1,721,135 research outputs found
Finite element analysis of no-tension structures as a topology optimization problem
Full text linkAn alternative numerical approach is presented for the analysis of no–tension masonry–like solids. Whereas most of the strategies available in the literature resort to non–linear finite element techniques, the proposed approach re–formulates the problem within the framework of topology optimization. The equilibrium of a two–dimensional no–tension body is found searching for the distribution of an equivalent orthotropic material, in which tensile principal stresses are not allowed by prescribing negligible stiffness in the relevant direction, such that the potential energy of the solid is minimized. Unlike many conventional approaches that deal with the tough non–linearity of the problem through step–wise incremental analyses, the proposed method efficiently solves the effect of compatible loads through a one–shot energy–based optimization. Analytical and numerical benchmarks from the literature are investigated to assess the effectiveness of the proposed procedure and to discuss convergence features and possible applications inspired by the limit analysis of masonry–like structures
Topology optimization with mixed finite elements on regular grids
Full text linkRecently, new families of mixed finite elements have been proposed to address the analysis of linear elastic bodies on regular grids adopting a limited number of degrees of freedom per element. A two-dimensional mixed discretization is implemented to formulate an alternative topology optimization problem where stresses play the role of main variables and both compressible and incompressible materials can be dealt with. The structural compliance is computed through the evaluation of the complementary energy, whereas the enforcement of stress constraints is straightforward. Numerical simulations investigate the features of the proposed approach: comparisons with a conventional displacement-based scheme are provided for compressible materials; stress-constrained solutions for structures made of incompressible media are introduced
On an alternative approach to stress constraints relaxation in topology optimization
No full textThe paper deals with the imposition of local stress constraints in topology optimization. The aim of the work is to analyze the performances of an alternative methodology to the ε-relaxation introduced in Cheng and Guo (Struct Optim 13:258–266, 1997), which handles the well-known stress singularity problem. The proposed methodology consists in introducing, in the SIMP law used to apply stress constraints, suitable penalty exponents that are different from those that interpolate stiffness parameters. The approach is similar to the classical one because its main effect is to produce a relaxation of the stress constraints, but it is different in terms of convergence features. The technique is compared with the classical one in the context of stress-constrained minimum-weight topology optimization. Firstly, the problem is studied in a modified truss design framework, where the arising of the singularity phenomenon can be easily shown analytically. Afterwards, the analysis is extended to its
natural context of topology bidimensional problems
On the solution of the checkerboard problem in mixed-FEM topology optimization
No full textThe paper deals with an alternative formulation for the classical topology optimization problem of getting structures with minimum compliance with constraint on volume, relying on the adoption of a mixed finite-element discretization scheme instead of a common displacement-based one. Using mixed methods not only displacements are main variables but also stresses enter the formulation. Two dual variational principles of Hellinger–Reissner are presented in their continuous and discrete form and included in the topology optimization problem that is solved through the method of moving asymptotes (MMA). Numerical simulations are performed for both the formulations and in particular for the truly-mixed setting coupled to a mixed-FEM discretization that uses the composite element of Johnson and Mercier referring to the discretization of the stress field. This formulation is shown to achieve pure 0–1 designs with the relevant feature of being checkerboard-free without the adoption of any filtering technique. Ongoing extensions are outlined including the optimization of incompressible materials and the imposition of stress constraints that both find in the truly-mixed setting their natural environment
Generating strut-and-tie patterns for reinforced concrete structures using topology optimization
No full textTopology optimization is a well-known design tool that may be also exploited for the optimal generation of feasible strut-and-tie models (STM) in reinforced concrete structures. The paper proposes a simple implementation for minimum compliance optimization relying on the finite element library and analysis capabilities of a commercial FEM-code and its Application Programming Interface. This methodology deals with the generation of truss-like designs to derive preliminary strut-and-tie models not only in the established bidimensional context but also in a 3D environment. This allows to cope with issues as torsional reinforcement or the design of the so-called discontinuity regions in box-shaped
structures
A numerical method to generate optimal load paths in plain and reinforced concrete structures
