Schalk Kok

University of Pretoria | UP · Department of Mechanical & Aeronautical Engineering

Shape optimization strategies based on error indicators usually require strict error control for every computed design during the optimization run. The strict error control serves two purposes. Firstly, it allows for the accurate computation of the structural response used to define the shape optimization problem itself. Secondly, it reduces the di...

We reflect on some theoretical aspects of gradient-only optimization for the unconstrained optimization of objective functions containing non-physical step or jump discontinuities. This kind of discontinuity arises when the optimization problem is based on the solutions of systems of partial differential equations, in combination with variable disc...

In this paper, we implement the method of proper orthogonal decomposition (POD) to generate a reduced order model (ROM) of an optimization-based mesh movement scheme. In this study it is shown that POD can be used effectively to generate an ROM, that accurately reproduces the full order mesh movement algorithm, with a decrease in computational time...

In this study, we investigate the significance of diversity in the particle swarm optimization (PSO) algorithm. To do so, we study two different implementations of the PSO, being the so-called linear and classical PSO formulations. While the behaviour of these two implementations is markedly different, they only differ in the formulation of the vel...

We study the minimization of objective functions containing non-physical jump discontinuities. These discontinuities arise when (partial) differential equations are discretized using non-constant methods and the resulting numerical solutions are used in computing the objective function. Although the functions may become discontinuous, gradient info...

The energy and power industry conventionally depends on large-scale turbomachinery to meet the ever-growing global energy demands. However, unplanned in-service failures remain a threat to sustainability with safety and economic consequences. The laser shock surface treatment technique is being considered a competitive alternative in mitigating cra...

This research compares the performance of space-time surrogate models (STSMs) and network surrogate models (NSMs). Specifically, when the system response varies over time (or pseudo-time), the surrogates must predict the system response. A surrogate model is used to approximate the response of computationally expensive spatial and temporal fields r...

Recent developments in surrogate construction predominantly focused on two strategies to improve surrogate accuracy. Firstly, component-wise domain scaling informed by cross-validation. Secondly, regression to construct response surfaces using additional information in the form of additional function-values sampled from multi-fidelity models and gr...

A failure mechanism prevalent with boiler tubes operating in harsh environmental conditions is localized erosion. The consequence of the erosion mechanism is a substantial reduction of the tube thickness, ultimately leading to plastic collapse and consequently rupturing of the tubes. Locating and repairing all the affected tubes within the boiler i...

Tyre forces are the primary external forces applied to a vehicle, especially at lower speeds, but are notoriously difficult to measure or predict. An intelligent tyre that allows the external forces to be determined from simple measurements can be used to improve vehicle safety systems like ABS and stability control and mitigate collisions. An inte...

In-service turbine blade failures remain a source of concern and research interest for engineers and industry professionals with attendant safety and economic implications. Very high-pressure shock impacts from laser shots represent an evolving technique currently gaining traction for surface improvement and failure mitigation in engineering compon...

The Prototype Bootstrapping Method (PBM) is a sampling technique for nonlinear system identification specifically when applied to Accelerated Fatigue Testing (AFT). This application requires the number of samples taken to be limited as much as possible to preserve the integrity of the test. The work presents a generalization of this technique by re...

The creep response and stress relaxation of X20 CrMoV12-1 steam piping under diverse operating conditions were simulated using finite element analysis (FEA) code, Abaqus alongside fe-safe/Turbolife software. In the study, steady-state creep and creep analysis characterized by 24 hours daily cycle consisting of a total of 6 hours peak, 4 hours trans...

This paper presents a general and reliable shape optimization scheme for snap-through structures to match a target load-deflection curve. The simulation of the snap-through structures typically requires the Arc Length Control (ALC) method. The adaptive stepping in ALC creates unavoidable discontinuities in the objective function. A discontinuous ob...

Response reconstruction is used to obtain accurate replication of vehicle structural responses of field recorded measurements in a laboratory environment, a crucial step in the process of Accelerated Destructive Testing (ADA). Response Reconstruction is cast as an inverse problem whereby an input signal is inferred to generate the desired outputs o...

This paper proposes a generic approach to obtain semi-analytical mesh sensitivities and shows how to compute mesh updates for any tetrahedral mesher. The proposed strategy allows sensitivities to be computed for a given mesh or first improve an initial mesh and then compute sensitivities. The strategy is based on a modification of Persson and Stran...

Steam piping is one of the major components of power generation plant because of its use in conveying steam from the boiler to the turbines compartment. Over time, these pipings are subjected to diverse operating conditions in an attempt to meet the daily electricity demand. Hence, the useful creep life of the piping is drastically affected. In thi...

