Electromagnetic optimization is becoming increasingly important with the rise of high-tech applications, such as metalenses. Among the different topology optimization methods applied, a recent method combining level set optimization, parametrized with radial basis functions (RBFs), with enriched finite element analysis (e-FEA) offers promising results by creating smooth material edges without the need to remesh. Having these smooth material edges is crucial because the quality of the material edges has a significant impact on the performance of wave propagation designs. This method could help design metalenses for a number of different applications, such as improving the light-collection efficiency of scintillators. The method exhibited oscillatory behavior in the objective function in earlier wave-front-dependent designs, a phenomenon that has not yet been fully investigated. In this study, we analyze the dependence of the level-set optimization on the key parameters to optimize these parameters to reduce oscillatory behavior in the objective function and increase the performance of the final design. These parameters include the RBF radii, mesh sizes for the design and simulation mesh, initial level set hole seed, various methods for finding the location of the enriched nodes, regularization of the level set, and optimizer parameters. We provide a series of tests that analyze the impact of RBF parameters on the simulation and optimization of an electromagnetic design with a simulation test, shape-matching optimization, and electromagnetic identification problem. The results show that, although even large RBF radii can represent fine features in a design, this is not the case during optimization. Furthermore, an overfitted initial design variable field can also oscillate during the optimization. This formulation is then applied to a metalens optimization applied to a scintillator case. Without the optimized parameters, the results showed oscillatory behavior and a large dependence of the performance of the final design on the RBF parameters. Once the optimized parameters were implemented, the oscillations disappeared until the best design of the optimization was reached, and the performance was increased by 12.4%.

The objective of particle detectors in high-energy physics research is to reveal the fundamental laws of nature. The Minimum Ionizing Particle Detector (MTD) has been designed to enhance the timing precision of theCMS (Compact Muon Solenoid) detector at CERN to 50 ps under the increased number of particle impacts after upgrading the Large Hadron Collider (LHC) to the High-Luminosity LHC. The Barrel Timing Layer (BTL) segment of the MTD uses silicon photodetectors (SiPMs), whose timing accuracy depends on their operating temperature and the number of photons they detect. This dissertation presents numerical methods to improve the timing precision of these SiPMs through the design of thermoelectrical coolers and scintillation crystals. On the one hand, thermoelectrical coolers (TECs) can lower the SiPMs temperature, reducing signal-to-noise ratio and recovering radiation-induced damage through controlled annealing procedures. We provide an analytical model to study the landscape of TEC topology optimization with a lower temperature objective, power constraints and two density design variables. This study leads to the recommendation of penalization coefficients for SIMP (solid isotropic material with penalization) in the form of kp = kσ > kα with kp the thermal conductivity, kσ the electrical conductivity and kα the Seebeck’s penalization coefficient to reduce the nonconvexity induced by the power constraint. These coefficients reduce nonconvexity from power constraints, allowing FEM topology optimization via SIMP to achieve lower material volumes and temperatures without volume constraints and filtering schemes. FEM optimization examples are provided, which incorporate electrical working points through a voltage gradient design variable and constant material properties. These examples reduce the temperature by up to 10 ◦C compared to the optimal electrical working point of the original designs. Finally, comparing these results with designs with non-linear, temperature-dependent properties shows that the use of constant material properties can lower computational costs and improve design performance. Although optimized designs achieve lower temperatures, TECs are fragile. The construction of the BTL highlights this fragility, prompting an extension of the design to address operational thermal and mechanical loads. This work introduces a FEM-based topology optimization for the coupled thermoelectromechanical problem using SIMP. This also includes the formulation with nonlinear material properties, and how to deal with the checkerboarding with the extended mechanical degree Celsiuss of freedom. The optimized designs reduce stress concentrations by half while enhancing cooling capabilities. On the other hand, we complement the lower signal-to-noise ratio obtained from using TECs, with an increased number of photon impacts enhancing the SiPM signal. The number of photons created or the scintillation light yield depends on the material composition of the scintillators. However, the photon arrival count at SiPMs is influenced by their reflective surfaces and volume. We provide a model of BTL within GEANT4, a ray-tracing particle-matter interaction software. This model incorporates the effect of the particle impact location and is used in conjunction with NSGAII (non-dominated sorting genetic algorithm) to optimize scintillator shapes to increase the photon detection count. The study uses multiple objective functions based on the stochastic nature of the arrival photons. From these results, the recommended objective function is the mean light collection per energy deposition and the ionizing particle track length, reducing statistical errors and accounting for energy deposition. The results provide relative gains to the original designs in the objective function between 15 and 38%. To overcome the computational limits of Monte Carlo methods, we follow up by translating the scintillation equations into a transient wave for FEM simulations, matching GEANT4 pulse shapes. Furthermore, we perform a shape optimization using a static frequency domain scintillation model replicating the variable influence within GEANT4. The optimal designs obtained with FEM are validated within GEANT4, obtaining gains of the order of 7.7%. These gains were achieved with less than 1% of the computational resources needed to perform the GEANT4 optimizations.

