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The primary objective of the current study is to introduce a potent computational model for analyzing the dynamic instability response of advanced sandwich plate models subjected to various time‐dependent in‐plane edge loadings. To achieve this, we employ the finite element formulations derived from high‐order shear deformation plate theory (HSDT) involving only three unknowns in conjunction with NURBS‐based isogeometric analysis. Additionally, advanced sandwich plate models are constituted by a middle layer with either a uniform or symmetric porosity distribution and two outer layers which are reinforced with graphene nanoplatelets (GNPs) to boost dynamic structural performance. The fundamental dynamic instability region of the sandwich plates can be then obtained by solving the Mathieu‐Hill equation using the Bolotin's method. Numerous numerical studies are performed to evaluate the impacts of numerous input parameters on the dynamic stability behavior of the cellular three‐layer plate structures. The crucial role of internal porosity distribution as well as GNPs reinforcement phase in enhancing the instability performance of the cellular structures is thoroughly evaluated. With the current results, this research provides important insights into the development and application of cellular materials as well as the GNPs for designing advanced engineering structures in the future. [ABSTRACT FROM AUTHOR]

In recent years, the research and development of high-speed trains has advanced rapidly. The main development trends of high-speed trains are higher speeds, lower energy consumption, higher safety, and better environmental protection. The realization of a lightweight high-speed car body is one of the key features in the development trend of high-speed trains. Firstly, the basic dimensions of the car body's geometric model are determined according to the external dimensions of the body of a CRH EMU, and the specific topology optimization design domain is selected to establish the finite element analysis model; secondly, the strength and modal analyses of the topology optimization design domain are carried out to check the accuracy of the design domain and provide a comparative analysis for subsequent design. Then, the variables, constraints, and objective functions of the topology optimization design are determined to establish the mathematical model of topology optimization, and the design domain is calculated for topology optimization under single and multiple conditions, respectively. Finally, based on the topology optimization calculation results, truss-type reconstruction modeling is carried out for the car body's side walls, roof, underframe, end walls, and other parts. Compared with the conventional EMU body structure, the weight of the reconstructed body structure is reduced by about 18%. The results of the finite element analysis of the reconstructed car-body structure prove the reliability and safety of the structure, indicating that the reconstructed car-body scheme meets the corresponding performance indicators. [ABSTRACT FROM AUTHOR]

The paper proposes solving transient heat transfer in plates using high-order isogeometric analysis and high-order time integration schemes. The problem is often faced in fire-structure interaction where the heat transfer is coupled with the stress analysis. A major advantage for the proposed approach comes from high order continuity between elements. Thus, the need for rotational degrees of freedom is eliminated when analyzing the stresses in plates and the same mesh can also be used to recover the heat transfer patterns. To achieve the full potential of such high-order finite elements in space, we also use high-order time integration schemes so that the numerical solution can be significantly more accurate than the standard approaches. Furthermore, the isogeometric analysis is also used to represent the exact geometry thanks to the basis functions generated from Non-Uniform Rational B-Splines. Several test examples for the transient diffusion problem are presented. Compared to standard methods and for a prescribed accuracy the proposed approach requires significantly fewer degrees of freedom and a corresponding improvement in the computational efficiency. [ABSTRACT FROM AUTHOR]

This paper aims to solve large-scale and complex isogeometric topology optimization problems that consume significant computational resources. A novel isogeometric topology optimization method with a hybrid parallel strategy of CPU/GPU is proposed, while the hybrid parallel strategies for stiffness matrix assembly, equation solving, sensitivity analysis, and design variable update are discussed in detail. To ensure the high efficiency of CPU/GPU computing, a workload balancing strategy is presented for optimally distributing the workload between CPU and GPU. To illustrate the advantages of the proposed method, three benchmark examples are tested to verify the hybrid parallel strategy in this paper. The results show that the efficiency of the hybrid method is faster than serial CPU and parallel GPU, while the speedups can be up to two orders of magnitude. [ABSTRACT FROM AUTHOR]

In this work, free vibration and transient response of porous metal foam magneto-electro-elastic (PMF-MEE) curved nanobeam with elastic boundary conditions (BCs) using an isogeometric analysis (IGA) based on nonlocal elastic and refined higher-order shear beam theories (HSDT) are investigated. The variation of electric and magnetic potentials through the thickness direction of the curved nanobeam is determined by the Maxwell equation and the magneto-electric boundary condition. The new point of this paper is that it does not use traditional boundary conditions, but instead, the first and last positions of the curved nanobeam are linked by an elastic system consisting of transrational springs and rotational springs with stiffness controlled to give arbitrary boundary conditions. Besides, the nonlocal coefficients vary with thickness like other material properties. Hamilton’s principle is applied to establish the governing equations of motion. The Newmark direct integration method is applied to derive the dynamic responses including deflection and phase trajectory. A comprehensive parametric study is carried out to evaluate the influence of input factors on the natural and forced oscillation capabilities of PMF-MEE curved nanobeams. The findings may benefit for the analysis and design of intelligent structures made of magneto-electro-elastic materials.