Timeous prevention of, and recovery from, downtimes due to in-service failure of crucial power plant components, like turbine blades, portends huge consequences in the form of operational and financial viability concerns. Intensive research and development in manufacturing, re-manufacturing and condition-based maintenance of these components have b...

In a bid to minimise the cost of electrical energy production through the reduction in the quantity of coal usage, the power generation companies resolved to operate different daily cycles characterized by peak and off-peak energy demand periods. These daily operational cycles have left the power plant components operating in a possible creep-fatig...

The possibility of accurately inferring the external forces applied to a vehicle can directly contribute to better safety systems and thus lowers the chance of injury or loss of life. These external forces are applied to a vehicle through the tyres and are challenging to measure directly. Still, it is possible to measure acceleration, deformation,...

The ever-increasing relationship between energy consumption and economic growth continues to reinforce functional power generation infrastructure as the centerpiece of development. However, downtimes from in-service failure of power plant components, such as turbine blades, portend dire consequences in the form of huge financial and safety concerns...

Localized erosion is one of the most common failure mechanisms associated with boiler tubes, driven by impaction of the tube surface by fly ash, soot blowing steam, falling slag or other abrasive substances from the boiler’s combustion chamber. The tubes may experience significant localized reduction in their wall thickness, becoming susceptible to...

In service, steam pipes are subjected to high temperature close to 0.4 Tm (melting temperature) or higher and pressure; thus, making them prone to failure due to creep. Often, the design methods for these steam pipes usually do not provide their specific in-service life; hence, some type of service fitness tests are performed, and data obtained fro...

Boiler tubes used in power plants and manufacturing industries are prone to failure due to the harsh environment they operate in, usually involving high temperature, pressure, and some erosive-corrosive mechanism. Among the wide range of failures associated with the tubes, localized external erosion continues to be a leading cause of tube leakages...

The geometrical increase in the demand for electrical energy has posed serious pressure on the power generation components such as the steam pipes due to the consequential increase in the operating parameters such as temperature and pressure. This increment in operating parameters tends to limit the useful life of these pipes. Thus, high creep resi...

An update to the original CSIR-ML6 method. The following changes have been made: SOCATv2020 is used; ERA5 wind data and MSLP are used (instead of ERA interim); SODA salinity is used instead of EN4 salinity. Please cite the dataset as well as the original publication (https://doi.org/10.5194/gmd-12-5113-2019).

The possibility of creep–fatigue interaction occurring in steam pipes of power generation plants during operation has been on the front burner for years. Often, failure of the pipes during operation is attributed to either creep alone or fatigue alone. Of recent, some failures are speculated to be due to simultaneously coupled interaction between c...

Creep behaviour of X20 (12Cr-1MoVNi) steam piping subjected to a typical operating pressure of 18 MPa and temperature of 550 °C have been investigated using finite element analysis code, Abaqus and fe-safe/Turbolife software. User subroutine script for the modified hyperbolic sine creep model used was developed in Fortran and implemented in Abaqus....

Components subjected to operation at a temperature in the range of 0.4 Tm (Melting temperature of component) and above are prone to failure due to creep. The failure becomes more severe when the component is further subjected to a sequence of start-up and shutdown cycles. If the cycles are enough to induce extensive plastic strain, the failure of t...

Over the last decade, advanced statistical inference and machine learning have been used to fill the gaps in sparse surface ocean CO2 measurements (Rödenbeck et al., 2015). The estimates from these methods have been used to constrain seasonal, interannual and decadal variability in sea–air CO2 fluxes and the drivers of these changes (Landschützer e...

Shot peening (SP) is a controlled and systematic process of surface treatment that has a large number of controllable process parameters that make its application highly challenging. It involves the shooting of small and hard metallic balls at a targeted surface, with the aim of enhancing the fatigue strength of the workpiece under unfavorable serv...

In this study we examine the rotational (in)variance of the differential evolution (DE) algorithm. We show that the classic DE/rand/1/bin algorithm, which uses constant mutation and standard crossover, is rotationally variant. We then study a previously proposed rotationally invariant formulation in which the crossover operation takes place in an o...

Bow shackle failures, over the years, raised the question whether these failures are attributed to microstructural changes along the profile of the shackle or due to the geometry of the shackle. Bow shackles forged from 080M40 (EN8) material were subjected to different heat treatments in order to alter the microstructure thereof. The shackles were...

