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The optimal design of the postbuckling response of variable angle tow composite structures is an important consideration for future lightweight, high-performing structures. Based on this premise, a new optimisation tool is presented for shell-type structures. The starting point is an isogeometric framework which uses NURBS interpolation functions to provide a smooth description of the deformed shapes, thereby reducing the number of degrees of freedom with respect to standard finite elements. The stiffness variation is obtained by exploiting the same NURBS interpolation to describe lamination parameters, employed as intermediate optimisation variables. This choice allows the design space to be thoroughly explored with relatively few design variables in a smooth optimisation space. Therefore, the optimisation strategy is divided into two stages. Firstly, the optimal distribution of lamination parameters is determined using a gradient based algorithm. Afterwards, an actual distribution of fibre orientation is retrieved. The viability of the tool is tested firstly onto a cylindrical panel under compressive loading. Then, the postbuckling optimisation of a composite wingbox is given. For both structures, the optimised postbuckling response is compared with those of the corresponding quasi-isotropic baselines showing significant improvements.

peer-reviewed The stiffness-tailoring capability of Variable Angle Tow (VAT) laminates gives enhanced freedom to design thin-walled structures. One key advantage of tow steering is the ability to redistribute stresses improving buckling performance, leading to reduction in material weight and costs. The aim of this work is to optimise the initial postbuckling behaviour of a recently proposed VAT composite wingbox. The optimisation process is based on a fibre path parameterisation. It involves seeking the stacking sequence that minimises the displacements occurring in the postbuckling regime. This problem is solved by coupling the multi-modal Koiter asymptotic approach implemented with a solid-shell Finite Element environment through stochastic optimisation strategies. Results obtained regarding different optimisation scenarios show a much improved performance for the buckling and postbuckling response of the wingbox with respect to the initial VAT design. Additionally, manufacturing constraints are readily included in the optimisation program. The possibility of performing an efficient and robust optimisation process of a complex structure with a multi-modal Koiter asymptotic approach is demonstrated, showing its viability as a design tool for buckling dominated structures. A parametric study regarding the influence of steering radii shows that overcoming the current manufacturing constraint on minimum radius is worthy of investigation.

A new computational strategy for the elasto-plastic analysis of framed structures is proposed. The approach is composed of two levels of analysis: the frame level, based on a 3D mixed beam element, and the cross-section level, described through the Generalized Eigenvectors approach whose formulation is here extended for the analysis of materials with elasto-plastic behaviour. The proposed method, suitable for analyzing single beams as well as assemblages, can tackle composite cross-sections by taking into account all the stress components of the 3D solution.

The optimal design of shell structures undergoing buckling phenomena is nowadays an open problem, whose solution would provide interesting answers to both academy and industry. The main difficulty is represented by the high computational cost required for optimising a full-scale structure characterised by a relatively complex postbuckling behaviour. In this work, this topic is addressed by proposing an isogeometric solid-shell model. The equilibrium path is evaluated through a multimodal Koiter's method. The resulting postbuckling analysis turns out to be efficient and accurate, as shown by numerical examples.

The starting point of this work is the definition of an automatic procedure for evaluating the axial force-biaxial bending yield surface of steel and reinforced concrete sections in fire. It provides an accurate time-dependent expression of the yield condition by a section analysis carried out once and for all, accounting for the strength reduction of the materials, which is a function of the fire duration. The equilibrium state of 3D frames with such yield conditions, once discretized using beam finite elements, is then formulated as a nonlinear vectorial equation defining a curve in the hyperspace of the discrete variables and the fire duration. An incremental-iterative strategy is proposed for tracing this curve evaluating a sequence of safe states at increasing fire durations up to the limit fire duration, that is the time of exposure which leads to structural collapse. The procedure represents a global fire analysis able to take account of the stress redistribution over the frame. Numerical examples are given to illustrate the proposal.

