Designing manufacturable viscoelastic devices using a topology optimization approach within a truly-mixed fem framework

A new approach to topology optimization is presented that is based on the minimization of the input/output transfer function H∞norm. Additionally, by properly selecting input and output vector, the approach is recognized to minimize an entirely new definition of frequency-based dynamic compliance. The method is applied to viscoelastic systems in plane strain conditions that are investigated by using the Arnold-Winther finite-element resorting to a generalized solid phenomenological model. Preliminary indications on how to address the actual manufacturability of the optimal specimen are eventually outlined

Masonry arches simulations using cohesion parameter as code enrichment for limit analysis approach

A significant number of scientific research groups are still nowadays dealing with masonry material as the main focus of study since it provides an open field of research that is far from resolution in a standardized manner. As masonry structures are highly vulnerable to any level of natural hazards, especially seismic activity, both traditional and composite materials have been used as reinforcements in masonry and provide different solutions that meet the key requirements set out by cultural heritage organizations. Extensive effort has gone into developing appropriate techniques of assessment, that usually demand an individualized methodology of analysis which is to be handled through comparative studies requiring results validation. A suitable field of study is the Limit Analysis approach towards masonry structures, as it offers quite accurate and, more importantly, robust results regarding the necessity to resolve the issues involved in the masonry numerical representation so that reliable outcomes are drawn to enable the assessment of such structures. The enrichment of a Limit Analysis homemade code with the inclusion of cohesion and frictional behaviour at the interface level is able to account, in a simplified but very robust manner, the perplexing issues involved with the numerical assessment of reinforced masonry structures with particular reference to arches. The cohesion incorporation iscalibrated for a variety of in-plane applications, accounting for the joints’ indirect tensile strength, that is able to simulate the strengthening measures. Results obtained are validated with literature results and included in a comparative study between discrete numerical models that utilize different modelling strategies

A new approach to optimization of viscoelastic beams: minimization of the input/output transfer function H∞ -norm

A new approach to structural optimization in dynamic regime is presented that is based on the minimization of the H∞ norm of the transfer function between the external loads and the structural response. The method is successfully applied to the sizing optimization of viscoelastic beams as shown by extensive numerical investigations that are presented in much detail. The abstract nature of the proposed approach makes it applicable to a wide class of dynamical systems including 2D and 3D systems within general topology optimization frameworks that are object of ongoing analysis

An innovative H∞–norm based worst case scenario approach for dynamic compliance optimization with applications to viscoelastic beams

A novel frequency–based definition of dynamic compliance is introduced within the framework of H∞–norm based structural dynamics in the presence of load uncertainties. The system itself is supposed to depend on a vector of design parameters with respect to which an optimal design is pursued. A three-step worst-case-scenario is then developed that finds the minimum-compliance structure capable of accounting for the entire norm–bounded load sets. Once the problem is initialized, the current worst load is found that is used as input to the minimization of the structural compliance and the procedure is repeated until convergence. Numerical examples are eventually proposed that deal with viscoelastic beams discretized via a truly–mixed finite–element scheme

Limit analysis approach for the in-plane collapse of masonry arches

This paper deals with the numerical evaluation of the in-plane collapse behaviour of unreinforced masonry arches and portals characterised by different geometries subjected to several loading conditions and modelled as assemblages of rigid blocks in contact through no-tensional and frictional interfaces. This study has been conducted using a new inhouse code, which represents the updated version of the numerical procedure presented in the pioneering work of Baggio and Trovalusci). The minimisation problem corresponding to the upper-bound (or kinematic) approach of limit analysis is written as a linear programming problem solved taking advantages of the algorithms nowadays available. An important feature of the code is the capability to provide information about the sliding collapse of masonry structures, adopting the assumption of dilatancy in the analytic description of the yielding surface, permitting to overcome the classical Heyman’s hypothesis, which limited the investigation of collapse to only hinging modes. A key contribution of this study is the comparison of results in terms of collapse multipliers and collapse mechanisms, considering different literature contributes as benchmark references. This research reveals the suitability of approaches based on mathematical programming and the crucial role played by sliding

Data from the parametric analysis of multi-ring masonry arches using a limit analysis approach for the span of 7m

The dataset is produced by running a series of 360 simulations using the in-house code ALMA (Analisi Limite Murature Attritive) that implements the upper bound approach of limit analysis to detect the collapse multiplier and mechanism for masonry structures. This set of data contains the results of 120 simulations achieved for the multi-ring masonry arches for span of 7m with different level of parameters considered, namely size of blocks, span of the arch, ring number, interlocking coefficient and the friction angle. In order to simplify references to figures an acronym system is used and it follows a sequence of "size_span_ring_interlock_friction". Size takes attributes as S-small and B-big while span takes number attributes based on the span like S3, S5, S7 for spans of 3, 5 and 7 meters, respectively. Ring number similarly is based on the number of rings as R2, R3, R4 and R5 and interlock takes the following attributes, I00, I15, I35 and I50 for the interlocking percentage considered such that 00-stacked, 15%, 35% and 50%, respectively. Finally friction takes attributes following the angle of friction such as F25—low level, F30—medium level, and F35—high level. The acronym used for the equivalent one-ring arches is used as simply EQ. For example, the acronym “S_S7_R4_I35_F30" refers to the arch with small blocks, span of 7 meters, consisting of 4 rings and by blocks interlocked at 35% with a joint friction of 30o. This database contains a *.txt, a *.vtk and a *.png file. In the .txt file the elapsed time and the collapse multiplier of each simulation can be found. The .vtk file contains all the geometry and displacement values of every masonry panel. Finally, the .png file presents the collapse mechanism obtained

Beam-based lattices: A novel geometry generation algorithm and thermo-mechanical characterization via Asymptotic Homogenization

