Continuum Structures Research Articles

On the Use of Fidelity Transformation Method for Stress‐Constrained Reliability‐Based Topology Optimization of Continuum Structure With High Accuracy

On the Use of Fidelity Transformation Method for Stress‐Constrained Reliability‐Based Topology Optimization of Continuum Structure With High Accuracy

Energy generation from friction-induced vibration of a piezoelectric beam

The primary challenge in harnessing vibration energy with piezoelectric materials is the discrepancy in frequency between the energy source and the energy generator, which lowers the efficiency of energy harvesting. To address the challenge, a piezoelectric beam under friction-induced vibration (FIV) is designed, modeled, and studied for the first time to realize the pronounced FIV contributing to energy generation by adapting the vibrations of the continuum structure to align close to its resonant frequencies. The Stribeck friction model is applied to characterize the variation of friction based on the relative sliding velocity vr between contacting objects. The analytical solution is derived to solve the dynamic responses, and transient charging simulation validated by the experiment is utilized to assess energy output. Furthermore, parameter studies are conducted based on the validated model with regard to the material properties of the beam and piezoelectric material, electrode connections of piezoelectric patches, and friction model parameters to investigate their influences on energy output. Considering the same dimensional properties, materials with low Young's modulus E and density ρ are desired for the host structure to facilitate large dynamic strain in piezoelectric materials. With an exponential decay factor C = 8, representing optimal material contact interface, pronounced higher FIV mode can be induced leading to higher output power. A root mean square charging power PeRMS of 42.4 mW and a peak instant charging power Pe − peak of 263 mW can be achieved. In the current study, the model is implemented on a beam coupled with one piezoelectric patch, which has potential applicability to non-uniform beams with various layouts of piezoelectric patches. The presented model enables efficient optimization of continuum structural design for higher piezoelectric energy generation under friction.

Voxel-based evolutionary topological optimization of connected structures for natural frequency optimization

AbstractThe topology optimization methodology is widely utilized in industrial engineering for designing lightweight and efficient components. In this framework, considering natural frequencies is crucial for adequately designing components and structures exposed to dynamic loads, as in aerospace or automotive applications. The scientific community has shown the efficiency of Bi-directional Evolutionary Structural Optimization (BESO), showcasing its ability to converge towards optimal solid-void or bi-material solutions for a wide range of frequency optimization problems in continuum structures. However, these methods show limits when the complexity of the domain volume increases; thus, they are well-suited for academic case studies but may fail when dealing with industrial applications that require more complex shapes. The connectivity of the structures resulting from the optimization also plays a fundamental role in choosing the best optimization approach, as some available commercial and open-source codes nowadays return unfeasible sparse structures. An improved voxel-based BESO algorithm has been developed in this work to cope with current limits in lightweight structure optimization. A significant case study has been developed to evaluate the performances of the new methodology and compare it with existing algorithms. In contrast to previous studies, the method we developed guarantees that the final structure respects constraints on the initial design volume and that the structure’s connection is preserved, thus enabling the manufacturing of the component with Additive Manufacturing technologies. The proposed approach can be complemented by smoothing algorithms to obtain a structure with externally appealing surfaces.

Non-probabilistic reliability-based multi-scale topology optimization of thermo-mechanical continuum structures with stress constraints

A reliability-based non-probabilistic multiscale topology optimization (NRBMTO) method with stress constraints is proposed for thermo-mechanical continuous structures with uncontrollable stresses. The physical parameters, external loads and temperature values at the macro scale, are regarded as non-probabilistic uncertain parameters in the optimization of structural topologies with complex physical fields at multi-scale. The homogenization-based finite element method is employed to quantify thermo-mechanical structures with multi-scale uncertain parameters in the established multi-scale topology model. The ellipsoid model is applied to describe the uncertainty of non-probabilistic random variables, and the non-probabilistic reliability index is obtained by estimating the failure probability based on the first-order reliability method (FORM). The unit stresses are aggregated to the global maximum stresses with the normalized p-norm function, taking into account the mechanical and thermal stresses. The sensitivity information of the compliance and stress constraint to the macro- and micro-design variables and uncertain variables are derived simultaneously. The macro- and micro- design variables are solved by the method of moving asymptotes (MMA), respectively. Several numerical examples are given to verify the effectiveness and feasibility of the proposed NRBMTO method. The results demonstrate that the optimized structure based on the NRBMTO method provides better security with reliability index β=3 and minimum compliance (244.39) while stress is controlled below 235 MPa compared to the classical deterministic multiscale topology optimization (DMTO) method.

