Development of geometrically exact new shell elements based on general curvilinear co‐ordinates

In the present study first‐order shear deformable shell finite elements based on general curvilinear co‐ordinates are proposed. For the development of the present shell elements, a partial mixed variational functional with independently assumed strains is provided in order to avoid the severe locking troubles known as transverse shear and membrane lockings. Bubble functions are included in the shape function of displacement to improve the performance of the developed element. The proposed assumed strain four‐ and nine‐node elements based on the general tensor shell theory provide an efficient linkage framework for shell surface modelling and finite element analysis. In the several benchmark problems, the present shell elements with exact geometric representations demonstrate their performance compared to previously reported results. Copyright © 2002 John Wiley & Sons, Ltd.     

Buckling analysis for delaminated composites using plate bending elements based on higher‐order zig‐zag theory

A finite element based on the efficient higher‐order zig‐zag theory with multiple delaminations is developed. The bending part of the formulation is constructed from the concept of DKQ element. Unlike conventional elements, a developed element has its reference in the bottom surface which simplifies zig‐zag terms on formulation. Exact patch solutions are developed on elements which have the bottom reference system. The present element passes proper bending patch tests in the arbitrary mesh configurations in isotropic materials. Zig‐zag formulation is adopted to model laminated plates with multiple delaminations. To assess the accuracy and efficiency of the present element based on higher‐order zig‐zag theory with multiple delaminations, the linear buckling problem of laminated plates with multiple delaminations has been analysed. The results have been compared with three‐dimensional elasticity solutions. The present element works as an efficient tool for analysing the behaviour of the laminated composites with multiple delaminations. Copyright © 2002 John Wiley & Sons, Ltd.     

A cross-sectional analysis of composite beams based on asymptotic framework

This paper presents the accurate prediction of static behavior of composite beams with arbitrary cross-sections. The asymptotic recursive formulation is reviewed first, where the initial three-dimensional problems are split into the macroscopic 1D problems and the microscopic 2D problems. The finite element formulation for the microscopic 2D problems is then presented in order to find the crosssectional warping solutions. The warping solutions obtained contribute the cross-sectional properties to the macroscopic 1D problems. The end effect of the 1D beam problem is also considered via the kinematic correction for a displacement prescribed boundary. The approach presented is applied to the beams with relatively complicated material distributions and cross-sectional geometry. As numerical test-beds, a three-layered sandwich beam and a composite beam with the multi-cell cross-section are taken to analyze the local deformation. A parametric study is also carried out to investigate the significance of shear deformation due to the cross-sectional orthotropic characteristics. The cross-sectional deformation is predicted based on the asymptotic framework. The accuracy of the present approach is assessed by comparing the results obtained with the 3D FEM solutions obtained by ANSYS.     

Neural network-based prediction of the long-term time-dependent mechanical behavior of laminated composite plates with arbitrary hygrothermal effects

Journal of Mechanical Science and Technology - Recurrent neural network (RNN)-based accelerated prediction was achieved for the long-term time-dependent behavior of viscoelastic composite laminated...     

A study on the prediction of the mechanical properties of nanoparticulate composites using the homogenization method with the effective interface concept

A sequential multi‐scale homogenization method combined with molecular dynamics (MD) simulation is developed for the mechanical characterization of nanoparticulate composites. In order to characterize the particle‐size effect of nanocomposites, the effective interface, which has been adopted in continuum micromechanics approaches, is considered as the characteristic phase. Owing to the existence of the interface and the size‐dependent elastic modulus that is observed from MD simulations, an analysis of the mechanical properties of nanocomposites with continuum micromechanics requires careful consideration of the particle‐concentration effect. Therefore, this study focuses on hierarchical information transfer from the molecular model to the continuum model through the homogenization method in lieu of an analytical micromechanics bridging method. Using the present multi‐scale homogenization method, the elastic properties of the effective interface are numerically evaluated and compared with the analytically obtained micromechanics solutions. In addition, the overall elastic modulus of nanocomposites is obtained from the present model and compared with the results of MD simulation, the micromechanics bridging model, and finite‐element analysis (FEA). Copyright © 2010 John Wiley & Sons, Ltd.     