Over the last decade, advanced statistical inference and machine learning have been used to fill the gaps in sparse surface ocean CO 2 measurements (Rödenbeck et al. 2015). The estimates from these methods have been used to constrain seasonal, interannual and decadal variability in sea­air CO 2 fluxes and the drivers of these changes (Landschützer...

The thermo-mechanical stress, strain and temperature distribution across the thickness of X20 steam pipe at region less susceptible to thermo-mechanical failure was simulated using finite element analysis software, Abaqus. The mesh convergence studies conducted showed that 10 mm mesh size was suitable for the simulation. The temperature distributio...

This paper presents the development and numerical implementation of a state variable based thermomechanical material model, intended for use within a fully implicit finite element formulation. Plastic hardening, thermal recovery and multiple cycles of recrystallisation can be tracked for single peak as well as multiple peak recrystallisation respon...

Room temperature experimental compression test data is available for different hardmetals. This data indicates the presence of some spatial inhomogeneity due to a compression instability, eccentric loading or time varying equivalent bending moment. To account for this, an inverse analysis is employed that determines not only the constitutive materi...

Boiler tubes experience reductions in wall thickness due to erosion and corrosion mechanisms while in use. Due to this localized thinning, the tube becomes susceptible to gross plastic deformation, which eventually causes the tube to rupture. This study presents a non-linear finite element analysis of different geometric configurations of localized...

Superplastic forming is a slow forming process. The forming time can be minimized by optimizing the pressure profile applied to the forming sheet. The optimization of the superplastic forming pressure is usually done such that a target strain rate at a high strain rate sensitivity is maintained. Careful consideration of the strain rate is required,...

Resolving and understanding the drivers of variability of CO2 in the Southern Ocean and its potential climate feedback is one of the major scientific challenges of the ocean-climate community. Here we use a regional approach on empirical estimates of pCO2 to understand the role that seasonal variability has in long-term CO2 changes in the Southern...

The Southern Ocean accounts for 40 % of oceanic CO2 uptake, but the estimates are bound by large uncertainties due to a paucity in observations. Gap-filling empirical methods have been used to good effect to approximate pCO2 from satellite observable variables in other parts of the ocean, but many of these methods are not in agreement in the Southe...

Machine learning methods (support vector regression and random forest regression) were used to map gridded estimates of ΔpCO2 in the Southern Ocean from SOCAT v3 data. A low (1° × monthly) and high (0.25° × 16-day) resolution implementation of each of these methods as well as the SOM-FFN method of Landschützer et al. (2014) were added to a five mem...

Accelerated destructive degradation testing is considered with the objective of reproducing high fatigue incidents for a severely nonlinear system in a lab environment. In the lab, a test specimen is mounted on servo hydraulic actuators which are then used to induce the same response in the system as was measured in field tests. Finding the inputs...

Different roll pass reduction schedules have different effects on the through-thickness properties of hot-rolled metal slabs. In order to assess or improve a reduction schedule using the finite element method, a material model is required that captures the relevant deformation mechanisms and physics. The model should also report relevant field quan...

The refractory linings used in smelting furnaces undergo cooling and heat-up cycles when the furnaces are shut down and restarted. Severe deformation, cracks and metal penetration have been observed during furnace excavation. To develop an improved understanding of furnace refractory linings under thermal and mechanical loads, a 3D finite element m...

The Southern Ocean accounts for 40 % of oceanic CO2 uptake, but the estimates are bound by large uncertainties due to a paucity in observations. Gap filling empirical methods have been used to good effect to approximate pCO2 from satellite observable variables in other parts of the ocean, but many of these methods are not in agreement in the Southe...

Material parameter identification is a technique that is used to calibrate material models, often a precursor to perform an industrial analysis. Conventional material parameter identification methods estimate the material parameters for a material model by solving an optimisation problem. An alternative but lesser-known approach, called a direct in...

Electromagnetic levitation melting shows some promise as a containerless heating method for measuring material properties. However, the design of the levitation cell influences what temperature ranges are achievable with certain sample materials and sample sizes. It is therefore desirable to have a numerical model available to design levitation cel...

A constitutive model that captures the dominant strengthening and softening physics or microstructural changes of metallic materials is needed within a numerical environment for the effective prediction and simulation of plasticity during hot working processes. Dislocation density or related stress values play the primary role of internal state dep...

Electromagnetic levitation melting shows some promise as a containerless heating method for measuring material properties. However, the design of the levitation cell influences what temperature ranges are achievable with certain sample materials and sample sizes. It is therefore desirable to have a numerical model available to design levitation cel...

