Robert John Nicholas Baldock

Structural topology optimization of braced steel frameworks using genetic programming

This paper presents a genetic programming method for the topological optimization of bracing systems for steel frameworks. The method aims to create novel, but practical, optimally-directed design solutions, the derivation of which can be readily understood. Designs are represented as trees with one-bay, one-story cellular bracing units, operated on by design modification functions. Genetic operators (reproduction, crossover, mutation) are applied to trees in the development of subsequent populations. The bracing design for a three-bay, 12-story steel framework provides a preliminary test problem, giving promising initial results that reduce the structural mass of the bracing in comparison to previous published benchmarks for a displacement constraint based on design codes. Further method development and investigations are discussed.

Determining pressure-temperature phase diagrams of materials

© 2016 American Physical Society. ©2016 American Physical Society. We extend the nested sampling algorithm to simulate materials under periodic boundary and constant pressure conditions, and show how it can be used to determine the complete equilibrium phase diagram for a given potential energy function, efficiently and in a highly automated fashion. The only inputs required are the composition and the desired pressure and temperature ranges, in particular, solid-solid phase transitions are recovered without any a priori knowledge about the structure of solid phases. We benchmark and showcase the algorithm on the periodic Lennard-Jones system, aluminum, and NiTi.

EVOLVING OPTIMIZED BRACED STEEL FRAMEWORKS FOR TALL BUILDINGS USING MODIFIED PATTERN SEARCH

Direct search methods offer potential for rapid exploration of a design space, enabling novel and optimized designs to be generated. We present the use of modified pattern search for optimizing the topological design of the bracing system for a free -form building of approximately 250m in height, carried out as part of a live building project, with the goal of generating alternative randomized patterns that meet structural performance. The methods developed successfully evolved efficient bracing configurations, in a procedure involving successive bracing element removal, with substantially less computational effor t than a basic automation method. The diversity of solutions introduced by adding a stochastic element to the search procedure and stochastic variation of the initial design proved beneficial for the structural design team. The project successfully applies an established search method, tailored for this scenario, to a complex, large -scale design task and provides a valuable case -study in applying structural topology optimization on live building projects.

Constant-pressure nested sampling with atomistic dynamics.

The nested sampling algorithm has been shown to be a general method for calculating the pressure-temperature-composition phase diagrams of materials. While the previous implementation used single-particle Monte Carlo moves, these are inefficient for condensed systems with general interactions where single-particle moves cannot be evaluated faster than the energy of the whole system. Here we enhance the method by using all-particle moves: either Galilean Monte Carlo or the total enthalpy Hamiltonian Monte Carlo algorithm, introduced in this paper. We show that these algorithms enable the determination of phase transition temperatures with equivalent accuracy to the previous method at 1/N of the cost for an N-particle system with general interactions, or at equal cost when single-particle moves can be done in 1/N of the cost of a full N-particle energy evaluation. We demonstrate this speed-up for the freezing and condensation transitions of the Lennard-Jones system and show the utility of the algorithms by calculating the order-disorder phase transition of a binary Lennard-Jones model alloy, the eutectic of copper-gold, the density anomaly of water, and the condensation and solidification of bead-spring polymers. The nested sampling method with all three algorithms is implemented in the pymatnest software.

Exploiting molecular dynamics in Nested Sampling simulations of small peptides

Nested Sampling (NS) is a parameter space sampling algorithm which can be used for sampling the equilibrium thermodynamics of atomistic systems. NS has previously been used to explore the potential energy surface of a coarse-grained protein model and has significantly outperformed parallel tempering when calculating heat capacity curves of Lennard-Jones clusters. The original NS algorithm uses Monte Carlo (MC) moves; however, a variant, Galilean NS, has recently been introduced which allows NS to be incorporated into a molecular dynamics framework, so NS can be used for systems which lack efficient prescribed MC moves. In this work we demonstrate the applicability of Galilean NS to atomistic systems. We present an implementation of Galilean NS using the Amber molecular dynamics package and demonstrate its viability by sampling alanine dipeptide, both in vacuo and implicit solvent. Unlike previous studies of this system, we present the heat capacity curves of alanine dipeptide, whose calculation provides a stringent test for sampling algorithms. We also compare our results with those calculated using replica exchange molecular dynamics (REMD) and find good agreement. We show the computational effort required for accurate heat capacity estimation for small peptides. We also calculate the alanine dipeptide Ramachandran free energy surface for a range of temperatures and use it to compare the results using the latest Amber force field with previous theoretical and experimental results.

A Primer in Probability

This section provides a summary of probability theory, as necessary to understand this thesis.

Equations of State

This chapter introduces an approach for calculating pressure-volume-temperature equations of state with nested sampling.

Hamiltonian Monte Carlo for Nested Sampling

This chapter introduces a Hamiltonian Monte Carlo algorithm for performing constant pressure nested sampling calculations.

Nested Sampling for Materials

This chapter develops nested sampling into a powerful tool for the calculation of pressure-temperature phase diagrams, and demonstrates how it may be applied to single species and binary systems, including the Lennard-Jones system, a binary Lennard-Jones alloy, and an EAM model for Aluminium. A comparison to parallel tempering is also presented.

Relating Probability Density Functions to the Behaviour of Systems

Introduction to phase transitions and phase diagrams. A number of important ideas from computational statistical mechanics are also discussed.