As the water pipe cooling system is widely applied to controlling temperature in mass concrete structures, the precise simulation of the temperature field in mass concrete with cooling pipes embedded is meaningful. This paper presents an isogeometric analysis (IGA) with NURBS for heat transfer in mass concrete with consideration of the cooling pipe. The proposed method not only achieves the same level of accuracy with fewer nodes but also eliminates the time-consuming process of mesh in the traditional FEM. The coarsest parameter space which depicts small pipe and large concrete precisely is constructed to create an efficient model for numerical computation. In addition, the unique k-refinement in IGA is supposed to be the most appropriate encryption mechanism, and the knot insertion vector for effective refinement is calculated by considering the characteristics of temperature gradient distribution around the cooling pipes. In addition, a different calculation parameter has been discussed to show the stability and flexibility of the IGA. The obtained numerical results demonstrate the accuracy and efficiency of the proposed scheme in the simulation of transient temperature fields in concrete structures with cooling systems.

This paper uses isogeometric analysis (IGA) based on higher-order shear deformation theory (HSDT) to study the dynamic response of bio-inspired helicoid laminated composite (B-iHLC) plates resting on Pasternak foundation (PF) excited by explosive loading. IGA takes advantage of non-uniform rational B-spline (NURBS) basic functions to exactly represent the structure geometry models and the attainment of higher-order approximation conditions. This method also ensures a C1 continuous function in the analysis of transverse shear deformation via HSDT. Furthermore, IGA eliminates the requirement for correction factors and delivers accurate results. Pasternak foundation with two stiffness parameters: springer stiffness (k1) and shear stiffness (k2). The derivation of the governing equations is based on Hamilton's principle. The proposed method is validated through numerical examples. A comprehensive analysis of the impact of geometrical parameters, material properties, boundary conditions (BCs), and foundation stiffness on dynamic response of B-iHLC plates is carried out.

In this paper, we extend our previous work on the dynamic buckling analysis of isogeometric shell structures to the stochastic situation where an isogeometric deterministic dynamic buckling analysis method is combined with spectral-based stochastic modeling of geometric imperfections. To be specific, a modified Generalized-α time integration scheme combined with a nonlinear isogeometric Kirchhoff–Love shell element is used to simulate the buckling and post-buckling problems of cylindrical shell structures. Additionally, geometric imperfections are constructed based on NURBS surface fitting, which can be naturally incorporated into the isogeometric analysis framework due to its seamless CAD/CAE integration feature. For stochastic analysis, the method of separation is adopted to model the stochastic geometric imperfections of cylindrical shells based on a set of measurements. We tested the accuracy and convergence properties of the proposed method with a cylindrical shell example, where measured geometric imperfections were incorporated. The ABAQUS reference solutions are also presented to demonstrate the superiority of the inherited smooth and high-order continuous properties of the isogeometric approach. For stochastic dynamic buckling analysis, we evaluated the buckling load variability and reliability functions of the cylindrical shell with 500 samples generated based on seven nominally identical shells reported in the geometric imperfection data bank. It is noted that the buckling load variability in the cylindrical shell obtained with static nonlinear analysis is also presented to show the differences between dynamic and static buckling analysis.

In this paper, we implement the finite detail technique primarily based on T-Splines for approximating solutions to the linear elasticity equations in the connected and bounded Lipschitz domain. Both theoretical and numerical analyses of the Dirichlet and Neumann boundary problems are presented. The Reissner–Mindlin (RM) hypothesis is considered for the investigation of the mechanical performance of a 3D cylindrical shell pipe without and with preformed hole problems under concentrated and compression loading in the linear elastic behavior for trimmed and untrimmed surfaces in structural engineering problems. Bézier extraction from T-Splines is integrated for an isogeometric analysis (IGA) approach. The numerical results obtained, particularly for the displacement and von Mises stress, are compared with and validated against the literature results, particularly with those for Non-Uniform Rational B-Spline (NURBS) IGA and the finite element method (FEM) Abaqus methods. The obtained results show that the computation time of the IGA based on the T-Spline method is shorter than that of the IGA NURBS and FEM Abaqus/CAE (computer-aided engineering) methods. Furthermore, the highlighted results confirm that the IGA approach based on the T-Spline method shows more success than numerical reference methods. We observed that the NURBS IGA method is very limited for studying trimmed surfaces. The T-Spline method shows its power and capability in computing trimmed and untrimmed surfaces.

Biomembranes play a central role in various phenomena like locomotion of cells, cell-cell interactions, packaging and transport of nutrients, transmission of nerve impulses, and in maintaining organelle morphology and functionality. During these processes, the membranes undergo significant morphological changes through deformation, scission, and fusion. Modelling the underlying mechanics of such morphological changes has traditionally relied on reduced order axisymmetric representations of membrane geometry and deformation. Axisymmetric representations, while robust and extensively deployed, suffer from their inability to model-symmetry breaking deformations and structural bifurcations. To address this limitation, a three-dimensional computational mechanics framework for high fidelity modelling of biomembrane deformation is presented. The proposed framework brings together Kirchhoff-Love thin-shell kinematics, Helfrich-energy-based mechanics, and state-of-the-art numerical techniques for modelling deformation of surface geometries. Lipid bilayers are represented as spline-based surface discretizations immersed in a three-dimensional space; this enables modelling of a wide spectrum of membrane geometries, boundary conditions, and deformations that are physically admissible in a three-dimensional space. The mathematical basis of the framework and its numerical machinery are presented, and their utility is demonstrated by modelling three classical, yet non-trivial, membrane deformation problems: formation of tubular shapes and their lateral constriction, Piezo1-induced membrane footprint generation and gating response, and the budding of membranes by protein coats during endocytosis. For each problem, the full three-dimensional membrane deformation is captured, potential symmetry-breaking deformation paths identified, and various case studies of boundary and load conditions are presented. Using the endocytic vesicle budding as a case study, we also present a 'phase diagram' for its symmetric and broken-symmetry states.