Presentation was on finite element analyses studies on boiler tubes that could help to predict whether a tube with a localized thinning is safe for continued operation or will fail. The outcome of the study helps to categorize the severity of failure of the tubes in order to prioritize repairs and maintenance spending. Generalized methodology which...

Creep data is rarely available in a form that allows for easy implementation into commercial FEA software. This paper presents a method for effectively creating a creep material model in the commercial FEA software ANSYS using experimental creep data from the Japanese National Institute for Materials Science (NIMS). An optimisation methodology is p...

The design of coupling algorithms for partitioned fluid–structure interaction (FSI) simulations are typically validated on FSI problems involving large deformations of thin elastic structures with large added mass ratios. A large number of FSI problems may however feature additional internal non-linearities, examples of which include problems with...

Blaze-DEMGPU is a modular GPU based discrete element method (DEM) framework that supports polyhedral shaped particles. The high level performance is attributed to the light weight and Single Instruction Multiple Data (SIMD) that the GPU architecture offers. Blaze-DEMGPU offers suitable algorithms to conduct DEM simulations on the GPU and these algo...

Control parameter studies assist practitioners to select optimization algorithm parameter values which are appropriate for the problem at hand. Parameters values are wellsuited to a problem if they result in a search which is effective given that problem's objective function(s), constraints and termination criteria. Given these considerations a man...

Electromagnetic levitation melting is a containerless technique to obtain material properties of reactive, electrically conductive materials that would otherwise result in sample contamination when in contact with a container at high temperatures. The levitation coil geometry, and the magnitude and frequency of the alternating current determine the...

Electromagnetic levitation melting is a containerless technique to obtain material properties of reactive, electrically conductive materials that would otherwise result in sample contamination when in contact with a container at high temperatures. The levitation coil geometry, and the magnitude and frequency of the alternating current determine the...

In this paper we introduce the idea of combining artificial compressibility (AC) with quasi-Newton (QN) methods to solve strongly coupled, fully/quasi-enclosed fluid–structure interaction (FSI) problems. Partitioned, incompressible, FSI based on Dirichlet-Neumann domain decomposition solution schemes cannot be applied to problems where the fluid do...

We examine the rotational (in)variance of the continuous-parameter genetic algorithm (CPGA). We show that a standard CPGA, using blend crossover and standard mutation, is rotationally variant. To construct a rotationally invariant CPGA it is possible to modify the crossover operation to be rotationally invariant. This however results in a loss of d...

The yield stress versus plastic strain curve of steel fibres is obtained by solving an inverse problem. The steel fibres find application to reinforce concrete, changing the failure mode from catastrophic brittle failure to pseudo-ductile. Conventional uniaxial testing proves ineffective due to early onset of necking. Consequently a wire bending te...

In this study we consider the characterisation problem of soil profiles, which is of practical importance in foundation engineering. Experimentally the dispersion curve is measured from which the soil profile is estimated using an inverse analysis. We consider two inverse approaches to estimate the soil profile in a virtual experiment from the mode...

Inverse identification methods are commonly used in engineering problems to indirectly identify systems parameters. However, solving an inverse problem is not always a straightforward task, and it may result in multivariate optimization problems. In this paper, radial basis function (RBF) interpolation of the inverse of the system is proposed to so...

Data is available for different hard metal samples tested in compression using a modified tensile test specimen. Three strain gauges were placed 120 degrees apart around the circumference of the centre of the test section. The spread of the strain data obtained from these tests indicate non-uniform compression. In this paper, the benefits of surrog...

In this paper we introduce a new multi-vector update quasi-Newton (MVQN) method for implicit coupling of partitioned, transient FSI solvers. The new quasi-Newton method facilitates the use of ‘black-box’ field solvers and under certain circumstances can be demonstrated to provide Newton-like convergence behaviour for strongly coupled FSI benchmark...

Goldmann Applanation Tonometry (GAT) is a method used to estimate the IntraOcular Pressure (IOP) by measuring the indentation resistance of the cornea. A popular approach to investigate the sensitivity of GAT results to material and geometry variations is to perform numerical modeling using the Finite Element (FE) method, for which a calibrated mat...

This study considers the numerical sensitivity calculation for discontinuous gradient-only optimization problems using the complex-step method. The complex-step method was initially introduced to differentiate analytical functions in the late 1960s, and is based on a Taylor series expansion using a pure imaginary step. The complex-step method is no...

This paper presents an inverse method to identify the true stress–strain behaviour of an elasticplastic material. Once such a stress‐strain curve is available, it is typically used to predict the behaviour of a specific design subjected to specific loads. The identification method consists of conducting experiments that impose loads on a specimen,...

