Carlo Cinquini

Optimal design of beams discretized by elastic plastic finite element

Abstract The optimum design of beams discretized by elastic plastic finite elements is formulated accounting for behavioural constraints. The novelty of the present work derives from adopting a beam model within which plasticity may spread. The corresponding optimality criterion is discussed, and an iterative procedure is proposed and applied to some meaningful examples.

Optimal plastic design of stiffened shells

Abstract This paper is concerned with the variational formulation of the optimum design of plastic cylindrical shells with stepwise varying thickness and stiffeners at joints (sections between two contiguous elements). The optimality criterion is attained by using a variational formulation. The saving achieved by using stiffeners is shown by means of an example.

Variational formulation of the optimal plastic design of circular plates

Abstract The problem of minimum-cost design of rigid-plastic circular plates under axysymmetric loading is studied by the variational approach. The optimality condition is discussed for “absolute” minimum-cost design as well as for design with technological constraints. A unified and fairly comprehensive treatment of these problems is presented.

Topology Optimization for Thermal Insulation: an Application to Building Engineering

This article deals with a numerical implementation for topology optimization that is based on the heat conduction equation and addresses problems such as the optimal design of thermal insulation in building engineering. The formulation handles heat diffusivity under the steady-state assumption for a domain with assigned convective-like boundary conditions. The optimization framework is implemented within a general-purpose finite-elements code that is set to solve the thermal problem iteratively, thus allowing for a straightforward handling of two-dimensional and three-dimensional problems. A few numerical results are firstly presented to compare classical formulations for maximum heat conduction and the addressed scheme for optimal thermal insulation. The proposed methodology is therefore exploited to cope with issues peculiar to the optimal design of building envelopes, such as the mitigation of the effects of thermal bridges and the design for minimum thermal transmittance of the components of a modular curtain wall.

Finite element iterative method for optimal elastic design of circular plates

Abstract An iterative procedure is presented for the optimal elastic design of circular or annular plates under axisymmetric loads. The deflection or slope at a given radius is prescribed, and technological constraints are taken into account. Some examples are discussed.

Limit Analysis of Circular Cylindrical Shells under Hydrostatic Pressure

ABSTRACT The problem of limit analysis of circular cylindrical shells under hydrostatic pressure is dealt with. On the basis of Hodge plastic yield condition, solutions are achieved by solving systems of simultaneous algebraic nonlinear equations. Several cases of different boundary conditions are considered.

Application of linear programming to the optimal plastic design of circular plates subject to technological constraints

Abstract This paper is concerned with plastic minimum-volume design of circular or annular plates under axially symmetric loading. Accordingly, all characteristics of the plate depend only on the radial coordinate r . The plate is divided into rings of constant yield moment. Other technological constraints may be added, for instance bounds on the yield moments of the rings. Linear programming is used to obtain an approximate solution of the problem, and the optimality criteria are derived from the duality relations. The method is illustrated by examples which show that it is quite accurate.

Iterative solutions for problems of optimal elastic design

Abstract An iterative procedure is presented for the optimal design of one-dimensional structures with prescribed linear or rotational displacement at a given point.

Topology Optimization of Multi-Loaded Structures with Mixed Finite Elements:

The paper presents a topology optimization formulation that uses mixed-finite elements, here specialized for the design of multi-loaded structures. The discretization scheme adopts stresses as primary variables in addition to displacements which usually are the only variables considered. Two dual variational formulations based on the Hellinger-Reissner variational principle are presented in continuous and discrete form. The use of the mixed approach coupled with the choice of nodal densities as optimization variables of the topology problem lead to 0–1 checkerboard-free solutions even in the case of multi-loaded structures design. The method of moving asymptotes (MMA) by Svanberg (1984) is adopted as minimization algorithm. Numerical examples are provided to show the capabilities of the presented method to generate families of designs responding to different requirements depending on stiffness criteria for common structural multi-load problems. Finally the ongoing research concerning the presence of stress constraints and the optimization of incompressible media is outlined.

Rayleigh-Ritz analysis of elastically constrained thin laminated plates on Winkler inhomogeneous foundations

Abstract Anisotropic layered composite plates laying on Winkler foundations are analyzed in this paper. Different boundary conditions are examined: ideal constraints as well as elastic ones are taken into account. For any given structure, i.e. for any lamination sequence, a method is developed to determine the relevant eigenproperties such as the first fundamental frequencies and the associated eigenmodes. The main objectives of the paper include: (i) identification of a lamination sequence so as to extremize the eigenvalues of the system; (ii) determination of the effects of elastic foundations, homogeneous as well as inhomogeneous, on the properties of the system; (iii) incorporating in the formulation constraints of elastic nature, for their relevance in view of practical applications; (iv) investigating the effectiveness of the Rayleigh-Ritz method in limit cases such as high gradients and stiffnesses. The Rayleigh-Ritz method is used herein as analysis method: polynomial functions defined over the entire domain of definition of the structure are derived which satisfy the geometric boundary conditions and may locally violate the natural ones. The solution is then expanded as a finite sum of such functions which thus constitute a basis of finite dimension. Numerical examples are worked out to demonstrate the monotonic convergence of the Rayleigh-Ritz based solution to the ideally constrained one when the stiffness of the boundaries grows large.