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Thin-walled structures inevitably always have manufacturing deviations, which affects the assembly quality of mechanical products. The assembly quality directly determines the performances, reliability and service life of the products. To achieve the automatic assembly of large-scale thin-walled structures, the sizing force of the structures with deviations should be calculated, and its assembling ability should be studied before assembly process. The purpose of this study is to establish a precise model to describe the deviations of structures and to study the variation propagation during assembly process.

Curved thin-walled structures are modeled by using the shell element via the absolute nodal coordinate formulation. Two typical deviation modes of the structure are defined. The generalized elastic force of shell elements with anisotropic materials is deduced based on a continuum mechanics approach to account for the geometric non-linearity. The quasi-static method is introduced to describe the assembly process. The effects of the deviation forms, geometrical parameters of the thin-walled structures and material properties on assembly quality are investigated numerically.

The geometric non-linearity of structure and anisotropy of materials strongly affect the variation propagation and the assembly quality. The transformation and accumulation effects of the deviations are apparent in the multiple assembly process. The constraints on the structures during assembly can reduce assembly deviation.

The plate element via the absolute nodal coordinate formulation is first introduced to the variation propagation analysis. Two typical shape deviation modes are defined. The elastic force of structures with anisotropic materials is deduced. The variation propagation during the assembly of structures with various geometrical and material parameters is investigated.

The load carrying capacity of steel structures, built of slender members like bridge cross‐sections, depends on coupled yielding and buckling of the stringers and the plate strips as well as on the global buckling. Therefore, the common techniques of modelling the limit load by an elasto‐plastic layer model fail. In order to overcome the difficulty a material law is developed, in which local buckling failure and yielding is considered. This is based on an energy function, which describes the elasto‐plastic intermediate and ultimate state of plates and webs dependent on only a few parameters. The application is shown on large scale examples of stiffened steel bridge decks.

A linear and geometrically non‐linear computation of a laminated composite torispherical shell subjected to internal pressure was performed by using the layered finite element whose formulation is based on degeneration principle. Geometric non‐linearity in terms of large deformations with total Lagrangian formulation was taken into account. The effect of the lamination schemes on geometric non‐linear behaviour and stress resultant distributions was analysed. The fibre directions have not a great influence on the shape of the load‐displacement curves. In contrast to the hoop stress resultant distribution, the moment distribution is significantly influenced by the lamination schemes. The influence of the lamination schemes on bending moments is greater in non‐linear than in linear computations. Likewise, the effect of the fibre orientation is greater on the hoop than on the meridional moment distribution. In unsymmetric laminated shells the values of the hoop moments exceed those of the meridional moments which is a considerable difference from metallic isotropic shells.

The purpose of this paper is to present an efficient engineering methodology for solving the problem of non‐linear (NL) damage and post‐buckling of large‐scale structures, which is of high importance mainly for the aircraft industry.

The methodology takes advantage of the capabilities of finite element substructuring technique in the simulation of large/complex structures and exploits the advantages of local‐global analysis logic. The main innovation deals with the appropriate modification of superelement method, such that it can deal with NL behaviour and efficiently model the entire large‐scale structure. In this study, the proposed methodology is demonstrated in the treatment of geometrical non‐linearity and its efficiency is assessed in the case of a large‐scale fuselage section.

A method capable of solving large‐scale NL problems by taking advantage of the linear response of the different model regions is developed.

Further development of the proposed method is required for handling other means of non‐linearity.

The proposed approach is advantageous in terms of computational effort over the corresponding conventional ones.