Most micro- and nanomechanical devices are designed to operate within the linear dynamic range by using simple geometries, primarily due to the limited knowledge in utilizing nonlinearity and constraints in fabrication techniques. However, it is anticipated that the scope of applications and fundamental research can be significantly expanded, if these tiny systems can be precisely engineered to account for and exploit their various nonlinear dynamic behaviors. This thesis provides a comprehensive study on the optimization of dynamical properties of high-Q nanomechanical resonators, spanning from linear to nonlinear dynamics and evolving from single-mode to multi-mode analysis.

We first give an introduction to the development of micro- and nanomechanical resonators in Chapter 1. We focus on their unique mechanics, including very low dissipation and strong nonlinearities. Furthermore, we elaborate on the motivation behind this thesis and the need for linking engineering optimization with micro- and nanomechanical resonators. Followed by Chapter 2, we elaborate on the methodology we use throughout this thesis, including fabrication techniques of nanomechanical Si3N4 devices, characterization approaches by optical measurements, and modeling procedures for structural dynamics. Among all methodologies, we highlight the Finite Element (FE)- based Reduced Order Models (ROMs) that can accurately capture the geometric details and boundary conditions, which facilitate the design of resonators with predictable dynamical properties.

We start from investigating linear dynamics of Si3N4 nanostrings in Chapter 3, where the tuning effects of their soft-clamping supports on resonance frequency and Q-factor are evaluated. We experimentally and theoretically reveal a trade-off between maintaining high stress and low stiffness of the supports in designing high-Q resonators fabricated with initial strain. By optimizing this trade-off with our soft-clamping design, we obtain a 50% enhancement of Q-factor compared to doubly-clamped string resonators. With stronger drive levels, in Chapter 4, we show that the nonlinear dynamics can also be substantially tailored by soft-clamping supports. Through careful engineering of support geometries, we introduce softening nonlinearity by stress-induced buckling, allowing precise control over the nonlinear dynamic responses in doubly supported nanostrings, which conventionally exhibit hardening behaviors.

Based on the accurate modeling of both linear and nonlinear dynamics that is validated by experiments, we integrate our FE-based ROM technique with a derivative-free optimization algorithm for the design of nonlinear mechanical resonators in Chapter 5. By optimizing the support’s geometry of our nanostrings, we show that the proposed methodology is not only capable of handling a single optimization goal, but also multiple conflicting objectives, such as the simultaneous enhancement of Q-factor and the Duffing constant. Besides, we generate Pareto frontiers that visualize the trade-offs among multiple optimization objectives, verify the optimized results with brute-force simulations and validate the numerical framework with experiments.

Apart from the dynamics in a single mode, we observe modal interactions between multiple vibrational modes of our nanostrings in the strong nonlinear regime. In Chapter 6, we demonstrate that soft-clamping techniques, commonly utilized to achieve high-Q resonators, can be employed to engineer mode coupling. We verify the analytically derived two-degree-of-freedom system between the lowest two out-of-plane modes by FE-based ROMs and experiments. We further reveal the significant impact of multi-mode interactions on the nanostrings’ frequency response, demonstrating additional opportunities to tailor the nonlinear dynamics of mechanical resonators facilitated by soft clamping. Moreover, we highlight the design potential of soft-clamping supports through the geometric optimization of two-mode coupling, showcasing the effective Duffing constant of the driven mode can be increased by 70%, as well as the onset of mode coupling can be geometrically programmed to either facilitate or inhibit its occurrence.

We conclude all works presented for achieving the optimization of nonlinear dynamics in nanomechanical resonators, and give an outlook for future directions in Chapter 7.