An improved evolutionary structure optimization method considering stress minimization and smooth design

AbstractThe design of continuum structures often presents challenges related to stress concentration, which can cause significant structural damage. To address this issue, the current study presents a new stress minimization method that utilizes the Windowed Evolutionary Structural Optimization (WESO) framework. The method aims to improve algorithm stability by optimizing design variables with an intermediate density. The use of a P‐norm stress aggregation method improves the assessment of global stress levels and enhances computational efficiency. Furthermore, a stable element sensitivity formulation, derived from the adjoint sensitivity analysis of the global stress measure, effectively handles the nonlinear stress behavior. Mesh filtering techniques are utilized to convert sensitivity from elements to nodes, and the structural topological solution is represented using the level set function (LSF) based on element‐node sensitivity. This method addresses the singularity issue commonly found in density‐based optimization methods and facilitates the achievement of smooth topological solutions. Through 2D and 3D benchmark designs, the proposed method's feasibility, stability, and superiority are thoroughly demonstrated. A parametric study is conducted to identify the optimal parameter range for the algorithm, leading to the development of a rational method for parameter selection. The optimized topology, with its smooth boundaries, can guide the design of structures without the need for redesign or post‐processing, helping to drive innovation and development in engineering.

Classification and Evaluation of Octopus-Inspired Suction Cups for Soft Continuum Robots.

The emergence of the field of soft robotics has led to an interest in suction cups as auxiliary structures on soft continuum arms to support the execution of manipulation tasks. This application poses demanding requirements on suction cups with respect to sensorization, adhesion under non-ideal contact conditions, and integration into fully soft systems. The octopus can serve as an important source of inspiration for addressing these challenges. This review aims to accelerate research in octopus-inspired suction cups by providing a detailed analysis of the octopus sucker, determining meaningful performance metrics for suction cups on the basis of this analysis, and evaluating the state-of-the-art in suction cups according to these performance metrics. In total, 47 records describing suction cups are found, classified according to the deployed actuation method, and evaluated on performance metrics reflecting the level of sensorization, adhesion, and integration. Despite significant advances in recent years, the octopus sucker outperforms all suction cups on all performance metrics. The realization of high resolution tactile sensing in suction cups and the integration of such sensorized suction cups in soft continuum structures are identified as two major hurdles toward the realization of octopus-inspired manipulation strategies in soft continuum robot arms.

Analysis of a tendon-based deformation aggregation mechanism to host discrete vibration absorbers in continuum structures

Analysis of a tendon-based deformation aggregation mechanism to host discrete vibration absorbers in continuum structures

Modal truncation method for continuum structures based on matrix norm: modal perturbation method

Modal truncation method for continuum structures based on matrix norm: modal perturbation method

Nonlinear dynamics of the reversed shear Alfvén eigenmode in burning plasmas

In a tokamak fusion reactor operated at steady state, the equilibrium magnetic field is likely to have reversed shear in the core region, as the noninductive bootstrap current profile generally peaks off-axis. The reversed shear Alfvén eigenmode (RSAE) as a unique branch of the shear Alfvén wave in this equilibrium, can exist with a broad spectrum in wavenumber and frequency, and be resonantly driven unstable by energetic particles (EP). After briefly discussing the RSAE linear properties in burning plasma condition, we review several key topics of the nonlinear dynamics for the RSAE through both wave-EP resonance and wave-wave coupling channels, and illustrate their potentially important role in reactor-scale fusion plasmas. By means of simplified hybrid MHD-kinetic simulations, the RSAEs are shown to have typically broad phase space resonance structure with both circulating and trapped EP, as results of weak/vanishing magnetic shear and relatively low frequency. Through the route of wave-EP nonlinearity, the dominant saturation mechanism is mainly due to the transported resonant EP radially decoupling with the localized RSAE mode structure, and the resultant EP transport generally has a convective feature. The saturated RSAEs also undergo various nonlinear couplings with other collective oscillations. Two typical routes as parametric decay and modulational instability are studied using nonlinear gyrokinetic theory, and applied to the scenario of spontaneous excitation by a finite amplitude pump RSAE. Multiple RSAEs could naturally couple and induce the spectral energy cascade into a low frequency Alfvénic mode, which may effectively transfer the EP energy to fuel ions via collisionless Landau damping. Moreover, zero frequency zonal field structure could be spontaneously excited by modulation of the pump RSAE envelope, and may also lead to saturation of the pump RSAE by both scattering into stable domain and local distortion of the continuum structure.

