Effect of continuous strain path changes on forming limit strains of DP600

The strain path may change in actual sheet metal‐forming processes, so the determination of formability of sheet metal should consider the nonlinear strain path. For identifying the forming limit (FL) strains under nonlinear strain path, a conventional two‐step procedure with unloading is classically used to produce the strain path change, which results in no continuous measure of strain. The in‐plane biaxial tensile test with a cruciform specimen is an interesting alternative to overcome the drawbacks of conventional method. The strain path change can be made without unloading during a single test. In this work, the experimental FL strains of DP600 sheets under two types of nonlinear strain path are investigated and then compared with those under linear strain paths. The Oyane ductile fracture criterion is used in the finite element simulation to predict the experimental results.     

Active control of FGM shells subjected to a temperature gradient via piezoelectric sensor/actuator patches

A generic static and dynamic finite element formulation is derived for the modelling and control of piezoelectric shell laminates under coupled displacement, temperature and electric potential fields. The base shell is of functionally graded material (FGM) type, which consists of combined ceramic–metal materials with different mixing ratios of the ceramic and metal constituents. A multi‐input–multi‐output (MIMO) system is applied to provide active feedback control of the laminated shell using self‐monitoring sensors and self‐controlling actuators through a close loop. Numerical studies clearly show the influence of the positional configurations of sensor/actuator pairs on the effectiveness of static and dynamic control for the shell laminates. The effects of the constituent volume fractions on the static and dynamic responses of the shell laminate are also elucidated. Copyright © 2002 John Wiley & Sons, Ltd.     

冲击块与金属圆柱壳相互作用的缓冲吸能分析

应用Johnson Cook本构方程, 结合Singace叠缩模型,考虑冲击作用引起材料的应变强化效应、应变率强化效应和温度效应,研究了冲击物体和金属圆柱壳相互作用的能量转化过程。运用角度增量叠缩法计算了圆柱壳的塑性变形能,根据冲击块和圆柱壳所组成系统能量守恒得到了冲击块速度位移、冲击块和圆柱壳之间瞬时载荷的解析表达式,以及圆柱壳塑性变形引起的温度分布函数。通过对不同材质的金属圆柱壳在冲击作用下塑性变形过程的计算分析,并和有限元计算结果比较,证明了本文计算方法的正确性。     

Optimal solid shell element for large deformable composite structures with piezoelectric layers and active vibration control

In this paper, we present an optimal low‐order accurate piezoelectric solid‐shell element formulation to model active composite shell structures that can undergo large deformation and large overall motion. This element has only displacement and electric degrees of freedom (dofs), with no rotational dofs, and an optimal number of enhancing assumed strain (EAS) parameters to pass the patch tests (both membrane and out‐of‐plane bending). The combination of the present optimal piezoelectric solid‐shell element and the optimal solid‐shell element previously developed allows for efficient and accurate analyses of large deformable composite multilayer shell structures with piezoelectric layers. To make the 3‐D analysis of active composite shells containing discrete piezoelectric sensors and actuators even more efficient, the composite solid‐shell element is further developed here. Based on the mixed Fraeijs de Veubeke–Hu–Washizu (FHW) variational principle, the in‐plane and out‐of‐plane bending behaviours are improved via a new and efficient enhancement of the strain tensor. Shear‐locking and curvature thickness locking are resolved effectively by using the assumed natural strain (ANS) method. We also present an optimal‐control design for vibration suppression of a large deformable structure based on the general finite element approach. The linear‐quadratic regulator control scheme with output feedback is used as a control law on the basis of the state space model of the system. Numerical examples involving static analyses and dynamic analyses of active shell structures having a large range of element aspect ratios are presented. Active vibration control of a composite multilayer shell with distributed piezoelectric sensors and actuators is performed to test the present element and the control design procedure. Copyright © 2005 John Wiley & Sons, Ltd.     

