A Simple Matlab Code for Material Design Optimization Using Reduced Order Models.

The main part of the computational cost required for solving the problem of optimal material design with extreme properties using a topology optimization formulation is devoted to solving the equilibrium system of equations derived through the implementation of the finite element method (FEM). To reduce this computational cost, among other methodologies, various model order reduction (MOR) approaches can be utilized. In this work, a simple Matlab code for solving the topology optimization for the design of materials combined with three different model order reduction approaches is presented. The three MOR approaches presented in the code implementation are the proper orthogonal decomposition (POD), the on-the-fly reduced order model construction and the approximate reanalysis (AR) following the combined approximations approach. The complete code, containing all participating functions (including the changes made to the original ones), is provided.

Design Aspects of Additive Manufacturing at Microscale: A Review.

Additive manufacturing (AM) technology has been researched and developed for almost three decades. Microscale AM is one of the fastest-growing fields of research within the AM area. Considerable progress has been made in the development and commercialization of new and innovative microscale AM processes, as well as several practical applications in a variety of fields. However, there are still significant challenges that exist in terms of design, available materials, processes, and the ability to fabricate true three-dimensional structures and systems at a microscale. For instance, microscale AM fabrication technologies are associated with certain limitations and constraints due to the scale aspect, which may require the establishment and use of specialized design methodologies in order to overcome them. The aim of this paper is to review the main processes, materials, and applications of the current microscale AM technology, to present future research needs for this technology, and to discuss the need for the introduction of a design methodology. Thus, one of the primary concerns of the current paper is to present the design aspects describing the comparative advantages and AM limitations at the microscale, as well as the selection of processes and materials.

Nonlinear Finite Element Analysis of γ-Graphyne Structures under Shearing.

In this study, a nonlinear, spring-based finite element approach is employed in order to predict the nonlinear mechanical response of graphyne structures under shear loading. Based on Morse potential functions, suitable nonlinear spring finite elements are formulated simulating the interatomic interactions of different graphyne types. Specifically, the four well-known types of γ-graphyne, i.e., graphyne-1 also known as graphyne, graphyne-2 also known as graphdiyne, graphyne-3, and graphyne-4 rectangular sheets are numerically investigated applying appropriate boundary conditions representing shear load. The obtained finite element analysis results are employed to calculate the in-plane shear stress-strain behaviour, as well as the corresponding mechanical properties as shear modulus and shear strength. Comparisons of the present graphyne shearing response predictions with other corresponding estimations are performed to validate the present research results.

SimNano: A Trust Region Strategy for Large-Scale Molecular Systems Energy Minimization Based on Exact Second-Order Derivative Information.

In this work, a new energy minimization strategy is presented that achieves better convergence properties than the standard algorithms employed in the field (fewer steps and usually a lower minimum) and is also computationally efficient; therefore, it becomes suitable for dealing with large-scale molecular systems. The proposed strategy is integrated into the SimNano energy minimization platform that is also described herein. SimNano relies on the analytical calculation of the molecular systems' gradient vectors and Hessian matrices using the computational modeling framework proposed by the authors ( Chatzieleftheriou , S. ; Adendorff , M. R. ; Lagaros , N. D. Generalized Potential Energy Finite Elements for Modeling Molecular Nanostructures . J. Chem. Inf. Model. 2016 , 56 ( 10 ), 1963 - 1978 ). The basis of the proposed minimization strategy is a trust region algorithm based on exact second-order derivative information. Taking advantage of the Hessian matrices' sparsity, a specialized treatment of the data structure is implemented. The latter is beneficial and often rather necessary, especially in the case of large-scale molecular systems, improving the speed and reducing the memory requirements. In order to demonstrate the efficiency of the proposed energy minimization strategy, several test examples are examined, and the results achieved are compared with those obtained by one of the most popular molecular simulation software packages, i.e., the Large-Scale Atomic/Molecular Massively Parallel Simulator (LAMMPS). The results indicate that the proposed minimization strategy exhibits superior convergence properties compared with the typical algorithms (i.e., nonlinear conjugate gradient algorithm, limited-memory Broyden-Fletcher-Goldfarb-Shanno (LBFGS) algorithm, etc.). The SimNano energy minimization platform can be downloaded from the site http://users.ntua.gr/nlagaros/simnano.html , enabling researchers in the field to build molecular systems and perform energy minimization runs using input files in LAMMPS format.

Topology optimization aided structural design: Interpretation, computational aspects and 3D printing.

Construction industry has a major impact on the environment that we spend most of our life. Therefore, it is important that the outcome of architectural intuition performs well and complies with the design requirements. Architects usually describe as "optimal design" their choice among a rather limited set of design alternatives, dictated by their experience and intuition. However, modern design of structures requires accounting for a great number of criteria derived from multiple disciplines, often of conflicting nature. Such criteria derived from structural engineering, eco-design, bioclimatic and acoustic performance. The resulting vast number of alternatives enhances the need for computer-aided architecture in order to increase the possibility of arriving at a more preferable solution. Therefore, the incorporation of smart, automatic tools in the design process, able to further guide designer's intuition becomes even more indispensable. The principal aim of this study is to present possibilities to integrate automatic computational techniques related to topology optimization in the phase of intuition of civil structures as part of computer aided architectural design. In this direction, different aspects of a new computer aided architectural era related to the interpretation of the optimized designs, difficulties resulted from the increased computational effort and 3D printing capabilities are covered here in.

Generalized Potential Energy Finite Elements for Modeling Molecular Nanostructures.

The potential energy of molecules and nanostructures is commonly calculated in the molecular mechanics formalism by superimposing bonded and nonbonded atomic energy terms, i.e. bonds between two atoms, bond angles involving three atoms, dihedral angles involving four atoms, nonbonded terms expressing the Coulomb and Lennard-Jones interactions, etc. In this work a new, generalized numerical simulation is presented for studying the mechanical behavior of three-dimensional nanostructures at the atomic scale. The energy gradient and Hessian matrix of such assemblies are usually computed numerically; a potential energy finite element model is proposed herein where these two components are expressed analytically. In particular, generalized finite elements are developed that express the interactions among atoms in a manner equivalent to that invoked in simulations performed based on the molecular dynamics method. Thus, the global tangent stiffness matrix for any nanostructure is formed as an assembly of the generalized finite elements and is directly equivalent to the Hessian matrix of the potential energy. The advantages of the proposed model are identified in terms of both accuracy and computational efficiency. In the case of popular force fields (e.g., CHARMM), the computation of the Hessian matrix by implementing the proposed method is of the same order as that of the gradient. This analysis can be used to minimize the potential energy of molecular systems under nodal loads in order to derive constitutive laws for molecular systems where the entropy and solvent effects are neglected and can be approximated as solids, such as double stranded DNA nanostructures. In this context, the sequence dependent stretch modulus for some typical base pairs step is calculated.