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.

SUMMARYThe problem of structural damage identification based on vibration measurements (eigenfrequencies and incomplete mode shapes) is generally formulated as an inverse problem aiming to identify changes encountered on the global stiffness matrix. In most cases, the measured quantities are less than the damage parameters to be identified; thus, an infinite number of possible damage configurations are expected to satisfy the measurements. Therefore, damage identification problems are often proven to be ill-conditioned. The problem becomes more complex when measurements' noise and model uncertainties are considered. Therefore, depending on the structural system, damage scenario and available vibration measurements, additional eigenmode data may need to be considered in order to increase the robustness of the damage identification procedure. In this work, a new two-loop trajectory method is presented, that relies on an iterative nonlinear sensitivity analysis procedure. The main advantage of the proposed method is its ability to identify damage scenarios that match the measured data with high accuracy as well as to explore effectively the solution space. This feature can be exploited in order to assess the adequacy of the measurements in noisy and/or uncertain environment.

The present work is concerned with the introduction of a new first level pre- and post-earthquake seismic assessment protocol for buildings that relies on the use of recorded structural response. As earthquakes represent a constant and unpredictable threat for the building stock around the globe, the protocols already in use for assessing the risk should be revised and should also take into account the information hidden in data recorded in the field. Nowadays, data collection does not require expensive equipment and over-qualified personnel. In this direction, the proposed seismic assessment protocol aims to illustrate the ease of widely adopting Structural Health Monitoring (SHM) equipment (e.g., accelerographs), based on the work that has been carried out over the past years on subjects related to earthquake risk estimation. Building taxonomy and damage estimation, like those found in Hazus®–MH and other hazard assessment tools, can be enriched and modified properly to distinguish and classify the very earthquake-prone buildings from the others, and tag them for further assessment and rehabilitation as seismic codes suggest.

Structural optimization over the past decades matured from an academic theoretical field, to an important tool in the design procedure in various engineering disciplines. Some commercial software applications provide some suites with optimization solutions, but they are focused mostly in the aeronautics, automotive and aerospace industry. High Performance Optimization Computing Platform (HP-OCP) is a software developed by the ISAAR-NTUA and provides a holistic optimization approach for civil engineering structures. More precisely, HP-OCP is a computational suite that has the ability to integrate with several structural analysis and design software and provide optimization solutions. Structural optimization is mainly divided in three groups, sizing (or parametric), shape and topology optimization. All of them are integrated in HP-OCP and the appropriate algorithms are provided in each category. Considering size and shape optimization, the parametric optimization module is developed, in which the design variables of the mathematical formulation can be the dimension of the section properties, the quality of the material, the coordinates of the nodes etc. In this module plenty of derivativebased and derivative-free algorithms are provided like the Projected Quasi-Newton, Constrained Optimization by Linear Approximation, Latin Hypercube Sampling etc. [1]. Considering the topology optimization module [2], the SIMP method is applied and the mathematical algorithms that are implemented are the Optimality Criteria and Method of Moving Asymptotes. HP-OCP was developed in C# programming language, making it a powerful suite that can be integrated with any commercial software that provide Application Programming Interface, batch analysis via XML files or any other type of data exchange format. In the current work the integration of HP-OCP with the SAP2000, ETABS and SCIA Engineering software is presented. Several examples considering parametric and topology optimization problems are examined. Remarkable cost reduction is succeeded in real-world structures, validating in this way the usefulness of HP-OCP not only in the research field but also in applied civil engineering problems.

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