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Recent research advances on the dynamic analysis of composite shells: 2000-2009

A modified leaky ReLU scheme (MLRS) for topology optimization with multiple materials

Linearly elastic two- and three-dimensional orthotropic materials are considered. The problems of optimal material orientation are studied in the cases of the Hill and Tsai–Wu strength criteria. The necessary optimality conditions are derived for a 3D orthotropic material. In the case of a 2D orthotropic material, an analytical solution is obtained. An analysis of global and local extrema is presented.

Orientational Design of Anisotropic Materials Using the Hill and Tsai–Wu Strength Criteria

This paper investigates the free vibration and compressive buckling characteristics of functionally graded graphene nanoplatelets reinforced composite (FG-GPLRC) beams containing open edge cracks by using the finite element method. The beam is a multilayer structure where the weight fraction of graphene nanoplatelets (GPLs) remains constant in each layer but varies along the thickness direction. The effective Young's modulus of each GPLRC layer is determined by the modified Halpin-Tsai micromechanics model while its Poisson's ratio and mass density are predicted according to the rule of mixture. The effects of GPLs distribution pattern, weight fraction, geometry, crack depth ratio (CDR), slenderness ratio as well as boundary conditions on the fundamental frequency and critical buckling load of the FG-GPLRC beam are studied in detail. It was found that distributing more GPLs on the top and bottom surfaces of the cracked FG-GPLRC beam provides the best reinforcing effect for improved vibrational and buckling performance. The fundamental frequency and critical buckling load are also considerably affected by the geometry and dimension of GPL nanofillers.

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Vibration and Buckling Characteristics of Functionally Graded Graphene Nanoplatelets Reinforced Composite Beams with Open Edge Cracks.

Size-efficient interval time stamps

The problem of minimization (or maximization) of the elastic energy density is solved in the two-dimensional case for a nonlinear elastic solid. The material behaviour is simulated on the basis of a power law stress-strain relation. Closed-form solutions which include corresponding solutions for a linear elastic solid are obtained. The latter may give local as well as global maxima and minima, respectively.

On optimal orientation of nonlinear elastic orthotropic materials

Thin-walled conical shells subjected to uniformly distributed external pressure loading are considered assuming that the thickness of the shells is piece-wise constant. Minimum weight designs are established under the condition that the load carrying capacity of the optimized shell coincides with that of the reference shell of constant thickness. The material of the shell is assumed to obey Tresca's yield condition and the associated flow law. The exact yield surface in the space of generalized stresses corresponding to the Tresca condition is approximated with the squares on the planes of membrane forces and moments, respectively.

Optimization of plastic conical shells of piece-wise constant thickness

An optimization technique is suggested for shallow spherical shells made of a ductile material and subjected to initial impact loading. The shell under consideration is pierced with a central hole and clamped at the outer edge. The optimal design of the shell of piece-wise constant thickness is established under the condition that the maximal residual deflection attains its minimal value for given total weight. The material of the shell is assumed to obey the Tresca yield condition and associated flow law. By the use of the method of mode form motions the problem is transformed into a particular problem of non-linear programming and solved numerically.

Optimization of clamped plastic shallow shells subjected to initial impulsive loading

The problems of the optimization of rigid-plastic cylindrical shells are studied under the condition that the shell wall thickness is piece-wise constant. It is assumed that the deflections of the shell are moderately large and the material obeys the von Mises yield condition and the associated deformation law. The optimization problem is posed as an optimal control problem and necessary optimality conditions are derived with the aid of the variational methods of optimality theory. The set of equations obtained is solved numerically. An example regarding the minimization of the central deflection of the shell with two steps in the thickness is presented.

Optimization of plastic cylindrical shells with stepwise varying thickness in the case of von Mises material

An approximate method developed earlier for the investigation of large plastic deflections of circular and annular plates is accommodated for shallow spherical shells The material of the shells is assumed to obey Tresca's yield condition and the associated deformation law The minimum weight problem concerning shells operating in the post-yield range is posed under the conditions that (i) the thickness of the structure is piece-wise constant and (ii) the maximal deflections of the optimized shell and a reference shell of constant thickness, respectively, coincide Necessary optimality conditions are derived with the aid of the variational methods of the optimal control theory The set of equations obtained is solved numerically

J. Lellep

Papers

On optimal orientation of nonlinear elastic orthotropic materials

Optimization of plastic conical shells of piece-wise constant thickness

Optimization of clamped plastic shallow shells subjected to initial impulsive loading

Optimization of plastic cylindrical shells with stepwise varying thickness in the case of von Mises material

Optimization of rigid-plastic shallow spherical shells of piecewise constant thickness