Increased capabilities of additive manufacturing technologies have opened up numerous possibilities in mandibular reconstruction surgery. For example, 3D scans can be used to design patient-specific reconstruction plates, resulting in designs that are tailored to prevent plate fracture, wound dehiscence, and malocclusion. However, screw loosening as a result of stress shielding is still an issue. This phenomenon is caused by the mismatch in stiffness between the bone and implant material. The stiff- ness of the titanium in these reconstruction plates can be reduced by using porous microstructures in the proximity of the remaining mandible. However, this makes intuition-based design impossible. This work applies computational tools to optimize the design of a mandibular reconstruction plate with varying microstructure porosity. To achieve this, Topology Optimization (TO) is used that accurately re- solves boundaries utilizing the Interface-enriched Generalized Finite Element Method (IGFEM), which results in a smooth representation of the design. In this work, this methodology is enhanced to result in an even smoother and more accurate boundary. Moreover, additions are made to account for varying material properties in the analytical sensitivities of the compliance objective. The functionally graded designs exhibit significantly higher compliance that should reduce stress shielding. Also, they feature a more porous microstructure near the bone, providing a basis for bone ingrowth. Thus, it is established that enriched TO can be used to optimize the design of mandibular reconstruction plates made out of functionally graded materials that could reduce the risk of screw loosening.

This thesis documents the performance of a p-hierarchical interface-enriched generelized finite element method (p-IGFEM) on weakly discontinuous beams and plates, which are modeled according to the first-order shear deformation theory (FSDT). Here the purpose of the higher-order shape functions is to reduce the shear locking that arises due to FSDT. In this report the examples will be limited to linear, static beams and plates with a single material discontinuity. The method will be assessed in both the convergence rate (in energy norm) and the stability. The method has shown to be very susceptible to small relative distances between enriched and standard nodes. Furthermore, the condition number could successfully be decreased by applying a Jacobi-like diagonal preconditioner.

Model Order Reduction is an essential tool in analysis of structures exhibiting nonlinear dynamic behaviour. In this work the model order reduction method of Modal Derivatives, which is an extension of the linear Modal Truncation method into the nonlinear regime, is implemented in an automated scheme starting from a Finite Element discretization based on a Kirchhoff-Love shell element. After validation of the implementation, multiple thin-walled examples are analyzed and the results of the reduced-order model are compared to results from literature.

We perform a study on acoustic metasurfaces, aiming to achieve simultaneously low resonance frequencies (below 400 Hz), high attenuation bandwidth (greater than 200 Hz), and high attenuation coefficient magnitudes (above 0.8), while maintaining a surface-like structure.
We propose the implementation of geometrical optimization through genetic algorithms, as well as the incorporation of a chamber to induce resonator coupling in a supercell hexagonal Helmholtz resonator metasurface, to achieve the stated objectives simultaneously.
Results show that genetic algorithms can effectively increase the attenuation bandwidth while maintaining a moderate attenuation coefficient magnitude. Incorporating a chamber induces resonator coupling, causing frequency locking and pulling phenomena. A narrow chamber can effectively lower the resonance frequencies and enhance the attenuation coefficients at those frequencies, while maintaining a surface-like structure. However, incorporating a chamber may lead to a reduction in bandwidth. By combining the genetic algorithm optimization with chamber integration, we observe a significant reduction in bandwidth narrowness, while the benefits of frequency locking and pulling are maintained.
In conclusion, genetic algorithms have the potential to achieve wide attenuation bandwidths, while chamber incorporation holds promise for attaining low resonance frequencies with high attenuation coefficients. Using both methods simultaneously may enable the achievement of all objectives.

The predominant influence of geometry and tensile stress on the Q factor of nanomechanical resonators is a phenomenon commonly described as dissipation dilution. In recent years, a variety of studies has looked into maximizing this effect, resulting in an assortment of softly-clamped resonator designs. This paper proposes a methodology that uses topology optimization (TO) to design nanomechanical structures with very high Q factors, by maximizing the effects of dissipation dilution. A novel equation, based on the tensile and bending energies of a prestressed finite element model, is proposed to capture this effect. Through adjoint sensitivity analysis, the sensitivity of this function with respect to (changes in) element-level design parameters was determined, which is a capability that is not available in commercial finite element packages. Furthermore, the absence of information required a priori to the optimization makes the proposed methodology versatile and easy to use. After verification of the equation and its sensitivity, it is used as an objective in TO to optimize resonator geometries inspired by state-of-the-art resonator designs. Given a thickness of 340nm and prestress of 1GPa, the final designs show a numerical Q × f0 that competes with optimized designs found in literature.

