Finite Strip Method for the Analysis of Visco-Elastic Two-Dimensional Structures

A general constraint-based formulation for the analysis and partial synthesis of two-dimensional truss structures is presented. This formulation is general in that it handles statically determinate and statically indeterminate trusses with pin and roller supports, and concentrated joint loads. The formulation is constraint-based in that the physical behavior of truss components is declaratively represented using constraints.The analysis and partial synthesis of a truss structure manifest themselves in proving the satisfiability of the constraints associated with the structural components. An artificial intelligence approach called constraint logic programming is used for representing and satisfying constraints. A constraint logic programming language, called CLP(R), is used for implementing the formulation. The implemented program consists of sixteen rules. These rules are used for both the analysis and partial synthesis of truss structures. Several truss analysis and synthesis examples using the formulation are presented.

We investigate two-dimensional cluster structures composed of ferromagnetic colloidal particles, based on a flexible chain model, by the configurational-bias Monte Carlo method. We clarify the dependence of the probabilities of the creation of different types of clusters on the dipole-dipole interactive energy and the cluster size.

In this paper, the boundary element method (BEM) based on elasticity theory is developed for two-dimensional (2-D) thin structures with the thickness to length ratio in the micro (10−6) or nano (10−9) scales. An efficient analytical method is developed to deal with the nearly-singular integrals in the boundary integral equation (BIE) for 2-D thin structures. The nearly-singular integrals, which are line integrals for 2-D problems and arise when two boundary curves are close to each other, are transformed into function evaluations at the two end points of the element of integration. In addition, a new nonlinear coordinate transformation is developed for nearly weakly-singular integrals to further increase the numerical accuracy. For the test problems studied, very promising results are obtained when the thickness to length ratio is in the orders of 10−6 to 10−9, which is sufficient for modeling most thin structures in the micro- or nano-scales. The developed method can be applied readily to model layered coatings, thin films or other layered structures to analyze contact stresses, interfacial cracks, thermal effects and nonlinear deformations.

Simulation analysis of III-N two-dimensional electron gas-based structures that could be used for stable monolithically integrated enhancement/depletion-mode circuits was carried out. Three different designs were proposed and analysed, including a novel p-GaN/AlN-GaN SPSL/GaN, which is expected to have lower ON-state resistance and higher transconductance than conventional normally-off GaN-based transistors.

Based on previous findings concerning the numerical solution of one-dimensional elastodynamical problems [Provatidis in Arch Appl Mech 78(4):241–250, 2008] this paper extends the methodology to the static analysis of two-dimensional problems in quadrilateral domains. This target is achieved by replacing the Galerkin/Ritz procedure involved in Lagrangian (or Gordon–Coons) type finite elements by a global collocation scheme. In brief, the boundary conditions are fulfilled at all boundary nodes, while the governing equation is fulfilled at internal points. The theory is supported by four test cases concerning rectangular and curvilinear structures under plane-stress or plane-strain conditions, where the convergence rate is successfully compared with that of conventional bilinear finite elements with the same mesh density.

The isogeometric analysis (IGA) that integrates Computer Aided Design(CAD) and Computer Aided Engineering (CAE) is found so far the effectively numerical tool for the analysis of a variety of practical problems. In this paper, we develop further the NURBS based isogeometric analysis framework for piezoelectric structures.The method employs the NURBS basis functions in both geometry representation and analysis. The main advantages of the present method are capable of handling the exactgeometry of conic sections and making the flexibility of refinement and degree elevationwith an arbitrary continuity of basic functions. These features results in high accuracy of approximate solutions for practical applications, especially piezoelectric problems. Three numerical examples are provided to validate excellent performance of the present method.

Tile vaults as integrated formwork for reinforced concrete: Construction, experimental testing and a method for the design and analysis of two-dimensional structures

In this study, a receptivity analysis of streaks, oblique and two-dimensional flow structures is presented with a stochastic receptivity framework for different inputs for supersonic adiabatic boundary layer flows. In particular, an active role of temperature fluctuation is identified for the amplification of oblique patterns, while a passive role is observed for the onset of streaks and two-dimensional flow structures. From a practical point of view, this study can help to improve the effectiveness of actuators aiming at a particular response in supersonic boundary layer flows.

An efficient meshless collocation method for the analysis of two-dimensional piezoelectric structures

An improved method of two-dimensional kinematical structural analysis of tides (the “method of the orbits”) is presented. This method allows us to determine the parameters of the primary tidal waves shaping the observed tidal structure. The construction of the vertical orbits for the individual tidal harmonics is performed along the horizontal coordinate axes; one of them is oriented along the so-called “reactive azimuth,” which coincides with the direction of the tidal current at the instant of the zero tidal level. In this case, the orbit parameters include information on the amplitude-phase relations of the interfering waves and allow us to determine the angle of the waves crossing. The suggested method enables us to quantitatively describe the mechanism of the tidal formation with oblique interference both close to the shore and in the open sea. We tested the new method in two local zones of the White Sea (Morzhovets Island and in the vicinity of the entrance to Kandalaksha Gulf) where the presence of rotating semidiurnal tidal currents evidences the significant role of oblique interference of tidal waves. In these zones, the developed method made it possible to perform a detailed quantitative analysis of the local tide structure caused by the M2 tidal wave, which plays the dominant role in the White Sea. The result describes the structure of the propagation of the primary tidal waves better than the field of “pure” energy fluxes that was used earlier.