A numerical stochastic strategy for optimising composite elastic shells undergoing buckling is presented. Its scope is to search for the best stacking sequence that maximises the collapse load considering the post-buckling behaviour. Its feasibility is due to a reduced order model built for each material setup starting from a hybrid solid-shell finite element model exploiting a multimodal Koiter method. The approach has no limitations concerning geometry, boundary conditions and material properties distribution. The collapse load is evaluated using a Monte Carlo simulation able to detect the worst imperfection shape, including a posteriori the imperfections in the reduced order model. For a limited number of parameters the proposal allows to analyse all the possible layups. In the general case, it uses a Monte Carlo scanning of the design parameters with different levels of adaptability. The optimisation of curved panels, also with stiffeners, confirms the feasibility and reliability of the proposed strategy.

In this paper a semi-analytic solution for the post-critical behavior of compressed thin walled members with generic cross sections is presented. It is based on the Koiter approach and the method of separation of variables. The buckling solution is exactly evaluated using a single sinusoidal function and the initial post-critical behavior is obtained as a decoupled sinusoidal series solution along the beam axis. A specialized integration scheme allows obtaining the solution with only a few terms and a very low cost, with respect to standard finite element analyses. This tool is then used to highlight the reason of the poor behavior of beam models enriched with cross section deformation modes in reconstructing the post-critical solution. Successful strategies are proposed in order to overcome these limitations. A series of numerical tests are reported.

In this paper we propose a powerful tool for the evaluation of the initial post-buckling behavior of multi-layered composite shells and beams in both bifurcation and limit load cases, including mode interaction and imperfection sensitivity. This tool, based on the joint use of a specialized Koiter asymptotic method and a mixed solid-shell finite element model, is accurate, simple and characterized by a computational cost far lower than standard path-following approaches and many advantages with respect to asymptotic analysis performed with shell elements. The method is very simple and easy to include in existing FE codes because it is based on the same ingredients of a linearized buckling analysis, with very light formula due to the presence of displacement degrees of freedom only. Due to its efficiency it is suitable for layup design when geometrical nonlinearities have to be considered.

The paper proposes a 3D mixed finite element and tests its performance in elasto-plastic and limit analysis problems. A composite tetrahedron mesh is assumed over the domain. Within each element the displacement field is described by a quadratic interpolation, while the stress field is represented by a piece-wise constant description by introducing a subdivision of the element into four tetrahedral regions. The assumptions for the unknown fields make the element computationally efficient and simple to implement also in existing codes. The limit and elasto-plastic analyses are formulated as a unified mathematical programming problem allowing the use of Interior Point like algorithms. A series of numerical experiments shows that the proposed finite element is locking free and has a good plastic behavior. HighlightsThe element is simple and easy nevertheless is accurate and robust in plasticity.The displacement and stress interpolations produces an isostatic element.The element is locking free.The piece-wise constant stress addresses the discontinuities in the plastic strain.T.The numerical experiments show that the element is stable also with irregular meshes.

This paper compares two distinct approaches for obtaining the cross-section deformation modes of thin-walled members with deformable cross-section, namely the method of Generalized Eigenvectors (GE) and the Generalized Beam Theory (GBT). First, both approaches are reviewed, emphasizing their differences and similarities, as well as their resulting semi-analytical solutions. Then, the GE/GBT deformation modes for four selected cross-sections are calculated and examined in detail. Subsequently, attention is turned to the efficiency and accuracy of the GE/GBT mode sets in typical benchmark problems, namely the calculation of the global–local–distortional first-order and buckling (bifurcation) behaviors of bars with the previously analyzed cross-sections. It is concluded that GE and GBT, both based on the method of separation of variables, yield accurate results although they use different structural models and mode selection strategies. Therefore they offer complementary advantages, which are put forward in the paper.

In this work an automatic procedure for evaluating the axial force-biaxial bending yield surface of reinforced concrete sections in fire is proposed. It provides an accurate time-dependent expression of the yield condition by a section analysis carried out once and for all, accounting for the strength reduction of the materials, which is a function of the fire duration. The equilibrium state of 3D frames with such yield conditions, once discretized using beam finite elements, is formulated as a nonlinear vectorial equation defining a curve in the hyperspace of the discrete variables and the fire duration. A generalized path-following strategy is proposed for tracing this curve and evaluating, if it exists, the limit fire duration, that is the time of exposure which leads to structural collapse. Compared to the previous proposals on the topic, which are limited to local sectional checks, this work is the first to present a global analysis for assessing the fire resistance of 3D frames, providing a time history of the fire event and taking account of the stress redistribution. Numerical examples are given to illustrate and validate the proposal.