In linear isogeometric analysis of beams, the success of selective reduced integration and B ¯ projection methods in mitigating the locking phenomenon has been proved. This study further extends these methods to the geometrically nonlinear analysis with two isogeometric Timoshenko–Ehrenfest beam formulations, that is, C 0 -continuous NURBS selective reduced integration and B ¯ formulations. Three numerical examples are presented examining overall structural responses, strain energy, recovery of cross-sectional stress resultants, and convergence properties. Although the two proposed formulations exhibit the locking-free behavior for highly flexible beam structures, the B ¯ formulation offers higher accuracy, and the proper recovery of strain measures and cross-sectional stress resultants. [ABSTRACT FROM AUTHOR]

Based on the explicit stiffness computation formula of NURBS (non‐uniform rational B‐splines) element and tensor product decomposed explicit filter, a novel multi‐material isogeometric topology optimization (MMITO) method is put forward to generate multi‐material structures efficiently. The explicit NURBS element stiffness computation formula is: derived from the Bėzier extraction operator under the combination of scaled and rotational geometric transformations between NURBS elements, and the stiffness matrices of NURBS elements can be computed by the stiffness matrix of a Bėzier element without resorting to the time‐consuming integral procedure. As the presented MMITO is a nested optimization framework, we apply the explicit filtering technique to update the multi‐phase design variables efficiently in combination with the tensor product decomposition method. With the decomposed weight matrices of the filter and the explicit form of the NURBS stiffness matrix, we obtain the equivalent but much simplified preprocessing procedure and sensitivity analysis for the MMITO method. A comprehensive set of multi‐material numerical examples are optimized to verify that, while improving the preprocessing efficiency and reducing the memory overhead, the present MMITO scheme is able to generate semblable two‐dimensional and three‐dimensional multi‐material structures with identical structural performance to the traditional scheme. Therefore, the proposed MMITO method is a promising approach to optimizing multi‐material structures. [ABSTRACT FROM AUTHOR]

This paper studies the dynamic deployment of cylindrical thin-shell structures with open cross section, attached to a rigid base. The structures are elastically folded and then released. Previous experiments have shown that the total energy decreases while a fold moves back and forth along the structure, which was explained in terms of energy losses related to the fold "bouncing" against the boundary. This paper uses a rigorous numerical simulation, based on an in-house isogeometric shell finite element code that simultaneously eliminates shear locking and hourglassing without any intrinsic energy dissipation, to show that the total energy of the system is conserved during deployment. The discrepancy with the previous results is explained by showing that energy transfers from low-frequency, "rigid body" modes, to higher frequency modes. [ABSTRACT FROM AUTHOR]

Flows with moving boundaries and interfaces (MBI) are a large class of problems that include fluid–particle and fluid–structure interactions, and in broader terms, moving solid surfaces. They also include multi-fluid flows, and as a special case of that, free-surface flows, sometimes in combination with moving solid surfaces. In some classes of MBI problems the solid surfaces could be in fast, linear or rotational relative motion or could come into contact. In almost all real-world applications, the solid surfaces would have complex geometries. All these problems are frequently encountered in engineering analysis and design, pose some of the most formidable computational challenges, and have a common core computational technology need. Bringing solution and analysis to them motivated the development of a good number of core computational methods and special methods targeting specific classes of MBI problems. This paper is an overview of some of those core and special methods. The focus is on isogeometric analysis, complex geometries, incompressible-flow Space–Time Variational Multiscale (ST-VMS) and Arbitrary Lagrangian–Eulerian VMS (ALE-VMS) methods, compressible-flow ST Streamline-Upwind/Petrov–Galerkin (ST-SUPG) and ALE-SUPG methods, and some of the special methods developed in connection with these core ST and ALE methods. The incompressible-flow ST-VMS and ALE-VMS and compressible-flow ST-SUPG and ALE-SUPG are moving-mesh methods, where the mesh moves to have mesh-resolution control near the fluid–solid interfaces, enabling high-resolution boundary-layer representation, an essential feature when the accuracy in representing the boundary layer is a priority. The computational examples presented are car and tire aerodynamics with road contact and tire deformation, ventricle–valve–aorta flow, and gas turbine flow. [ABSTRACT FROM AUTHOR]

Physically based cloth simulation with nonlinear behaviors is studied in this article by employing isogeometric analysis (IGA) for the surface deformation in 3D space. State‐of‐the‐art simulation techniques, which primarily rely on the triangular mesh to calculate physical points on the cloth directly, require a large number of degrees of freedom. An effective method for the cloth deformation that employs high‐order continuous B‐spline surfaces dependent on control points is proposed. This method leads to the merit of fewer degrees of freedom and superior smoothness. The deformation gradient on the high‐order IGA element is then represented by the gradient of the B‐spline function. An iterative method for solving the nonlinear optimization transferred from the implicit integration and a direct implicit–explicit method are derived on the basis of elastic force calculation to improve efficiency. The knots of the representation are effectively utilized in collision detection and response to reduce the computational burden. Experiments of nonlinear cloth simulation demonstrate the superiority of the proposed method considering performance and efficiency, achieving accurate, efficient, and stable deformation. [ABSTRACT FROM AUTHOR]