In recent decades, analysis of structures considering variability of some parameters for more reliable design has attracted the attention of researchers. In this paper, the stochastic analysis of a cantilever deep beam made of large deformable neo-hookean material is carried out. For this purpose, the meshless local Petrov-Galerkin (MLPG) method is developed to obtain the geometrically non-linear equilibrium equations. The radial point interpolation method is used for generating the shape functions. The incremental iterative Newton-Raphson method with suitable load steps is used to solve the non-linear governing equations. The results of deterministic analysis obtained with proposed method are compared with the finite element results and good agreement is achieved. The initial elasticity modulus of neo-hookean material is considered to be uncertain variable. To generate random field of uncertain variable with normal, lognormal and uniform probability density functions (PDFs), the Monte Carlo Simulation (MCS) technique was employed. The sufficient number of simulations for convergence the results was determined experimentally. The effect of elasticity modulus, PDF and coefficients of variation (COV) on maximum vertical displacement, PDF and COV of results are studied in details. Comparing the stochastic and deterministic results shows that the uncertainty in mechanical properties has significant effect on results.

Purpose – The purpose of this paper is to present an efficient smoothed particle hydrodynamics (SPH) method particularly adapted for the geometrically nonlinear analysis of structures. Design/methodology/approach – In order to resolve the inconsistency phenomenon which systematically occurs in the standard SPH method at the domain’s boundaries of the studied structure, the classical kernel function and its spatial derivatives were modified by the use of Taylor series expansion. The well-known tensile instabilities inherent to the Eulerian SPH formulation were attenuated by the use of the Total Lagrangian Formulation (TLF). Findings – In order to demonstrate the effectiveness of the present improved SPH method, several numerical applications involving geometrically nonlinear behaviors were carried out using the explicit dynamics scheme for the time integration of the PDEs. Comparisons of the obtained results using the present SPH model with analytical reference solutions and with those obtained using ABAQUS finite element (FE) commercial software, show its good accuracy and robustness. Practical implications – An additional application including a multilayered composite structure and involving buckling and delamination was investigated using the present improved SPH model and the results are compared to the FE results, they confirmed both the efficiency and the accuracy of the proposed method. Originality/value – An efficient 2D-continuum SPH model for the geometrically nonlinear analysis of thin and thick structures is proposed. Contrarily to the classical SPH approaches, here the constitutive material relations are used to link naturally the stresses and strains. The Total Lagrangian approach is investigated to alleviate the tensile instabilities problem, allowing at the same time to avoid the updating procedure of the neighboring particles search and therefore reducing CPU usage. The proposed approach is valid for isotropic and multilayered composites structures undergoing large transformations. CPU time savings and better results with the new 2D-continuum SPH formulation compared to the classical continuum SPH. The explicit dynamic scheme was used for time integration allowing a fast resolution algorithm even for highly nonlinear problems.

<abstract> <p>We propose an asymptotic concentration approach combined with isogeometric analysis (IGA) for the topology optimization of two-dimensional (2D) linear elasticity structures under the commonly-used framework of the solid isotropic materials and penalty (SIMP) model. Based on the SIMP framework, the B-splines are used as basis functions to describe geometric model in structural finite element analysis, which closely combines geometric modeling with structural analysis. Isogeometric analysis is utilized to define the geometric characteristics of the 2D linear elasticity structures, which can greatly improve the calculation accuracy. In addition, to eliminate the gray-scale intervals usually caused by the intermediate density in the SIMP approach, we utilize the asymptotic concentration method to concentrate the intermediate density values on either 0 or 1 gradually. Consequently, the intermediate densities representing gray-scale intervals in topology optimization results are sufficiently eliminated by virtue of the asymptotic concentration method. The effectiveness and applicability of the proposed method are illustrated by several typical examples.</p> </abstract>

Holes, cracks, or inclusions in two-dimensional linear anisotropic viscoelastic solids

Making use of field expansion and the equivalent boundary, an analytical model is set up to describe the multi-mode intercoupling in two-dimensional coaxial Bragg structures with either one or both of the conductors corrugated with helical ripples. The coupled-mode equations and the explicit formulae of the coupling coefficients for all possible mode combinations are derived, and the general mode coupling rules are discussed. Based on the analytical model, the dependence of the coupling coefficients on structural parameters of the two-dimensional coaxial Bragg structures with overmoded operation is investigated by numerical calculation. The results show that the additional conductor provides more flexibility for adjustment of coupling coefficients compared with other types of two-dimensional Bragg structures with a single conductor. Taking advantage of this feature, a two-dimensional coaxial Bragg structure can provide strong reflection with high mode purity under overmoded operation by suppressing the parasitic coupling using an optimized combination of corrugated outer and inner conductors. In this way, the structure has potential applications in the design of high-Q improved Bragg resonators for high-power microwave oscillators operating in the millimeter wave or terahertz range.