Most sensitivity analysis studies of optimization algorithm control parameters are restricted to a single objective function evaluation (OFE) budget. This restriction is problematic because the optimality of control parameter values (CPVs) is dependent not only on the problem’s fitness landscape, but also on the OFE budget available to explore that...

Numerical results of the pull-out of a single hooked end steel fibre from a dog-bone shaped epoxy matrix are reported in this paper. The plasticity of the steel fibre was investigated during evolution of the pull-out process. A three-dimensional finite element model built in ANSYS, incorporating nonlinear contact, finite deformations and plasticity...

Foundation engineering requires accurate characterization of the soil of which direct measurement is often costly or impractical. Alternatively, an inverse problem can be solved to estimate soil layer characteristics from experimentally measured seismic surface wave data. This however requires the accurate and robust computation of smooth Rayleigh...

When solving multi-objective optimization problems, practitioners desire the most accurate solution possible given the available objective function evaluation (OFE) budget. Since OFE budgets vary largely in practice, it is important to gauge the sensitivity of an optimization algorithm to OFE budget constraints. To this end, a method is presented f...

Traditionally primary irradiation creep is introduced into graphite analysis by applying the appropriate amount of creep strain to the model at the initial time-step. This is valid for graphite components that are subjected to high fast neutron flux fields and constant stress fields, but it does not allow for the effect of movement of stress locati...

Kriging is used extensively as a metamodel in multidisciplinary design optimization. The correlation matrix used in Kriging metamodeling frequently becomes ill-conditioned. Therefore different numerical methods used to solve the Kriging equations affect the search for the optimum Kriging parameters and the ability of the Kriging surface to accurate...

This abstract was presented at the ‘Studentesimposium in die Natuurwetenskappe 2011’, presented under the protection of the Suid- Afrikaanse Akademie vir Wetenskap en Kuns. The symposium was held at the University of South Africa on 27–28 October 2011.

The strain rate dependent behaviour of some visco-elastic materials can be modelled accurately in 1-D by including a stress contribution which depends non-linearly on strain rate. A visco-elastic model by Shim et al.[3] comprises a Voigt and Maxwell element in parallel and provides an effective representation of cancellous bone from the human cervi...

Understanding the dynamical behavior of Granular Media (GM) is extremely important to many industrial processes. Thus simulating the dynamics of GM is critical in the design and optimization of such processes. However, the dynamics of GM is complex in nature and cannot be described by a closed form solution for more than a few particles. A popular...

Since plasticity is path dependent, it is necessary to properly take into account the deformation, strain rate and temperature history in applications such as crash worthiness and ballistics simulations. To accurately model the evolution of the yield stress, the incremental (differential) update from a previous converged time step is required inste...

This work details the development of a computational tool that can accurately model strongly-coupled fluid-structure interaction (FSI) problems, with a particular focus on thin-walled structures undergoing large, non-linear deformations. The first part of the work investigates improving the efficiency with which a stable and robust in-house code mo...

Tests were done on the compressive behaviour of different metal matrix composite materials. These extremely hard engineering materials consist of ceramic particles embedded in a metal alloy binder. Due to the high stiffness and brittle nature of the material, compression tests were only performed to about 2% uniaxial strain as measured by the displ...

This study reports on the asymptotic behavior of the maximum likelihood function, encountered when constructing Kriging approximations using the Gaussian correlation function. Of specific interest is a maximum likelihood function that decreases continuously as the correlation function hyper-parameters approach zero. Since the global minimizer of th...

This conference contribution focusses on the invertibility of non-ideal material tests to accurately determine material parameters. This is done by attempting to model non-ideal test cases and comparing strains as well as force history to the experimental data. An inverse analysis is performed that determines material properties and boundary condit...

Variation in masticatory induced stress, caused by shape changes in the human skull, is quantified in this article. A comparison on masticatory induced stress is presented subject to a variation in human skull shape. Non-rigid registration is employed to obtain appropriate computational domain representations. This procedure allows the isolation of...

This paper presents a tutorial on geometrically nonlinear finite element analysis. The main contribution is the simplicity of the development of the discretized finite element equations. The total Lagrangian formulation is used, and a Saint-Venant Kirchoff material is selected. The weighted residual technique is selected as the basis for the develo...

Corneal biomechanical properties are an important element in the study of corneal biomechanics. There are currently two techniques to obtain these properties; an inflation test and the strip extensiometry test. As the inflation test has been numerically modelled in several studies, this study focusses on accurately modelling the strip extensiometry...