For the direct differentiation technique-based modeling of acoustic fluid–structure interaction and structural-acoustic sensitivity analysis, a coupling algorithm based on the finite element method (FEM) and the fast multipole boundary element method (FMBEM) is suggested. By bypassing the challenging volume parameterization process in isogeometric finite element techniques and the laborious meshing process in traditional FEM/BEM, non-uniform rational B-splines (NURBS) isogeometric analysis (IGA) is utilized to immediately perform numerical analysis on CAD models. The matrix-vector products in the boundary element analysis are accelerated using the fast multipole method (FMM). To hasten the solution of the linear system of equations, the iterative solver GMRES is used. The numerical prediction of the effects of arbitrarily shaped vibrating structures on the sound field is made feasible by the FEM/FMBEM technique. A number of numerical examples are provided to show the applicability and effectiveness of the suggested approach. [ABSTRACT FROM AUTHOR]

Numerically interpolated contour lines (NICL) developed from a high-resolution, accurate digital elevation model (DEM) can be considered the most accurate contour baseline available from surveyed data. Displays of this baseline, however, can exhibit an undesirable angularity and clutter that impedes human understanding of the data and defies the universal appeal of a smooth curve. To achieve smooth, readable lines, the prevailing wisdom today is to either 1) smooth the underlying surface model before creating the lines or 2) use mathematical methods adapted from computer-aided design (CAD) to smooth the lines in x and y. However, these smoothing methods can result in an inaccurate rendition of the original data that undermines their subsequent use in analysis and modeling applications. Upon close inspection, lines generated from such methods can depart from the baseline by more than a definable and acceptable distance in x and y, particularly noticeable in important areas of slope change. Here, we argue that generalized contours have a geometric accuracy requirement that must be observed. We present a novel alternative to the prevailing methods that 1) presents an incremental smoothing method that is a logical complement to Douglas-Poiker thinning; 2) introduces the use of slope as a means of controlling the degree of smoothing locally; 3) produces novel, operational definitions of tests for smoothness and accuracy as well as for line symmetry; and 4) introduces the notion of a topological TIN as a new type of terrain model and a medium for edits of contours. The method only manipulates the baseline contours in x and y. By using only simple proportions of sides and self-similar geometry to smooth the original lines, we at the same time impose computable, dynamic constraints on the smoothing. This combination ensures the accuracy and acceptability of the final contours at scales appropriate for working GIS displays. The result is a Locally Adjusted Curve Approximation (LACA) technique for contour line smoothing. [ABSTRACT FROM AUTHOR]

The key aim of this paper is to provide a new nth generalized order perturbed isogeometric fast multistage technique of boundary elements to compute the propagation of time harmonics in an infinite region. Structural geometry and boundary integral equations are constructed by using non-uniform rational B-splines. The source of system uncertainty is believed to be the incident plane wave number's unpredictability. The actual field, depending on the input random variables, is simulated using the extended nth-order perturbation method. The field and kernel values for boundary integral formulas are generated via the nth-order generalized series of Taylor expansions using perturbation parameters. The fast multipole method (FMM) is utilized to speed up the process. The effectiveness and correctness of the proposed algorithm are verified by Monte Carlo simulations (MCs) with numerical examples. [ABSTRACT FROM AUTHOR]

This article shows how to develop an efficient solver for a stabilized numerical space-time formulation of the advection-dominated diffusion transient equation. At the discrete space-time level, we approximate the solution using higher-order continuous B-spline basis functions in both spatial and temporal dimensions. This problem is very difficult to solve numerically using the standard Galerkin finite element method due to artificial oscillations present when the advection term dominates the diffusion term. However, a first-order constraint least-square formulation allows us to obtain numerical solutions avoiding oscillations. The advantages of space-time formulations are the use of high-order methods and the feasibility of developing space-time mesh adaptive techniques on well-defined discrete problems. We develop a solver for a least-square formulation to obtain a stabilized and symmetric problem on finite element meshes. The computational cost of our solver is bounded by the cost of the inversion of the space-time mass and stiffness (with one value fixed at a point) matrices and the cost of the GMRES solver applied for the symmetric and positive definite problem. We illustrate our findings on an advection-dominated diffusion space-time model problem and present two numerical examples: one with isogeometric analysis discretizations and the second one with an adaptive space-time finite element method. [ABSTRACT FROM AUTHOR]

The construction industry is responsible for nearly half of the UK's carbon dioxide emissions and the use of an extremely large volume of concrete – the world's most widely used man-made material – accounts for more than 7% of global carbon dioxide emissions. The scale of this problem spawned research to explore the potential for structurally efficient non-prismatic geometries to reduce the amount of concrete used in building elements substantially, thus also reducing their embodied carbon dioxide footprint. In particular, the research focused on segmented thin concrete shells as floor slabs, leveraging computational design and digital fabrication methodologies to automate their production off site. An important part of this research was the development of a computational framework for the design of thin concrete shells in order to make such a construction methodology accessible to building designers in practice. The framework combines solutions for parametric modelling, finite-element analysis, isogeometric analysis, form-finding and optimisation, along with embedded fabrication constraints specific to the project's automated manufacturing system. The application of the developed computational framework in the design of a 4.5 m × 4.5 m prototype is documented in this paper, illustrating how automating concrete construction can transform the industry towards net-zero. [ABSTRACT FROM AUTHOR]