FAUST

Context. The origin of the chemical diversity observed around low-mass protostars probably resides in the earliest history of these systems. Aims. We aim to investigate the impact of protostellar feedback on the chemistry and grain growth in the circumstellar medium of multiple stellar systems. Methods. In the context of the ALMA Large Program FAUST, we present high-resolution (50 au) observations of CH3OH, H2CO, and SiO and continuum emission at 1.3 mm and 3 mm towards the Corona Australis star cluster. Results. Methanol emission reveals an arc-like structure at ∼1800 au from the protostellar system IRS7B along the direction perpendicular to the major axis of the disc. The arc is located at the edge of two elongated continuum structures that define a cone emerging from IRS7B. The region inside the cone is probed by H2CO, while the eastern wall of the arc shows bright emission in SiO, a typical shock tracer. Taking into account the association with a previously detected radio jet imaged with JVLA at 6 cm, the molecular arc reveals for the first time a bow shock driven by IRS7B and a two-sided dust cavity opened by the mass-loss process. For each cavity wall, we derive an average H2 column density of ∼7 × 1021 cm−2, a mass of ∼9 × 10−3 M⊙, and a lower limit on the dust spectral index of 1.4. Conclusions. These observations provide the first evidence of a shock and a conical dust cavity opened by the jet driven by IRS7B, with important implications for the chemical enrichment and grain growth in the envelope of Solar System analogues.

CN stretches around 4.4 microns dominate the IR absorption spectra of cyano-polycyclic aromatic hydrocarbons

ABSTRACT Anharmonic quantum chemical computations reveal a strong, narrow (width = 0.075 $\mu$m) band in the 4.3–4.5 $\mu$m region of the absorption spectra of the cyano-substituted polycyclic aromatic hydrocarbons (CN-PAHs) cyanonaphthalene, cyanoanthracene, cyanophenanthrene, and cyanopyrene. This narrow window with intense IR lines implies that CN-PAHs of various shapes and sizes offer little variation in both wavelength and intensity in this region. Subsequently, this band can be used as a tracer for CN-PAHs. The distinct features making up the band are assigned to mixed vibrational states consisting of the CN stretch fundamental and various combination bands, including in-plane CH bends, CC skeletal bends, and CC skeletal breathing motions. The extraordinarily large intrinsic intensity of the fundamental CN stretch is redistributed to nearby states via anharmonic coupling, which is readily captured when using second order vibrational perturbation theory with resonance polyad matrices. This redistribution of intensity leads to a complex spectrum. The intense bands in this wavelength region may contribute to the baseline continuum and undulating macroscopic structure seen in recent JWST NIRSpec observations.

Topology optimization for rigid and compliant hybrid mechanisms

This paper proposes a topology optimization method integrating the variable trajectory constraints to design rigid and compliant hybrid mechanisms. The variable trajectory constraints are distributed in the design domain and are uniformly modeled by nonlinear spring model. Each of the variable trajectory constraints has an active or inactive state and different states map various mechanical properties of the nonlinear springs. The nonlinear relation between force and displacement of the spring is formulated. A new group of design variables denoting the states of the springs is introduced into the traditional density-based topology optimization model. The design variables representing the element density of the continuum structure and the states of the variable trajectory constraints are uniformly penalized to avoid intermediate values in order to obtain a physically realizable mechanism. Sensitivity analysis is performed by the adjoint equation method. To demonstrate the versatility and the generality of the proposed method, the typical numerical examples including linear, spline and circular trajectory constraints were implemented. The numerical comparisons between the nonlinear spring model and the actual trajectory constraints verify the accuracy. The proposed method expands the application of topology optimization and can be extensively employed to design the mechanisms integrating both the compliant members and rigid parts.