Inverse Sub‐structuring Method for Multi‐coordinate Rigidly Coupled Product Transport System based on a Novel Shearing Probe Technique

The inverse sub‐structuring method can predict the component‐level frequency response functions (FRFs) of product (critical component) for product transport system from only measured system‐level FRFs, facilitating the cushioning packaging design. However, the FRFs of the coupling interface between product and vehicle are usually of extreme difficulty to be measured due to the limited accessible space. To overcome this difficulty, the authors suggested a so‐called FRF probe technique method in the previous study, which may be more suitable for the single‐coordinate coupled system. In practice, most of the product transport systems should be treated as multi‐coordinate coupled system. The aim of this paper is to derive a new FRF‐based inverse sub‐structuring method for multi‐coordinate rigidly coupled product transport system and develop a new shearing probe technique to obtain the difficult‐to‐monitor FRFs at the coupling interface, which will be validated by a lumped mass model and finite element models, respectively, showing perfect agreement. Finally, the experiment on a physical prototype of multi‐coordinate rigidly coupled product transport system is performed to further check the feasibility of the application prospect of the shearing probe technique for inverse analysis of product transport system. The method proposed in this study will provide the packaging designers an alternative method to monitor the integrity of product transport system. Copyright © 2017 John Wiley & Sons, Ltd.     

Mixed shell element for seven‐parameter formulation

A new mixed shell element is developed for a seven‐parameter formulation in this paper. The mixed shell element is constructed by assuming stress field and displacement field together. Assumed stress field and assumed displacement field can be combined by stress–strain relationship with Hu‐Washizu functional. The developed mixed shell element can provide more flexible stiffness than other commercial softwares. Additionally, seven‐parameter shell formulation is used instead of Reissner/Mindlin formulation, since it can provide the thickness change. Even though some commercial engineering software are not proper for very thick shell structure, the developed mixed shell element for seven‐parameter formulation can be used without distinction of thick shell and thin shell. An example of shell models with different thickness is provided with solid model. Static and modal analyses are also performed for verification. Copyright © 2005 John Wiley & Sons, Ltd.     

Shell topology optimization using the layered artificial material model

A general methodology for topology optimization using the finite element method is described for shell structures. Four‐ and nine‐node Reissner–Mindlin shell elements with drilling degrees of freedom are used for the finite element response analysis. The artificial material model is used in the topology optimization and in particular, an isotropic multi‐layer shell model is introduced to allow the formation of holes or stiffening zones. In addition, a single design variable resizing algorithm is implemented based on the existing criterion which is found to be adequate for the artificial material model. Several benchmark tests are presented to show the overall performance of the proposed methodology. The strain energy variation together with the variation of the layout of the structure is monitored. Some detailed examples are provided with comparisons of the use of the four‐ and nine‐node elements and studies of critical solution parameters. Copyright 2000 John Wiley & Sons, Ltd.     

Fast simulation of incremental sheet metal forming by adaptive remeshing and subcycling

In order to use incremental sheet forming (ISF) in an industrial context, it is necessary to provide fast and accurate simulation methods for virtual process design. Without reliable process simulations, first-time right production seams infeasible and the process loses its advantage of offering a short lead time. Previous work indicates that implicit finite element (FE) methods are at present not efficient enough to allow for the simulation of AISF for industrially relevant parts, mostly due to the fact that the moving contact requires a very small time step. Finite element methods based on explicit time integration can be sped up using mass or time scaling to enable the simulation of large-scale sheet metal forming problems. However, AISF still requires dedicated adaptive meshing methods to further reduce the calculation times. In this paper, an adaptive remeshing strategy based on a multi-mesh method is developed and applied to the simulation of AISF. It is combined with subcycling to further reduce the calculation times. For the forming of a cone shape, it is shown that savings in CPU time of up to 80 % are possible with acceptable loss of accuracy, and that the simulation time scales more moderately when the part size is increased, so that larger, industrially relevant parts become feasible.     