Full text linkA numerical method based on topology optimization is proposed to generate optimal strut-only models for structures made of plain concrete and optimal strut-and-tie models for concrete structures where fixed regions of reinforcement are prescribed. Assuming concrete as a hyper-elastic material carrying
only compression, both the inherently nonlinear equilibrium equation and the energy-based topology optimization problem are solved within the same minimization procedure. Numerical simulations investigate load paths within the two-dimensional domain in case of conventional rebar cages. A stress
diffusion problem is considered as well
Un metodo automatico per il progetto ottimale del rinforzo di piastre in calcestruzzo armato mediante FRP
No full textThe achievement of an optimal arrangement of fiber-reinforcement is a crucial issue for the efficient retrofitting of concrete structural elements. Numerical approaches to the optimal distribution of strips of fiber???reinforced polymers (FRPs) have been recently proposed for in-plane elements, based on methods for the research of optimal load paths that mainly descend from the so-called strut-and-tie modeling. This contribution investigates the adoption of optimization techniques to search for the best distribution of a given amount of unidirectional FRP, along with its optimal orientation, such that the elastic strain energy of a concrete slab to be reinforced at both sides is minimized. Numerical simulations are presented to discuss features of the computed optimal layouts, along with their possible application as preliminary design for retrofitting concrete slabs. The achieved layouts are compared with solutions inspired by the limit analysis theory, which suggests reinforcing slabs perpendicularly to the plastic hinges that arise in the unreinforced elements
On the automatic generation of strut and tie patterns under multiple load cases with application to the aseismic design of concrete structures
No full textStrut-and-tie modelling (STM) is a well-known technique for the design of the discontinuity regions in reinforced concrete structures, that is mainly based on the research of suitable load paths to transfer external forces to constraints. A simple energetic approach resorting to the minimum compliance optimization is herein implemented to derive truss-like models for the preliminary design of discontinuity regions under multiple load conditions. Peculiar attention is paid to the effect of the horizontal forces, as the ones induced by the seismic action, which act upon corbels
and beam-column connections along with gravity loads. Numerical investigations in the bidimensional framework point out the remarkable crossing of stress-fluxes that must be handled in the bulk of the joints and calls for ad hoc shear reinforcement in the critical zone at the top of the columns. The methodology is also applied within the three-dimensional framework, addressing the design of box-shaped structures under
multiple load cases. The achieved results show the arising of helix-shaped strut-and-tie layouts that are well-suited to cope with torsional actions. In the case of holes in the sides of the specimen, such a reinforcement must be detailed in order to handle peak stresses in the corner regions
An alternative truly-mixed formulation to solve pressure load problems in topology optimization
No full textThe paper deals with an alternative formulation for the topology optimization of structures acted upon by pressure loads, exploiting finite elements techniques that are able to handle incompressible materials. The method, firstly presented in [O. Sigmund, P.M. Clausen, Topology optimization using a mixed formulation: an alternative way to solve pressure load problems, Comput. Methods Appl. Mech. Engrg. 196 (2007) 1874–1889, [33]], consists in exploiting the modeling of fluid incompressibility within a topology optimization framework. The implementation of a fluid phase enables to transfer pressure loads from the domain boundaries to the evolving edges of optimal design, without relying on more complex techniques traditionally employed to recover the load application surfaces at each step of the minimization process. In this context, the main numerical trouble is therefore the application of finite elements techniques to solve incompressible materials analysis. This topic in fact cannot be tackled using most of the approaches of the current literature that are mainly based on displacement finite elements which are well known to
be affected by the locking phenomenon. While Sigmund and Clausen (2007) uses a displacement–pressure finite element discretization to solve the problem, the approach herein presented consists in the adoption of a ‘‘truly-mixed” variational formulation coupled to a discretization based on the Johnson and Mercier finite element, that both pass the inf–sup conditions of the problem even in the presence of incompressible materials. The well-known method of moving asymptotes (MMA) is adopted in the numerical studies presented, along with a particular density interpolation to model the presence of a fluid and solid phase within the same design. The adopted scheme is especially conceived to avoid the
arising of numerical instabilities that may arise within the optimization procedure when handling incompressible material. Moreover, the accuracy and stability in stress evaluation provided by the ‘‘truly-mixed” setting are herein exploited to introduce an alternative procedure that implements
pressure constraints to avoid optimal designs that present cavities filled by fluid
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