QUANTITATIVE PREDICTION FOR SPRINGBACK OF UNLOADING AND TRIMMING IN SHEET METAL STAMPING FORMING

Based on the elastic-plastic large deformation finite element formulation as well as the shell element combined discrete Kirchhoff theoretical plate element (DKT) with membrane square element, deep-drawing bending springback of typical U-pattern is studied. At the same time the springback values of the drawing of patterns' unloading and trimming about the satellite aerial reflecting surface are predicted and also compared with those of the practical punch. Above two springbacks all obtain satisfactory results, which provide a kind of effective quantitative pre-prediction of springback for the practical engineers.

A new approach for free vibration analysis of a system of elastically interconnected similar rectangular plates

A new procedure is proposed to ease the analyses of the free vibration of an elastically connected identical plates system with respect to Kirchhoff plate theory.A structure of n parallel,elastically connected rectangular plates is of concern,whereby the motion is explained by a set of n coupled partial differential equations.The method involves a new change in variables to uncouple equations and form an equal system of n decoupled plates,while each is assumed to be elastically connected to the ground.The differential quadrature method is adopted to solve the decoupled equations.To unravel the original system,the inverse transform is applied.Decoupling the equations enables one to solve them based on the solution methods available for a single plate system.This also diminishes the computational costs of such problems.By considering different boundary conditions,a case study is run to present the method and to validate the results with its counterparts,for which excellent agreement is observed.Assessing the influence of dimensionless thickness,aspect ratio,and stiffness coefficients on the frequencies reveals the different effects of them at the low order of dimensionless natural frequencies in comparison with high orders and for different boundary conditions.

Shape Sensing of Thin Shell Structure Based on Inverse Finite Element Method

Shape sensing as a crucial component of structural health monitoring plays a vital role in real-time actuation and control of smart structures,and monitoring of structural integrity.As a model-based method,the inverse finite element method(iFEM)has been proved to be a valuable shape sensing tool that is suitable for complex structures.In this paper,we propose a novel approach for the shape sensing of thin shell structures with iFEM.Considering the structural form and stress characteristics of thin-walled structure,the error function consists of membrane and bending section strains only which is consistent with the Kirchhoff–Love shell theory.For numerical implementation,a new four-node quadrilateral inverse-shell element,iDKQ4,is developed by utilizing the kinematics of the classical shell theory.This new element includes hierarchical drilling rotation degrees-of-freedom(DOF)which enhance applicability to complex structures.Firstly,the reconstruction performance is examined numerically using a cantilever plate model.Following the validation cases,the applicability of the iDKQ4 element to more complex structures is demonstrated by the analysis of a thin wallpanel.Finally,the deformation of a typical aerospace thin-wall structure(the composite tank)is reconstructed with sparse strain data with the help of iDKQ4 element.

Topology optimization of plate structures using plate element-based moving morphable component(MMC)approach

A topology optimization approach for designing the layout of plate structures is proposed in this article.In this approach,structural mechanical behavior is analyzed under the framework of Kirchhoff plate theory,and structural topology is described explicitly by a set of moving morphable components.Compared to the existing treatments where structural topology is generally described in an implicit manner,the adopted explicit geometry/layout description has demonstrated its advantages on several aspects.Firstly,the number of design variables is reduced substantially.Secondly,the obtained optimized designs are pure black-and-white and contain no gray regions.Besides,numerical experiments show that the use of Kirchhoff plate element helps save 95-99%computational time,compared with traditional treatments where solid elements are used for finite element analysis.Moreover the accuracy of the proposed method is also validated through a comparison with the corresponding theoretical solutions.Several numerical examples are also provided to demonstrate the effectiveness of the proposed approach.

MECHANICAL MODELING OF THE BISTABLE BACTERIAL FLAGELLAR FILAMENT

We extend the 2D Landau phase transition theory to the bacterial flagellar filament which displays the phase transition between the left handed normal form and the right handed semi-coiled form. The bacterial flagellar filament is treated as an elastic thin rod based on the Kirchhoff’s thin rod theory. Mechanical analysis is performed on the periodical phase transition of the filament between the two helical structures of the opposite charity. The curvature and twist are chosen as the order parameters in constructing the phase transition model of the filament. The established model is applied to study the instability properties of the filament and to investigate the loading and deformation conditions of the phase transition. In addition, the curvature and twist gradient energy are considered to describe the interface properties of the two phases.

Simulating an Elastic Ring with Bend and Twist by an Adaptive Generalized Immersed Boundary Method

Many problems involving the interaction of an elastic structure and a viscous fluid can be solved by the immersed boundary(IB)method.In the IB approach to such problems,the elastic forces generated by the immersed structure are applied to the surrounding fluid,and the motion of the immersed structure is determined by the local motion of the fluid.Recently,the IB method has been extended to treatmore general elasticity models that include both positional and rotational degrees of freedom.For such models,force and torque must both be applied to the fluid.The positional degrees of freedomof the immersed structuremove according to the local linear velocity of the fluid,whereas the rotational degrees of freedom move according to the local angular velocity.This paper introduces a spatially adaptive,formally second-order accurate version of this generalized immersed boundary method.We use this adaptive scheme to simulate the dynamics of an elastic ring immersed in fluid.To describe the elasticity of the ring,we use an unconstrained version of Kirchhoff rod theory.We demonstrate empirically that our numerical scheme yields essentially second-order convergence rates when applied to such problems.We also study dynamical instabilities of such fluid-structure systems,and we compare numerical results produced by our method to classical analytic results from elastic rod theory.