Current service and installation activities for offshore wind turbines are carried out by jack-up vessels, which eliminate wave disturbances to a large extent. The use of these vessels imposes several disadvantages, including high operational costs and the limitation of operating in restricted water depths. An alternative is a crane mounted on a floating vessel (monohull), which is quicker in operation and multi-deployable. With these vessels, however, a motion compensator is needed to eliminate most of the hydrodynamic disturbances. The purpose of this graduation assignment is to develop a concept design for a passive motion compensator (PMC) to isolate the vessel motion from the payload.

This goal is achieved by the implementation of a multi-objective optimization algorithm based on genetic programming (GP) that constructs a two-dimensional PMC based on the principle of quasi-zero stiffness. The GP employs a set of genetic operators to explore the design space in terms of topology and design variables, which effectively mimics Darwin’s Theory of Evolution. The better a mechanism performs, the higher the fitness, and thus the higher the chance this design appear in future generations.

Each design is a composition of cylinders and nodes that are assembled into a mechanism. During the fitness evaluation, all mechanisms are examined by a nonlinear finite element method to extract the force-displacement relations. The arc-length control method is used due to the large displacements and rotations of the members in the mechanism, whereby both the nodal displacement vector and external load vector are varied to follow an equilibrium path in an incremental-iterative way. To provide sufficient support to the payload, the mechanism is prestressed, which is applied by using the arc-length procedure as well.

Static and dynamic results show that the GP is suitable for constructing a high-level planar QZS mechanism for the intended application in various sea states. From multiple runs, it can be concluded that the optimizer generally produces designs with the same topology. Dynamic analyses in the time domain show that motions are effectively mitigated in the horizontal and vertical directions for the chosen designs. In addition, analysis in the frequency domain shows that the mechanisms effectively attenuate motions in the frequencies of interest.

Origami has many advantages, such as deployability, low mass, and ease of miniaturization; it has potential contributions in many applications. Specifically, origami that has been designed to fold into a target shape can be used in deployable tents, bridges, grippers, packaging, and deformable mirrors for laser communication. This work presents a two-step methodology for optimizing origami designs such that the distance between the bottom side of an origami and its target surface is minimized—the origami will thus lay “on top” of its target surface. The method combines the strengths of rigid origami and non-rigid origami: it starts with a non-foldable rigid origami Miura-ori tessellation that matches the target surface and optimizes this design such that it becomes foldable. Then it uses this crease pattern as the initial design for an optimization cycle that includes the nonlinear N5B8 bar-and-hinge non-rigid origami model and converges to the crease pattern that folds into the target shape, demonstrated in this work with a saddle, dome, and arch. The results show that for an 800 mm by 800 mm design, the folded saddle origami has a maximum distance to its target surface of 24 mm, with the other tested shapes having similar outcomes. This performance will be sufficient for some use cases, but more work is required for high-accuracy applications.

Acoustic waves due to their non-destructive and non-reactive nature, have been extensively used as information carriers in various applications including, medical imaging, material characterization, distance and velocity measurement, and flow rate measurement, among others. In an ultrasonic flowmeter (UF), the upstream and downstream travel times of ultrasound pulses across the fluid are measured, whose difference is directly related to the flow rate. However, during the measurement, a significant amount of the pulse’s energy leaks through the solid pipe (parasitic signal) and interferes with the fluid signal (working signal) known as crosstalk. Since crosstalk can lead to measurement errors and in extreme cases complete signal losses, we explore possibilities of phononic crystals (PnCs) to mitigate crosstalk from UFs.
PnCs are periodic structures possessing unusual dynamic characteristics due to the presence of band gaps (BGs)—frequency ranges where elastic and acoustic waves are attenuated. Because of BGs, they are explored in several applications, including vibration isolation, energy harvesting, acoustic wave steering, super/hyperlens, wave focusing, and cloaking. However, extending the PnCs to real applications such as the crosstalk reduction in UFs, is still very challenging since the application has multiple requirements and can be subjected to extreme environmental conditions. We design PnC waveguides to possess BGs in the UF’s operating frequencies, thereby acting as wave filters to alleviate crosstalk....

