[en] In this paper, the static response of three-dimensional beams made of functionally graded materials is investigated through a family of hierarchical one-dimensional finite elements. A wide variety of elements is proposed differing by the kinematic formulation and the number of nodes per elements along the beam axis. Elements’ stiffness matrix and load vector are derived in a unified nuclear form that does not depend upon the a priori expansion order over the cross-section nor the finite element approximation along the beam axis. Results are validated towards three-dimensional finite element models as well as equivalent Navier-type analytical solutions. The numerical investigations show that accurate and efficient solutions (when compared with full three-dimensional FEM solutions) can be obtained by the proposed family of hierarchical one-dimensional elements’ family

[en] This paper deals with the optimization of tube hydroforming parameters in order reduce defects which may occur at the end of forming process such as necking and wrinkling. We propose a specific methodology based on the coupling between an inverse method for the rapid simulation of tube hydroforming process, and a Response Surface Method based on diffuse approximation. The response surfaces are built using Moving Least Squares approximations and constructed within a moving region of interest which moves across a predefined discrete grid of authorized experimental designs. An application of hydroforming of a bulge from aluminium alloy 6061-T6 tubing has been utilized to validate our methodology. The final design is validated with ABAQUS Explicit Dynamic commercial code

[en] This paper proposes several axiomatic refined theories for the linear static analysis of beams made of functionally graded materials. A bi-directional variation upon the cross-section is accounted for. Via a unified formulation, a generic N-order approximation is assumed for the displacement unknown variables over the beam cross-section. The governing differential equations and the boundary conditions are derived in terms of a fundamental nucleo that does not depend upon the approximation order. A Navier type, closed form solution is adopted. Beams undergo bending and torsional loadings. Deep beams are investigated. Comparisons with three-dimensional finite element models are given. The numerical investigation shows that the proposed unified formulation yields the complete three-dimensional displacement and stress fields as long as the appropriate approximation order is considered.

[en] Research highlights: → Crack growth measurements are better estimated by the potential drop technique. → Crack propagation is faster at 550 than 450 ^oC for all the materials. → The crack propagates faster in the U720LC than in the U720PM mono-material. → The content of U720PM and U720LC mono-materials is very stochastic at the interface. → The heterogeneity at the interface affects the behaviour of the joint material. -- Abstract: In the present work, fatigue crack growth in two nickel-base mono-materials and one bi-material has been investigated at 450 and 550 ^oC. The electric potential drop technique was found to better estimate the crack length during cycling as compared to the compliance method. This finding is supported by microscopic observations of the fracture surface and also by the numerical simulation using finite element code Castem2000. The crack was found to grow faster in the coarse grained material than in the fine grained one. The fracture surface observation showed that the performance of the bi-material is linked to the mono-material content at the interface. In addition, the content of each mono-material at the interface was found to be very stochastic. This heterogeneity, due to the assembly process, strongly affects the behaviour of the biomaterial. Finite element computation showed a good agreement between numerical and experimental results in term of stress intensity factor.

[en] The present study deals with the 'automatic' determination of the initial blank shape contour for 3D thin metallic precision parts obtained by stamping, knowing the 3D CAD geometry of the final part (the desired product). The forming process can involve several steps presented in this paper that consists in applying a heuristic method of optimization to find out the initial blank shape of thin precision metallic part in order to obtain a final part, with a required 3D geometry (specified). The purpose of the present approach is to replace the experimental trial and error optimization method used currently, which is expensive and time consuming. The principle of the 'heuristic' optimization method is to first estimate the blank shape using the Inverse Approach, then to compensate the shape error calculated in each node of the blank contour. The 'heuristic' optimization loop is done using a precise incremental code (Abaqus Explicit or Stampack) and, the iterations loop is stopped when the shape errors are within some initially fixed tolerances. The method is tested in the case of a special stamping process where the parts are pressed in one or more steps using a manual press, without blank holder and by the mean of tools having complex shape. The sensitivities of the process parameters regarding the optimal solution are investigated