Solutions to many partial differential equations satisfy certain bounds or constraints. For example, the density and pressure are positive for equations of fluid dynamics, and in the relativistic case the fluid velocity is upper bounded by the speed of light, etc. As widely realized, it is crucial to develop bound-preserving numerical methods that preserve such intrinsic constraints. Exploring provably bound-preserving schemes has attracted much attention and has been actively studied in recent years. This is, however, still a challenging task for many systems, especially those involving nonlinear constraints. Based on some key insights from geometry, we systematically propose an innovative and general framework, referred to as geometric quasilinearization (GQL), which paves a new effective way for studying bound-preserving problems with nonlinear constraints. The essential idea of GQL is to equivalently transform all nonlinear constraints to linear ones, by properly introducing some free auxiliary variables. We establish the fundamental principle and general theory of GQL via the geometric properties of convex regions and propose three simple effective methods for constructing GQL. We apply the GQL approach to a variety of partial differential equations and demonstrate its effectiveness and remarkable advantages for studying bound-preserving schemes, using diverse challenging examples and applications which cannot be easily handled by direct or traditional approaches. [ABSTRACT FROM AUTHOR]

We propose a simulator for time-dependent Maxwell's equations with linear computational cost. We employ B-spline basis functions as considered in the isogeometric analysis (IGA). We focus on non-stationary Maxwell's equations defined on a regular patch of elements. We employ the idea of alternating-directions splitting (ADS) and employ a second-order accurate time-integration scheme for the time-dependent Maxwell's equations in a weak form. After discretization, the resulting stiffness matrix exhibits a Kronecker product structure. Thus, it enables linear computational cost LU factorization. Additionally, we derive a formulation for absorbing boundary conditions (ABCs) suitable for direction splitting. We perform numerical simulations of the scattering problem (traveling pulse wave) to verify the ABC. We simulate the radiation of electromagnetic (EM) waves from the dipole antenna. We verify the order of the time integration scheme using a manufactured solution problem. We then simulate magnetotelluric measurements. Our simulator is implemented in a shared memory parallel machine, with the GALOIS library supporting the parallelization. We illustrate the parallel efficiency with strong and weak scalability tests corresponding to non-stationary Maxwell simulations. [ABSTRACT FROM AUTHOR]

Unstructured quadrilateral meshes are widely used in representing surfaces of arbitrary topology. However, in connection with isogeometric analysis, unstructured meshes suffer from sub-optimal convergence rates in extraordinary regions, especially for solving higher-order PDEs (partial differential equations). In this work, a rational reparameterization method is proposed to achieve optimal convergence rates for isogeometric analysis using Catmull-Clark surfaces. The scheme lifts the convergence of analysis solutions by tuning the weights of control vertices of the input geometry in extraordinary regions, which are often neglected in constructing analysis-suitable parameterizations. Preferred tuning parameters with optimal convergence rates in L 2 -norm are determined statistically based on a test suite composed of typical testing solutions with a range of parameters. Numerical experiments confirm the validity of the proposed method for PDEs up to the fourth-order. Comparisons with the original Catmull-Clark scheme and a state-of-the-art tuned subdivision scheme also show the superiority of the proposed method in terms of both optimal convergence and reduced absolute errors of resulting analysis solutions. • A rational reparameterization method to recover optimal convergence for IGA based on Catmull-Clark subdivision. • Weights of control points are used in the proposed method for achieving higher order convergence. • Applicable to fourth-order PDEs, which is highly challenging for subdivision schemes to achieve optimal convergence. • Compatible with relevant subdivision surfaces, unstructured T-splines, and other relevant spline constructions. • Computationally efficient with only 2-ring control points at extraordinary corner positions involved. [ABSTRACT FROM AUTHOR]

Jellyfish are one of the earliest example of animal that actively regulate swimming, but the mechanisms governing the locomotion are still a matter of research. Jellyfish obtain locomotion by activating the subumbrellar muscle layer. Sensory inputs trigger the contraction of the bell and the fluid-structure interaction effects driving locomotion. These have been extensively studied, whereas a representation of the full neuro-mechanical locomotion chain, with focus on the actuation-locomotion dynamics, has not been proposed yet. A model of such a complex multi-physical phenomenon would be informative for several purposes, ranging from the comprehension of behavioral aspects to the design of soft actuators and bio-inspired devices. In this regard, we propose a computational framework to address the coupled electrophysiological, elastic, and fluid aspects of the locomotion of the Scyphozoan group. This relies on the sequential coupling of segregated solvers, such that each sub-problem can be addressed with the most computationally effective technique. The spatial discretization is addressed by isogeometric analysis for the electrophysiological and elastic sub-problems, and by finite differences for the fluid sub-problem. The active strain approach allows to distribute the active contraction of radial and coronal muscle fibers following the biological architecture. The inherent multi-scale nature of the model is addressed by means of a nested grid approach and multiple time-advancement lines. In view of a reasonable computational effort, we enforce the hypothesis of axial symmetry limiting the number of degrees of freedom used in the simulations. The effectiveness of the scheme employed for each sub-problem is verified against different test-cases of engineering and biologic inspiration. Finally, we carry out an extensive comparison between the simulation output and the in-vivo measurements on a 3-cm specimen of Aurelia Aurita. • Formulation of an axisymmetric model for the straight propulsion of jellyfish. • Coupling of a neuronal excitation model with a fluid-structure computational framework. • Flexible handling of coupled sub-problems by staggered time schemes and nested grids. • Tuning an active-strain approach to replicate high-fidelity muscle contractions. [ABSTRACT FROM AUTHOR]