For their ease of production through additive manufacturing, beam-based lattices have been extensively used in engineering applications. However, a rigorous methodology for the generation of unit-cell geometry is not exhaustively treated in the literature and geometrical intuition, rather than proper algorithms, is usually employed for design. This fact also confuses the taxonomy, as authors suggest different names for the same cell type. In this talk, a novel geometrical algorithm for the generation of beam-based cubic unit cells with spherical inertia ellipsoid and thermal conductivity tensor is presented. The algorithm allows the production of complex but self-connecting - that impart structural integrity to the lattice - unit cells that otherwise are difficult to devise and suggests a novel taxonomy based on the parameters adopted. Under this categorization, classes of unit cells are defined by the variation of a single geometrical variable. Furthermore, a thermo-mechanical characterization of the static effective properties is presented for each cell class by means of a FEM implementation of the Asymptotic Homogenization method. The results are presented as gridded data, made available on GitHub repository, dependent on the unit cell’s volume fraction (solid-to-void ratio), on the Poisson’s ratio (spanning in the thermodynamically admissible range for conventional materials 0 < ν < 0.5), and on the class of geometrical parameter of the cell. The effective parameters are normalized with respect to the solid bulk properties, thus becoming purely geometrical properties of the unit cell family, and act as scaling functions on the bulk properties. These results can be readily implemented in any optimization scheme for the optimization of the static performance of lattices, providing a useful tool for real-world engineering applications

Designing manufacturable viscoelastic devices using a topology optimization approach within a truly-mixed fem framework

A new approach to topology optimization is presented that is based on the minimization of the input/output transfer function H∞norm. Additionally, by properly selecting input and output vector, the approach is recognized to minimize an entirely new definition of frequency-based dynamic compliance. The method is applied to viscoelastic systems in plane strain conditions that are investigated by using the Arnold-Winther finite-element resorting to a generalized solid phenomenological model. Preliminary indications on how to address the actual manufacturability of the optimal specimen are eventually outlined

Data from the parametric analysis of multi-ring masonry arches using a limit analysis approach for the span of 5m

The dataset is produced by running a series of 360 simulations using the in-house code ALMA (Analisi Limite Murature Attritive) that implements the upper bound approach of limit analysis to detect the collapse multiplier and mechanism for masonry structures. This set of data contains the results of 120 simulations achieved for the multi-ring masonry arches for span of 5m with different level of parameters considered, namely size of blocks, span of the arch, ring number, interlocking coefficient and the friction angle. In order to simplify references to figures an acronym system is used and it follows a sequence of "size_span_ring_interlock_friction". Size takes attributes as S-small and B-big while span takes number attributes based on the span like S3, S5, S7 for spans of 3, 5 and 7 meters, respectively. Ring number similarly is based on the number of rings as R2, R3, R4 and R5 and interlock takes the following attributes, I00, I15, I35 and I50 for the interlocking percentage considered such that 00-stacked, 15%, 35% and 50%, respectively. Finally friction takes attributes following the angle of friction such as F25—low level, F30—medium level, and F35—high level. The acronym used for the equivalent one-ring arches is used as simply EQ. For example, the acronym “S_S7_R4_I35_F30" refers to the arch with small blocks, span of 7 meters, consisting of 4 rings and by blocks interlocked at 35% with a joint friction of 30o. This database contains a *.txt, a *.vtk and a *.png file. In the .txt file the elapsed time and the collapse multiplier of each simulation can be found. The .vtk file contains all the geometry and displacement values of every masonry panel. Finally, the .png file presents the collapse mechanism obtained

Integrated Procedure for Homogenization of Particle Random Com- posites Using Virtual Element Method

Particle-based composites, used in many engineering applications or present in nature, exhibit a mi- crostructure made of randomly distributed inclusions (particles) embedded into a dissimilar matrix. A key aspect, recently investigated by many researchers, is the evaluation of appropriate mechanical properties to be adopted for the study of their behavior. Homogenization procedures may be adopted for the definition of equivalent moduli able to take into account at the macroscale the material prop- erties emerging from the internal microstructure. Respect to the classic homogenization approach, in the case of materials with random microstructure it is not possible to a-priori define a Represen- tative Volume Element (RVE), this being an unknown of the problem. A possible way to solve this problem is to approach the RVE using finite–size scaling of intermediate control volume elements, named Statistical Volume Elements (SVEs), and proceed to homogenization. Here homogenization, consistent with a generalized Hill–Mandel condition, is adopted in conjunction with a statistical procedure, by which scale–dependent bounds on classical moduli are obtained using Dirichlet and Neumann boundary conditions for solving boundary value problems. The outlined procedure has provided significant results, also extended to non–classical continuum formulations [1], but with high computational cost which prevents the possibility to perform series of parametric analyses. The procedure here proposed automates all the steps to perform: from the simulations of each ran- dom realization of the microstructure to the solutions of the boundary value problems for the SVEs, up to the evaluation of the final size of the RVE for the homogenization of the random medium. Moreover, the adoption of an innovative computational method, such as the Virtual Element Method (VEM) [2], allow us to reduce the computational burden. The VEM methodology has many compu- tational advantages such as robust stiffness matrix (can be exactly computed in precision machine) and accuracy versus the number of degrees of freedom. For the numerical analysis we adopt a polygonal mesh for the matrix and a single VEM element for the inclusions. The results obtained by adopting this integrated homogenization procedure with VEM are compared with the results pre- viously obtained, by some of the authors, using a standard Finite Elements procedure taking into account two different types of inclusions, either stiffer or softer than the matrix. Several simulations are then performed by modifying the material contrast (ratio between the moduli of the materials components) deriving the size of the RVE for performing homogenization on various kinds of two– phases random composites