This research explores the integration of Neural Architecture Search with Optical Neural Networks to optimize the efficiency and performance in traditional visual image classification tasks. The study introduces a new approach that applies Neural Architecture Search, a technique traditionally used to optimize the performance of Artificial Neural Networks, to the field of Optical Neural Networks.

From the motion of electrons in an atom to the orbits of celestial bodies in the cosmos, governing equations are essential to the characterisation of dynamical systems. They facilitate an understanding of the physics of a system, which enables the development of useful techniques such as predictive control. An increasingly popular method to obtain these equations is Symbolic Regression, where governing laws are discovered from observations of the system. In this work, we extend the Deep Symbolic Regression package to the identification of dynamical systems. Preliminary tests revealed the limits of the method as applied to dynamical systems, and new methods of incorporating domain knowledge to constrain the expression space are added. We test the extended package on 3 strongly nonlinear ODEs that exhibit different dynamics as their parameterisation varies. Finally, we demonstrate the working of this method in practice by discovering the governing equation of a pendulum, from a video of its oscillation. This method achieved a 100% equation recovery rate on our tests, and was able to consistently retrieve the correct equation from datasets representing a diverse range of dynamics.

In this report a new enriched finite volume method is introduced. This method will be particularly useful for fluid-structure interaction problems. In engineering many problems are in the domain of fluidstructure interaction. Examples of these are water in sea locks, blood flowing in vessels and sailing ships. Fluid problems are usually solved with the finite volume method (FVM), and structures in this fluid flow are handled by discretizing the fluid flow around this structure. The mesh therefore needs to be conforming around the structure, and remeshing is needed when the the structure is moving over time. Remeshing is a computationally expensive process, therefore in FEM a method called enriched FEM is developed, which removes the need for remeshing. Enriched FEM uses so-called enrichment functions; these enrichment functions decouple the structure from the mesh. This concept is implemented in the finite volume method to get an enriched FVM. In order to come up with this method; FVM and enriched FEM are compared to see if the concepts of enriched FEM can be implemented in FVM. The FE method that is used is the discontinuous Galerkin (DG) method, which is a method that uses components of FEM and FVM. It discretizes equations as in FEM, but the elements are connected using flux functions as in FVM. DG is used to develop a high-order FVM and to introduce enrichments in FVM. The result of this thesis is a method which can implement enrichment functions in FVM, such that remeshing is no longer needed. The method is compared with conforming FVM and enriched DG, and it uses less computational power than both methods. The method also recovers the optimal convergence rate for a non-conforming FVM discretization. The enrichment functions are decoupled from the FVM discretization, therefore the method can be added to existing FVM solvers without changing the non-enriched part. The method is tested on a problem where waves are generated in a box.

Phononic crystals can be designed to have bandgaps---ranges of frequencies whose propagation through the material is prevented. They are therefore attractive for vibration isolation applications in different industries, where unwanted vibrations reduce performance. Yet, important steps are still to be made for the integration of phononic crystals into engineering practice. For instance, methods for large scale production are still in development. Furthermore, it is essential that design methods are established to enable the design of phononic crystals that meet all of the, often conflicting, requirements for practical applications. This thesis focuses on the latter challenge by proposing a computational design method for phononic crystals based on the combination of an advanced finite element method and level set-based topology optimization.

In this 3D fracture-based topology optimization framework, the author extended the 2D framework on tailoring fracture resistance for brittle materials (Zhang et al., 2022) to 3D. In the optimization, the topology is described by radial basis functions interpolated level set function, and the problem is solved by the Interface-enriched Generalized Finite Element Method (IGFEM). Cracks are assumed to exist on enriched nodes that are added on the boundary of the geometry to increase the accuracy of approximation. The first part of the work assumes cracks to be semi-circular with the crack plane perpendicular to the boundary, and the crack opening direction to be either parallel to the KM- or LM-plane of the global coordinates. An extended framework that assumes crack opening direction perpendicular to the surface first principal stress is also developed at the end. The energy release rates (ERRs) of the cracks are evaluated with the topological derivative method, which requires only a stress field of the geometry and weight functions that relate the stress and stress intensity factors (SIFs). The weight functions are found by a finite element analysis on a cuboid with a crack. This approach is computationally efficient because it eliminates the need of actually modeling and meshing the crack planes in the geometry during optimization. Moreover, a 3D stress recovery technique (or stress improvement procedure, SIP) is used to recover the nodal stress non-locally to improve the accuracy. The objective function is then established with the ]-mean aggregation of the ERRs. Finally, Numerical examples in 3D, including the famous L-bracket benchmark problem, are performed to prove the correctness and capacity of the framework. In conclusion, this extended framework shows more flexibility and provides more information to the optimized design than the 2D framework by considering an added dimension both in analyzed geometry and crack shape, i.e., the effect of the anisotropy of cracks can be captured.