• New curvature Euler-Bernoulli and Timoshenko beams based on the couple stress and its flexoelectric theory are presented. • Analytical solutions for bending and free vibration of Euler-Bernoulli and Timoshenko nanobeam are derived. • An IGA is developed for extending the applicability of the curvature-based flexoelectric nanobeam. • The accuracy of analytical solution is verified through IGA numerical solutions. • The flexoelectric effects, microstructure effects and boundary conditions on mechanical behavior of nanobeams are studied. In this paper, new curvature-based flexoelectric Euler-Bernoulli and Timoshenko beam models are derived based on the couple stress and its flexoelectric theory. These models consider both the microstructure and flexoelectric effects. The governing equations and boundary conditions are obtained using the variational formula of Hamilton's principle. Analytical solutions for the static bending and free vibration problems of Euler-Bernoulli and Timoshenko beam models with a simply supported nanobeam are presented. To extend the applicability of the curvature-based flexoelectric beam models, an isogeometric analysis (IGA) numerical approach which satisfy the needs of C 1 continuity is developed. Numerical results are provided to verify the accuracy of the analytical and IGA numerical solutions, and the influence of flexoelectric effects, microstructure effects and boundary conditions on the mechanical behavior of nanobeams is analyzed. [ABSTRACT FROM AUTHOR]

In this work, a hybrid, that is, discrete in time and continuous in space, sensitivity analysis for dynamic structures using isogeometric analysis is presented. The main focus is placed on using a direct differentiation technique to derive sensitivity matrices for displacement, velocity and acceleration. To gain further understanding of the sensitivity information, a singular value decomposition is used to decompose these sensitivity matrices. The findings are exemplified on an academic example. [ABSTRACT FROM AUTHOR]

In reinforced concrete structures, the correct representation of the bond between concrete and reinforcement is a challenging task, since different mechanisms are acting simultaneously. On the other hand, the exact description of the reinforcement's geometry is not sufficient when using Lagrange shape functions and can additionally alter the modeling of this interaction. Isogeometric analysis enables the exact representation of complex geometries, and thus, can improve the correct description of the interface mechanisms. The concrete matrix and the reinforcement are modeled using boundary representation together with Non‐Uniform Rational B‐Spline (NURBS) and B‐splines Scaled Boundary Isogeometric Analysis (SBIGA) which is in accordance with the modeling technique in Computer Aided Design (CAD) tools. This allows for a straightforward use of the design model in the analysis process. The interaction mechanisms between reinforcement and concrete are modeled using a zero‐thickness interface in combination with a thermodynamically consistent cohesive zone model that captures the decohesion, compression and sliding effects. It includes a coupled damage‐plasticity dissipation for the normal and tangential direction. The model is verified using experimental results and a comparison to the standard finite element method (FEM) is carried out in order to investigate the benefits of applying isogeometric analysis for the exact representation of the reinforcement. [ABSTRACT FROM AUTHOR]

In order to overcome locking effects that especially occur for lower order finite element formulations, different methods can be employed. This can be conducted using mixed formulations or adapted approximation orders, for instance. Hence, in order to tackle shear locking that is caused by non‐matching interpolation degrees in the shear strain equation, an irreducible and a mixed Reissner‐Mindlin plate formulation with accordingly adapted conforming discretizations are derived within the scope of this contribution. In addition, non‐uniform rational B‐splines (NURBS) are employed therefore, in order to benefit from the properties and refinement strategies offered by isogeometric analysis (IGA) and to achieve more accurate results. The effect of various combinations of interpolation orders on the convergence behavior and the ability to alleviate locking is investigated for both the irreducible and the mixed isogeometric plate formulation and examined for a benchmark example. This is also supplemented by investigations on the stability of the considered variants, tested by the existence of the correct number of zero‐energy modes. [ABSTRACT FROM AUTHOR]

Multivariate basis splines (B‐splines) and Non‐uniform rational B‐splines (NURBS) lack adaptivity due to their tensor product structure. Truncated hierarchical B‐splines (THB‐splines) provide a solution for this. THB‐splines organize the parameter space into a hierarchical structure, which enables efficient approximation and representation of functions with different levels of detail. The truncation mechanism ensures the partition of unity property of B‐splines and defines a more scattered set of basis functions without overlapping on the multi‐level spline space. Transferring these multi‐level splines into Bézier elements representation facilitates straightforward incorporation into existing finite element (FE) codes. By separating the multi‐level extraction of the THB‐splines from the standard Bézier extraction, a more general independent framework applicable to any sequence of nested spaces is created. The operators for the multi‐level structure of THB‐splines and the operators of Bézier extraction are constructed in a local approach. Adjusting the operators for the multi‐level structure from an element point of view and multiplying with the Bézier extraction operators of those elements, a direct map between Bézier elements and a hierarchical structure is obtained. The presented implementation involves the use of an open‐source Octave/MATLAB isogeometric analysis (IGA) code called GeoPDEs. A basic Poisson problem is presented to investigate the performance of multi‐level Bézier extraction compared to a standard THB‐spline approach. [ABSTRACT FROM AUTHOR]

A doubly curved surface can be approximated with a piecewise developable surface by constructing the envelope of the family of the tangent planes along given curves on the input surface. In this paper, we utilize this fact to approximate a doubly curved input surface by a piecewise ruled B-spline surface with high developability. This brings advantages to downstream applications such as ease of fabrication and ease of covering the surfaces with non-extendable materials such as film-based perovskite solar modules. We also present a method for transforming the thereby defined piecewise developable surface into a watertight B-spline geometry that can be used for numerically solving partial differential equations using isogeometric analysis. In our approach, we compute the intersection points of neighboring developable surfaces starting from the first pair and propagate the parameterization of the first intersection curve to all other pairs, thereby maintaining accuracy and developability when approximating the points with a ruled B-spline surface. [ABSTRACT FROM AUTHOR]