Purpose – The aim of this work is to provide a global 3D finite element (FE) model devoted to the modelling of superficial soil ploughing in the large deformation range and for a vast class of soil treatment tools. Design/methodology/approach – We introduced soil constitutive equation in a FE software initially designed for the metal forming. We performed the numerical integration of the non‐linear ploughing problem. Non‐linearities encountered by the problem can be summed up: as soil constitutive equation (idealized with non‐associated compressible plastic law), unilateral frictional contact conditions (with a rigid body), geometrical non‐linearities (the ploughing tool) and large deformation range. To handle such difficulties we performed several numerical methods as implicit temporal scheme, Newton‐Raphson, non‐symmetric iterative solver, as well as proper approximation on stress and strain measures. Findings – Main results deal with the validation of the integration of the non‐linear constitutive equation in the code and a parametric study of the ploughing process. The influence of tool geometric parameters on the soil deformation modes and on the force experienced on the tools had been point out. As well, the influence of soil characteristics as compressibility had been analyzed. Research limitations/implications – This research is devoted to perform a numerical model applicable for a large range of soil treatment tools and for a large class of soil. However, taking into account all kind of soil is utopist. So limitations met are essentially related to the limit of the accuracy of the elasto‐plastic idealization for the soil. Practical implications – In practice the numerical model exposed in the paper can clearly help to improve and optimize any process involving superficial soil submitted to the mechanical action of a rigid body. Originality/value – The original value of the paper is to provide a global and an applicable numerical model able to take into account the main topics related to the ploughing of superficial soils. Industrials in geotechnics, in agriculture or in military purposes can benefit in using such numerical model.

This paper deals with the well known degenerated shell element of Ahmad. The main concern focuses on the rank of the element stiffness matrix and the zero energy modes. Element formulation includes geometrical and material non‐linearities. The Lagrangian, heterosis and serendipity variants of displacement approximation are studied using full, selective or reduced in‐plane numerical integration. In the third direction the layered concept is adopted. The obtained results do not fully coincide with those published in References 2 and 3. The Figures presented in this paper, showing the displacement modes, clarify in a convenient form some of the element properties associated with particular element formulations. The work also shows the influence of the plastic and cracked material conditions on the stiffness matrix of the element.

The comparative efficiency of three flat triangular shell elements is being assessed for analysing non‐linear behaviour of general shell structures. The bending formulation of the three elements is based on a discrete Kirchhoff model (namely the well‐known 3‐node DKT element and a new 6‐node DKTP element). The in‐plane behaviour is defined by constant (CST), linear (LST)and quadratic (QST) strain approximations. The super‐position of bending and membrane elements leads to the 3‐node DCT element (DKT plus CST), the 3‐node DQT element (DKT plus QST) and the 6‐node DLT element (DKTP plus LST). The geometrically non‐linear formulation is based on an approximate updated Lagrangian formulation (AULF) and the solution is obtained by using the Newton‐Raphson method with an automatic arc‐length control method. Illustrative examples include pre‐ and post‐buckling of different shell structures showing, in particular, some bifurcation points, large rotations and displacements and very important membrane‐bending coupling.

The paper reviews the application of the finite element method to the analysis of large‐deflection elasto‐plastic behaviour and traces the development of such a solution for plated structures. The accuracy of the approach is established by many comparisons with available solutions for isolated plates and conclusions are drawn on suitable idealizations for plated structures. The results of an analysis of a typical plate girder, allowing fully for the interaction between the component plates, are presented. Comparisons with experimentally measured values for the girder confirm the validity of the proposed approach for the study of the collapse modes of plated structures. The need for expensive experimentation is thereby reduced.

Nowadays, simplified inverse or one step approaches for the sheet forming modeling are increasingly used in the automobile industry, since they allow to quickly realize the preliminary design and especially to optimize the process parameters. These methods often based on implicit static algorithms cause sometimes convergence problems because of strong non‐linearities. This paper deals with several initial guess methods to speed up the convergence of the implicit static solver used in the inverse approach for stamping modeling. The blank's mesh as initial solution is obtained by geometrical considerations based on the known shape of the final 3D workpiece. Three algorithms for the estimation of the blank's mesh have been developed and compared. The application to several industrial problems shows their efficiency and performance.

During the 1970s 4 steel bridges in Australia, England, Austria and Germany, failed due to the buckling of their compressed plates. As a result of these failures much research, both theoretical and experimental, has been initiated.