Reformulation for stress topology optimization of continuum structures by floating projection

Stress topology optimization of continuum structures is an important topic for structural design and has been widely investigated. However, stress topology optimization itself is ill-conditioned and the resulting optimized designs highly depend on the used parameters, mesh size, and so on. In this paper, stress minimization and stress-constrained topology optimization problems are reformulated by introducing a global measure of an optimized design, the average solid stress. The floating projection topology optimization method is established with ε-relaxation and the p-norm function. Due to the modified problem formulations, the optimized design becomes insensitive to the selection of p in the p-norm function once p is large enough, such as p=16, to ensure the total elimination of stress concentration. Numerical results show the uniform stress distribution of optimized designs, demonstrating the effectiveness of the proposed method. Some findings on the elimination of stress concentration, mesh-independent optimized topology, equivalent smooth design, and impractical design are presented and discussed.

Discrete variable topology optimization for maximizing single/multiple natural frequencies and frequency gaps considering the topological constraint

AbstractFinding optimized structural topology design for maximizing natural frequencies and frequency gaps of continuum structures is crucial for engineering applications. However, two significant numerical issues must be addressed: non‐smoothness caused by multiple frequencies and Artificial Localized Rigid Motion (ALRM) modes due to the violation of the topological constraint related to isolated islands and point‐connections. The above two issues are solved by employing the discrete variable topology optimization method based on Sequential Approximate Integer Programming (SAIP). First, the directional differentiability and multiple frequencies preservation constraints are formulated as the linear integer constraints. And then, the integer programming with these linear integer constraints is established and solved by the discrete variable linear or quadratic programming solver with multi‐constraint Canonical Relaxation Algorithm (CRA). We also prove that the popular Average Modal Frequencies (AMF) strategy, like the Kreisselmeier‐Steinhauser (KS) function, cannot rigorously tackle this non‐smoothness caused by multiple frequencies. Furthermore, to eliminate the ALRM modes and concentrate on the real structural global modes, the burning method is employed to impose the topological constraint of the first Betti number that represents the number of isolated islands and point‐connections. Numerical examples, including 2D and 3D, two‐fold and three‐fold multiple frequencies, natural frequencies and frequency gaps, are presented to show the effectiveness of the proposed method.

Radio Continuum and Water Maser Observations of the High-mass Protostar IRAS 19035+0641 A

We present Very Large Array 1.3 cm continuum and 22.2 GHz H2O maser observations of the high-mass protostellar object IRAS 19035+0641 A. Our observations unveil an elongated bipolar 1.3 cm continuum structure at scales ≲500 au, which, together with a rising in-band spectral index, strongly suggests that the radio emission toward IRAS 19035+0641 A arises from an ionized jet. In addition, eight individual water maser spots well aligned with the jet axis were identified. The Stokes V spectrum of the brightest H2O maser line (∼100 Jy) shows a possible Zeeman splitting and is well represented by the derivatives of two Gaussian components fitted to the Stokes I profile. The measured B los are 123 (±27) and 156 (±8) mG, translating to a preshock magnetic field of ≈7 mG. Subsequent observations to confirm the Zeeman splitting showed intense variability in all the water maser spots, with the brightest maser completely disappearing. The observed variability in a 1 yr timescale could be the result of an accretion event. These findings strengthen our interpretation of IRAS 19035+0641 A as a high-mass protostar in an early accretion/outflow evolutionary phase.

Structure, variability, and origin of the low-latitude nightglow continuum between 300 and 1800 nm: evidence for HO2 emission in the near-infrared