This paper presents a computationally efficient MATLAB implementation of two-dimensional/three-dimensional (2D/3D) topology optimization in non-uniform rational basis spline (NURBS) framework for educational purposes. The pseudo-densities and the related weights at control points define the NURBS-based density surface and are also simultaneously taken as the design variables, which extremely increases the computational expense due to the iterative numerical operations at Gauss integration points for isogeometric analysis (IGA) and sensitivity calculation. Thus, this paper designs the page-wise matrix operation and its implementation on graphics processing unit (GPU) to replace the element loop-based iteration to improve the computational efficiency. For the 2D problems, the main program of valid 34 lines of code (Appendix 1) is mainly divided by initialization of lines 3–11, IGA and sensitivity analysis of lines 13–30, and optimizer of lines 32–34. The sensitivity analysis function of valid 51 lines of code (Appendix 2) is programmed by the page-wise matrix operation. The optimization problems are solved by the Method of Moving Asymptotes (MMA) algorithm. The computational efficiency is largely improved in terms of the performance evaluation of the benchmark cases between the page-wise matrix-based procedure structure and the conventional element loop-based iteration algorithm. All programs that support the results of this study are completely provided and serve educational purposes for students and newcomers. [ABSTRACT FROM AUTHOR]

Topology design of compliant mechanisms has gained wide popularity among the scientific community, and their use in the mechanical engineering field is being of upmost importance. In this paper, an isogeometric analysis (IGA) formulation is used to solve the topology optimization problem of compliant mechanisms. Stress constraints are introduced in the problem to guarantee the attainment of realistic solutions. For this purpose, an overweight constraint is considered for the design process, replacing the use of local stress constraints. The material distribution in the domain is modeled with quadratic B-splines and with a uniform relative density within each element of the mesh. These strategies to define the material layout are used to compare the IGA-based formulation with the finite element (FEM) formulation. The IGA formulation provides several advantages with respect to the classical FEM-based approaches that are shown and analyzed with an input-parameters sensitivity analysis. The sensitivity analysis and the assessment of the importance of introducing of stress constraints in the problem are developed by solving two benchmark problems. Regarding the sensitivity analysis of input parameters, the results show that the ratio between the material and the springs stiffnesses is the parameter with the largest influence on the solutions of the problem. Moreover, the advantages of the IGA formulations over FEM formulations are related with the computational time, the smoothness of the structural borders, and the non-appearance of the checkerboard patterns. With respect to the stress constraints, the results show that they have to be considered in order to avoid instability and structural integrity problems. [ABSTRACT FROM AUTHOR]

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We propose an unified λ-subdivision scheme with a continuous family of tuned subdivisions for quadrilateral meshes. Main subdivision stencil parameters of the unified scheme are represented as spline functions of the subdominant eigenvalue λ of respective subdivision matrices and the λ value can be selected within a wide range to produce desired properties of refined meshes and limit surfaces with optimal curvature performance in extraordinary regions. Spline representations of stencil parameters are constructed based on discrete optimized stencil coefficients obtained by a general tuning framework that optimizes eigenvectors of subdivision matrices towards curvature continuity conditions. To further improve the quality of limit surfaces, a weighting function is devised to penalize sign changes of Gauss curvatures on respective second order characteristic maps. By selecting an appropriate λ, the resulting unified subdivision scheme produces anticipated properties towards different target applications, including nice properties of several other existing tuned subdivision schemes. Comparison results also validate the advantage of the proposed scheme with higher quality surfaces for subdivision at lower λ values, a challenging task for other related tuned subdivision schemes. [ABSTRACT FROM AUTHOR]

We present a method for the generation of higher-order tetrahedral meshes. In contrast to previous methods, the curved tetrahedral elements are guaranteed to be free of degeneracies and inversions while conforming exactly to prescribed piecewise polynomial surfaces, such as domain boundaries or material interfaces. Arbitrary polynomial order is supported. Algorithmically, the polynomial input surfaces are first covered by a single layer of carefully constructed curved elements using a recursive refinement procedure that provably avoids degeneracies and inversions. These tetrahedral elements are designed such that the remaining space is bounded piecewise linearly. In this way, our method effectively reduces the curved meshing problem to the classical problem of linear mesh generation (for the remaining space). [ABSTRACT FROM AUTHOR]

Free vibration and buckling analyses of the magneto-electro-elastic functionally graded (MEE FG) microplates in thermal environment are investigated for the first time. The MEE FG microplate is composed of two phases: piezoelectric (barium titanate) and piezomagnetic (cobalt ferrite) materials, which are distributed across the thickness direction based on the power law model. To satisfy Maxwell's equation in the quasi-static approximation, the electric and magnetic fields are assumed a combination of trigonometric and linear functions across the plate thickness. To capture small effects on microstructures, the modified strain gradient theory (MSGT), including three length scale parameters combined with the generalized higher-order shear deformation theory (HSDT), is presented. The equilibrium equations for free vibration and buckling analyses of MEE FG microplates are derived by using Hamilton's principle. Through those equations, the natural frequency and critical buckling load of MEE FG microplates are computed by using isogeometric analysis (IGA). Based on the Non-uniform rational B-splines (NURBs) basic functions, which achieve any desired degree of continuity of basis functions, the IGA easily satisfy the MSGT model's higher-order derivatives. The advantage and accuracy of the proposed model are demonstrated through comparisons between the present results and those provided in the literature. The effect of the electric voltage, magnetic potential, power index, geometrical parameter and length scale parameters on the dimensionless frequencies and critical buckling loads of the MEE FG microplates is fully reported. The article's results can be considered as benchmark solutions for the vibration and buckling of MEE FG microplates and they are helpful for manufacturing sensors, actuators, stability control, etc. [ABSTRACT FROM AUTHOR]