Shakedown analysis of 3D frames subjected to complex load combinations is presented.The strategy is suitable to treat n-dimensional load space (n of order of hundred).The algorithm avoids redundant constraints improving computational performances.The method deals with seismic actions coming from response spectrum analysis. A strategy for an efficient treatment of load combinations is proposed with the aim of making the shakedown analysis an affordable design tool to be used in practical applications. The paper refers to 3D frames subjected to complex combinations of statical and dynamical loads defined according to Eurocode rules. The yield surface of the sections is defined by its support function values associated to presso-flexural mechanisms and it is approximated as Minkowski sum of ellipsoids. An algorithm capable of detecting the significant vertexes of the elastic envelope and suitable for use in the case of response spectrum analyses, is proposed.

The classical Eurocode-compliant ultimate limit state (ULS) analysis of reinforced concrete sections is investigated in the paper with the aim of verifying if and how this well-established design procedure can be related to plasticity theory. For this reason, a comparative analysis concerning capacity surfaces of reinforced concrete cross sections, computed via a ULS procedure and a limit analysis approach, is presented. To this end, a preliminary qualitative discussion outlines modeling assumptions aiming to reproduce the physical behavior of reinforced concrete cross sections with respect to ductility and confinement issues. Besides the theoretical importance of the proposed approach, numerical experiments prove that limit analysis yields not only very accurate results but also a computationally effective procedure that can be affordably used in common design practice.

A geometrically nonlinear beam model suitable for describing complex 3D effects due to non-uniform warpings including non-standard in-plane distortions of the cross-section is presented and applied to the buckling analysis of beams. Each section is endowed with a corotational frame where statics and kinematics are described using a refined linear elastic model which exploits a semi-analytical solution of the Cauchy continuum problem based on a FEM discretization of the cross-section. The stress field in this way is fully 3D, allowing both the exact recovery of the standard Saint Venant solution and the consideration of some additional relevant strain modes of the cross-section that are evaluated in a simple and effective way. Numerical results are presented and compared with 3D shell reference solutions obtained by using the commercial code ABAQUS.

Shakedown analysis for elastic–perfect plastic structures is discussed and a fast incremental-iterative solution method is proposed, suitable for the FEM analyses of large structures. The theoretical motivations of the proposed method are discussed in detail and an example of its implementation is described with reference to plane frame analysis. Some numerical results are presented showing the numerical performances of the method.

The analysis of slender structures, characterized by complex buckling and postbuckling phenomena and by a strong imperfection sensitivity, is heavily penalized by the lack of adequate computational tools. Standard incremental iterative approaches are computationally expensive and unaffordable, while FEM implementation of the Koiter method is a convenient alternative. The analysis is very fast, its computational burden is of the same order as a linearized buckling load evaluation and the simulation of different imperfections costs only a fraction of that needed to characterize the perfect structure. In this respect it can be considered as a direct method for the evaluation of the critical and post-critical behaviour of geometrically nonlinear elastic structures. The main objective of the present work is to show that finite element implementations of the Koiter method can be both accurate and reliable and to highlight the aspects that require further investigation.

SUMMARY This paper refers to the analysis of the postbuckling behaviour of thin-walled structures by means of an asymptotic approach based on a finite element implementation of Koiter’s non-linear theory of instability. The analysis has been accomplished by using the following assumptions: (i) the structure is described as an assemblage of flat slender rectangular panels; (ii) a non-linear Kirchhoff-type plate theory is used to model each panel; (iii) HC finite elements discretization is used; (iv) linear and quadratic extrapolations are assumed for the fundamental and the postbuckling paths, respectively; (v) multimodal buckling is considered; and (vi) imperfection sensitivity analysis is performed in both multimodal and monomodal form based on the steepest-descent path criterion. Several numerical results are presented and discussed. Comparisons with numerical solution obtained by standard incremental codes are given, which show the accuracy and reliability of the proposed approach.