength-core dielectric photonic nanowire embedded in a properly designed photonic crystal fiber cladding shows evidence of a previously unknown kind of nonlinearity (the magnitude of which is strongly dependent on the waveguide parameters) which acts on solitons so as to considerably reduce their Raman self-frequency shift. An explanation of the phenomenon in terms of indirect pulse negative chirping and broadening is given by using the moment method. Our conclusions are supported by detailed numerical simulations.Comment: 5 pages, 3 figure