Abstract. The Earth's mesopause region between about 75 and 105 km is characterised by chemiluminescent emission from various lines of different molecules and atoms. This emission was and is important for the study of the chemistry and dynamics in this altitude region at nighttime. However, our understanding is still very limited with respect to molecular emissions with low intensities and high line densities that are challenging to resolve. Based on 10 years of data from the astronomical X-shooter echelle spectrograph at Cerro Paranal in Chile, we have characterised in detail this nightglow (pseudo-)continuum in the wavelength range from 300 to 1800 nm. We studied the spectral features, derived continuum components with similar variability, calculated climatologies, studied the response to solar activity, and even estimated the effective emission heights. The results indicate that the nightglow continuum at Cerro Paranal essentially consists of only two components, which exhibit very different properties. The main structures of these components peak at 595 and 1510 nm. While the former was previously identified as the main peak of the FeO “orange arc” bands, the latter is a new discovery. Laboratory data and theory indicate that this feature and other structures between about 800 and at least 1800 nm are caused by emission from the low-lying A′′ and A′ states of HO2. In order to test this assumption, we performed runs with the Whole Atmosphere Community Climate Model (WACCM) with modified chemistry and found that the total intensity, layer profile, and variability indeed support this interpretation, where the excited HO2 radicals are mostly produced from the termolecular recombination of H and O2. The WACCM results for the continuum component that dominates at visual wavelengths show good agreement for FeO from the reaction of Fe and O3. However, the simulated total emission appears to be too low, which would require additional mechanisms where the variability is dominated by O3. A possible (but nevertheless insufficient) process could be the production of excited OFeOH by the reaction of FeOH and O3.

Active Learning-Based Kriging Model with Noise Responses and Its Application to Reliability Analysis of Structures

This study introduces a reliability analysis methodology employing Kriging modeling enriched by a hybrid active learning process. Emphasizing noise integration into structural response predictions, this research presents a framework that combines Kriging modeling with regression to handle noisy data. The framework accommodates either constant variance of noise for all observed responses or varying, uncorrelated noise variances. Hyperparameters and the variance of the Kriging model with noisy data are determined through maximum likelihood estimation to address inherent uncertainties in structural predictions. An adaptive hybrid learning function guides design of experiment (DoE) point identification through an iterative enrichment process. This function strategically targets points near the limit-state approximation, farthest from existing training points, and explores candidate points to maximize the probability of misclassification. The framework’s application is demonstrated through metamodel-based reliability analysis for continuum and discrete structures with relatively large degrees of freedom, employing subset simulations. Numerical examples validate the framework’s effectiveness, highlighting its potential for accurate and efficient reliability assessments in complex structural systems.

Mechanical design principles in frustrated thin elastic sheets.

Using a geometric formalism of elasticity theory we develop a systematic theoretical framework for shaping and manipulating the energy landscape of slender solids, and consequently their mechanical response to external perturbations. We formally express global mechanical properties associated with non-Euclidean thin sheets in terms of their local rest lengths and rest curvatures, and we interpret the expressions as both forward and inverse problems for designing the desired mechanical properties. We show that by wisely designing geometric frustration, anomalous mechanical properties can be encoded into a material using accessible experimental techniques. To test the methodology we derive a family of ribbon-springs with extreme mechanical behavior such as tunable, anharmonic, and even vanishing rigidities. The presented formalism can be discretized, offering a new methodology for designing mechanical properties and thus opens a new pathway for the design of both continuum and discrete solids and structures.

An Overview of Sequential Approximation in Topology Optimization of Continuum Structure

An Overview of Sequential Approximation in Topology Optimization of Continuum Structure

Topological Optimization of Bi-Directional Progressive Structures with Dynamic Stress Constraints under Aperiodic Load

The topology optimization of dynamic stress constraints is highly nonlinear and singular and has been little studied. Dynamic stress based on progressive structural optimization is only available by applying the modal iteration method, but due to the nonlinear limitations of the modal superposition method, there is an urgent need to develop a progressive structural optimization method based on dynamic stress sensitivity under direct integration. This method is for the dynamic stresses under non-periodic loading with iterative cycle updating variations. This article proposes a topological optimization method of continuum structures with stress constraints under an aperiodic load based on the Bi-directional Evolutionary Structural Optimization Method (BESO). First, the P-norm condensation function was used to obtain the global stress to approximate maximum stress. By introducing the Lagrange multiplier, the design goal was to increase the P-norm stress on the basis of the smallest volume. After that, based on the dynamic finite element theory, the sensitivity of each cell formula of the objective function and the constraint conditions of the design variables were strictly derived. Then, the performance evaluation index was put forward based on volume and stress, and the convergence criterion based on the performance evaluation index was defined. This method solves the topology optimization problem of stress constraints under a non-periodic load and the topology optimization problem of stress constraints under a periodic load, such as a simple harmonic load.