This study uses iso-geometric investigation, which is based on the non-uniform rational B-splines (NURBS) basis function, to investigate natural oscillation of bi-directional functionally graded porous (BFGP) doubly-curved shallow microshells placed on Pasternak foundations with any boundary conditions. The characteristics of the present material vary in both thickness and axial directions along the x-axis. To be more specific, a material length-scale coefficient of the microshell varies in both thickness and length directions as the material's mechanical properties. One is able to develop a differential equation system with varying coefficients that regulate the motion of BFGP double-curved shallow microshells by using Hamilton principle, Kirchhoff–Love hypothesis, and modified couple stress theory. The numerical findings are reported for thin microshells that are spherical, cylindrical, and hyperbolic paraboloidal, with a variety of planforms, including rectangles and circles. The validity and effectiveness of the established model are shown by comparing the numerical results given by the proposed formulations with previously published findings in many specific circumstances. In addition, influences of length scale parameters, power-law indexes, thickness-to-side ratio, and radius ratio on natural oscillation responses of BFGP microshells are investigated in detail. [ABSTRACT FROM AUTHOR]

Cycloid drives are generally used in precision machinery requiring high-reduction ratios, such as robot joint (RV) reducers. The contact stress of cycloidal gears greatly affects lifetime and transmission performance. Traditional finite element method (FEM) has less computational efficiency for contact analysis of complex surface. Therefore, in this paper, isogeometric analysis (IGA) was employed to explore the multi-tooth contact problem of the cycloid pinwheel drive. Based on the nonuniform rational B spline (NURBS) curved surface generation method, the NURBS tooth profile of the cycloid gear was reconstructed. In addition, the NURBS surface of the cycloid gear–pin tooth–output pin was generated via the element splicing method. A geometrical analysis model of cycloid pinwheel drive was established to solve the contact force of the meshing pair under different input angles and compared with the finite element method in terms of convergence, resultant accuracy, and solving timeliness. The results show that isogeometric analysis has higher accuracy and efficiency than the finite element method in calculating the contact stress and contact force. The error of the IGA is only 8.8% for 10 × 10 elements in contact, while the error of the finite element method reaches about 40%. The method can improve the contact simulation accuracy of the cycloid drive and provides a reference for the design evaluation of RV reducer. [ABSTRACT FROM AUTHOR]

Let Γ = q 1 Z ⊕ q 2 Z ⊕ ⋯ ⊕ q d Z with arbitrary positive integers q l , l = 1 , 2 , ⋯ , d. Let Δ discrete + V be the discrete Schrödinger operator on Z d , where Δ discrete is the discrete Laplacian on Z d and the function V : Z d → C is Γ-periodic. We prove two rigidity theorems for discrete periodic Schrödinger operators: (1) If for real-valued Γ-periodic functions V and Y , the operators Δ discrete + V and Δ discrete + Y are Floquet isospectral and Y is separable, then V is separable. (2) If for complex-valued Γ-periodic functions V and Y , the operators Δ discrete + V and Δ discrete + Y are Floquet isospectral, and both V = ⨁ j = 1 r V j and Y = ⨁ j = 1 r Y j are separable functions, then, up to a constant, lower dimensional decompositions V j and Y j are Floquet isospectral, j = 1 , 2 , ⋯ , r. Our theorems extend the results of Kappeler. Our approach is developed from the author's recent work on Fermi isospectrality and can be applied to studying more general lattices. [ABSTRACT FROM AUTHOR]

This paper thoroughly discusses the electric activities generated by ion communication between cells and their surrounding environment. Specifically, it focuses on the transients of firing activities of a four-dimensional pituitary model that evolves on three disparate timescales. To examine the impact of inward rectifying K + current and calcium concentration on the firing activities, a bifurcation analysis is conducted, categorizing three primary behaviors: resting, tonic spiking, and bursting. Each behavior is validated through their respective time courses, with the pituitary cells showing higher secretion rates of hormones and neurotransmitters during bursting than spiking. The geometric singular perturbed theory is applied to reveal hidden geometric features and the transient mechanisms associated with bursting, particularly mixed-mode oscillations (MMOs). Singular orbit construction performed in two-timescale separation with different viewpoints offers clarity on the underlying dynamic mechanisms. Canard-induced MMOs are observed in the context of 1 fast/3 slow and 2 fast/2 slow separations, facilitated by the presence of folded saddle-node and folded node, respectively. Additionally, the fast–slow analysis of the 3 fast/1 slow subsystem, which treats calcium concentration c as a parameter, in conjunction with the singular orbit constructions, effectively illustrates the system's complex dynamics. Furthermore, the information obtained in 1 fast/3 slow and 3 fast/1 slow discussions is interplayed in the context of three-timescale separation. The singular orbits identified within three-timescale framework offer a supplemental perspective to the delicate firing patterns observed in two-timescale analysis, enriching the overall understanding of the transient and long-term firing behaviors of the pituitary cells. This study presents valuable insights into the firing features in pituitary cells from the perspectives of dynamic systems. The singular perturbation analysis provides useful viewpoints for accessing firing patterns in multi-timescale systems. [ABSTRACT FROM AUTHOR]