Historically, contact analysis has been an important design tool for various applications such as vehicle crash analysis or manufacturing. It is also becoming increasingly more relevant in newer fields such compliant mechanism or metamaterial design. Even though contact has been a topic of discussion for decades, there are still challenges that need to be solved before a truly general contact analysis and optimization framework can be developed. As a milestone towards such framework, this project builds upon an existing novel linear contact analysis and a geometry immersion methodology developed in Interface-enriched Generalized Finite Element Method (IGFEM), to extend its capabilities to support large deformations (geometric non-linearities). Furthermore, a solution is presented to overcome void element over-stiffening in immersed large deformation contact analyses.

High-dimensional optimization problems with expensive and non-convex cost functions pose a significant challenge, as the non-convexity limits the viability of local optimization, where the results are sensitive to initial guesses and often only represent local minima. But as the number of expensive cost function evaluations required for a full exploration of the search space grows exponentially with the increasing number of dimensions, the use of standard global optimization algorithms is also not practical. To overcome this obstacle and to lower the dimensionality of the problem, the use of an autoencoder for model order reduction is proposed. In the resulting lower dimensional space, standard global optimization methods can then be utilized, as fewer cost functions evaluations are necessary. For problems with comparatively more expensive cost functions, this optimization includes the employment of a surrogate model, which reduces the necessary number of these computationally expensive evaluations further. This proposed method is then tested firstly on a number of benchmark functions, where it shows the ability to find global optima under certain conditions. Secondly, the proposed method is used to solve a compliance minimization problem, where it shows the ability to improve upon a large number of designs generated by local optimization.

It is relevant for various applications to seek a material that could be used for the active control of wave propagation. In this study, we explore tunablemetamaterials based on foldable origami sheets where the size of the bandgap can be tuned by the rigid folding along predefined crease lines. A combination of out-of-plane components and a crease results in the coupling and separation of bands in the band structure and eventually in a (modal) bandgap. The location, size, and vibration isolation performance are optimized and analyzed for a set of geometrical and material parameters, resulting in a potential design of aMiura-Ori structure. The methods used in this paper could be used for any kind of origami structure, which may lead to various new applications in the field of vibrations and acoustics.

The computational modeling of crack propagation is important in aerospace and automotive industries because cracks play a significant role in structural failure. In comparison with the quasi-static case, inertial effects are significant in dynamic crack propagation. The classical numerical tool for modeling dynamic crack propagation is the standard finite element method (FEM). However, the method suffers from problem of mesh-dependency. Enriched finite element procedures such as the eXtended/Generalized finite element method (X/GFEM) are able to solve this issue by adding enriched degrees of freedom (DOFs) to nodes of the original mesh, thereby providing full decoupling between the mesh and cracks. Yet, X/GFEM suffers from other issues that are inherent to the formulation such as the need for more complicated methods for applying non-zero Dirichlet boundary condition, and an intricate computer implementation. In the thesis, the Discontinuity-Enriched Finite Element Method (DE-FEM) is used to simulate dynamic crack propagation as an alternative to X/GFEM. DE-FEM also decouples cracks from the background mesh while solving X/GFEM’s aforementioned issues. This is achieved by adding enriched DOFs along cracks. Prescribing non-zero essential boundary conditions is as straightforward as in standard FEM. Moreover, DE-FEM’s enrichment strategy provides simplicity on crack propagation, as the crack tip node can be transformed into a crack segment node directly with little effort. Also, fewer enriched DOFs than in X/GFEM are appended while advancing cracks. In the numerical examples of either stationary crack with dynamic loading or dynamically propagating cracks, DE-FEM is able to reproduce analytical and/or experimental results. Both Bathe’s time integration method and the classical Newmark constant average acceleration method are applied and compared. Results show DE-FEM is a suitable candidate to solve dynamic fracture problems.