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This paper aims to study the static behavior of carbon nanotubes (CNTs) reinforced functionally graded shells using an efficient solid-shell element with parabolic transverse shear strain. Four different types of reinforcement along the thickness are considered.

Furthermore, the developed solid-shell element allows an efficient and accurate analysis of CNT-reinforced functionally graded shells under linear static conditions.

The validity and accuracy of the developed solid-shell element are illustrated through the solution of deflection and stress distribution problems of shell structures taken from the literature. The influences of some geometrical and material parameters on the static behavior of shell structures are discussed.

The finite element formulation is based on a modified first-order enhanced solid-shell element formulation with an imposed parabolic shear strain distribution through the shell thickness in the compatible strain part. This formulation guarantees a zero transverse shear stress on the top and bottom surfaces of the shell and the shear correction factors is no longer needed.

This paper aims to describe a shape optimization for hyperelastic axisymmetric structure with an exact sensitivity method.

The whole shape optimization process is carried out by integrating a closed geometric shape in the real space R2 with boundaries defined by B-splines curves. An exact sensitivity analysis and a mathematical programming method (SQP: Sequential Quadratic Programming) are implemented. The design variables are the control points' coordinates which minimize the Von-Mises criteria, with a constraint that the total material volume of the structure remains constant. The feasibility of the proposed methods is carried out by two numerical examples. Results show that the exact Jacobian has an important computing time reduction.

Numerical examples are presented to illustrate its performance.

In this work, the sensitivity performance is computed using two numerical methods: the efficient finite difference scheme and the exact Jacobian.

The purpose of this paper is to describe a general theoretical and finite element implementation framework for the constitutive modelling of biological soft tissues.

The model is based on continuum fibers reinforced composites in finite strains. As an extension of the isotropic hyperelasticity, it is assumed that the strain energy function is decomposed into a fully isotropic component and an anisotropic component. Closed form expressions of the stress tensor and elasticity tensor are first established in the general case of fully incompressible plane stress which orthotropic and transversely isotropic hyperelasticity. The incompressibility is satisfied exactly.

Numerical examples are presented to illustrate the model's performance.

The paper presents a constitutive model for incompressible plane stress transversely isotropic and orthotropic hyperelastic materials.