A neural network constitutive model for hyperelasticity based on molecular dynamics simulations

Numerical analysis of the hyperelastic behavior of polymer materials has drawn significant interest from within the field of mechanical engineering. Currently, hyperelastic models based on the energy density function, such as the Neo-Hookean, Mooney-Rivlin, and Ogden models, are used to investigate the hyperelastic responses of materials. Conventionally, constants relating to materials were determined from experimental data by using global least-squares fitting. However, formulating a constitutive equation to capture the complex behavior of hyperelastic materials was difficult owing to the limitations of the analytical model and experimental data. This study addresses these limitations by using a system of neural networks (NNs) to design a data-driven surrogate model without a specific function formula, and employs molecular dynamics (MD) simulations to calculate the massive amount of combined loading data of hyperelastic materials. Thus, MD simulations were used to propose an NN constitutive model for hyperelasticity to derive the constitutive equation to model the complex hyperelastic response. In addition, the probability distributions of the numerical solutions of hyperelasticity are used to characterize the uncertainty of the MD models. These statistical finite element results not only present numerical results with reliability ranges but also scattered distributions of the solution obtained from the MD-based probability distributions.     

Efficient design optimization strategy for structural dynamic systems using a reduced basis method combined with an equivalent static load

This paper presents an efficient structural design optimization strategy that combines the reduced basis method (RBM) with the equivalent static load (ESL). In dynamic response optimization using ESL, the computation of a static system optimization is repeatedly executed under multiple static loads. In this process, we propose parametrizing the static system and employing the RBM with global proper orthogonal decomposition (POD). In general, the snapshots for the sampling procedure under multiple loads increase proportionally to the number of loads, which results in an inefficient computational procedure. Thus, we propose taking snapshots with a proper orthogonal mode (POM) of the multiple loads rather than for the multiple loads themselves. The number of snapshots then decreases, and the original system can be efficiently reduced. We directly employ the framework of the proposed RBM with the POM of multiple loads to ESL-based design optimization, and the results indicate that the proposed method is more efficient than conventional ESL-based optimization as well as a full order model. Various numerical examples, including comparisons of relative errors and the dynamic response optimizations, support the strength of the proposed strategy.     

A coupled finite element analysis of independently modeled substructures by penalty frame method

A penalty frame method is proposed for the coupled analysis of finite elements with independently modeled substructures. Although previously reported hybrid interface method by Aminpour et al (IJNME, Vol 38, 1995) is accurate and reliable, it requires non-conventional special solution algorithm such as multifrontal solver. In present study, an alternative method has been developed using penalty frame constraints, which results in positive symmetric global stiffness matrices. Thus the conventional skyline solver or band solver can be utilized in the solution routine, which makes the present method applicable in the environment of conventional finite element commercial software. Numerical examples show applicability of the present method.     

Kirigami/Origami‐Based Soft Deployable Reflector for Optical Beam Steering

The beam steering mechanism has been a key element for various applications ranging from sensing and imaging to solar tracking systems. However, conventional beam steering systems are bulky and complex and present significant challenges for scaling up. This work introduces the use of soft deployable reflectors combining a soft deployable structure with simple kirigami/origami reflective films. This structure can be used as a macroscale beam steering mechanism that is both simple and compact. This work first develops a soft deployable structure that is easily scalable by patterning of soft linear actuators. This soft deployable structure is capable of increasing its height several folds by expanding in a continuous and controllable manner, which can be used as a frame to deform the linearly stretchable kirigami/origami structures integrated into the structure. Experiments on the reflective capability of the reflectors are conducted and show a good fit to the modeling results. The proposed principles for deployment and for beam steering can be used to realize novel active beam steering devices, highlighting the use of soft robotic principles to produce scalable morphing structures.     

Three dimensional stress analysis of a composite patch using stress functions

A stress function-based analysis is proposed to provide a simple and efficient approximation method of three-dimensional (3D) state of stress that exists near the free edge of bonded composite patches. In order to apply plane strain assumption in a composite patch, a linear superposition of sliced section from a bonded patch is used. In addition, to describe the load transfer mechanism from the substrate to the composite patch, a simple shear lag model is introduced. The 3D stress behavior at the free edge of the composite patch is modeled by Lekhnitskii stress functions, and the governing equations of the given composite patch are obtained by applying the principle of complementary virtual work. After a suitable expansion of the functions, the governing equations are transformed into two coupled ordinary differential equations, and they are solved by a general eigenvalue solution procedure. As the number of base functions increases, the interlaminar stresses converge. The interlaminar stresses reach maximum at the free edge and decrease sharply at the inner part of the patch. The interlaminar stresses are concentrated at the interface between the layers because of the mismatch of material properties and the geometric singularity. Since the proposed method accurately predicts the 3D stresses in a composite patch bonded on the metal substrate, it can be used as a simple and efficient analytical tool for designing such structural components.