Overview and comparison of various test methods to determine formability of a sheet metal cut‐edge and approaches to the test results application in forming analysis

This paper presents an overview of published test methods for determination of formability of a sheet metal cut‐edge. The presented test methods were developed to evaluate formability of a sheet metal edge that was produced by shear cutting. Due to high local strains, hardening, or even microcracks, the cut‐edge might have less formability than the base material. The presentation of the tests is structured according to the three steps each test can be divided into: cutting, forming and evaluation. Similarities and differences concerning these steps were worked out. Additionally, a classification of the tests is made regarding their strain gradients in the vicinity of the cut‐edge. For this, finite element models of exemplary tests were built up using LS‐DYNA explicit and analyzed accordingly. Evaluation approaches that go beyond the common hole expansion ratio (HER) from the hole expansion test (HET) standardized in the ISO 16630 are also described. The tests can be used not only for a quantitative comparison of materials and cutting processes with regard to the cut‐edge formability but to determine input data for the finite element analysis (FEA) of forming processes to allow a simulation based cut‐edge failure prediction. The paper also presents appropriate procedures on the transfer of the test results into the FEA of forming of a workpiece with a cut‐edge.     

ANSYS在水电站固卷机架结构设计中的应用

针对糯扎渡水电站2x800kN固定卷扬机的设计,分析了固卷的计算工况及计算载荷,用ANSYS软件建立SHELL63弹性壳单元模型,对金属结构的连接、约束、载荷进行有效处理,对固卷机架的应力、变形进行有限元计算,并对机架进行了模态分析,为结构系统的振动特性分析、振动故障诊断和预报以及结构动力特性的优化设计提供依据。     

Applications of linear inverse finite element method in prediction of the optimum blank in sheet metal forming

A linear inverse finite element method has been developed and investigated to predict the optimum blank. To reduce the computation time, the part is unfolded properly on the flat sheet and treated as a 2D problem. This approach is employed primarily to design the optimum blank shape from the desired final shape with the linear formulations. The procedure is based on the minimization of energy for the unfolded elements. Two solution methods, Direct and Newton–Raphson methods have been examined for the solution of nodal displacements in the equilibrium equations. The convergence show high sensitivity to the initial guess for the strain path when assumed to be linear at the first step. Two applied examples are implemented to show the efficiency of this method. In S rail example, the thickness distributions have been compared with experimental analysis after obtaining the optimum blank with Linear IFEM. In circular cup example, the results have been compared with conventional forward incremental method. New calculation of the external forces vector has been displayed. In this calculation, both blank holder force (BHF) vector and in-plane force vector have been shown. Finally, in this approach good agreement was found between the forward incremental and Linear IFEM results.     

A reduced integration solid‐shell finite element based on the EAS and the ANS concept—Geometrically linear problems

In this paper a new reduced integration eight‐node solid‐shell finite element is presented. The enhanced assumed strain (EAS) concept based on the Hu–Washizu variational principle requires only one EAS degree‐of‐freedom to cure volumetric and Poisson thickness locking. One key point of the derivation is the Taylor expansion of the inverse Jacobian with respect to the element center, which closely approximates the element shape and allows us to implement the assumed natural strain (ANS) concept to eliminate the curvature thickness and the transverse shear locking. The second crucial point is a combined Taylor expansion of the compatible strain with respect to the center of the element and the normal through the element center leading to an efficient and locking‐free hourglass stabilization without rank deficiency. Hence, the element requires only a single integration point in the shell plane and at least two integration points in thickness direction. The formulation fulfills both the membrane and the bending patch test exactly, which has, to the authors' knowledge, not yet been achieved for reduced integration eight‐node solid‐shell elements in the literature. Owing to the three‐dimensional modeling of the structure, fully three‐dimensional material models can be implemented without additional assumptions. Copyright © 2009 John Wiley & Sons, Ltd.     

A parametric study on fatigue strength of spot‐weld joints

Fastening elements usually lead to high stress concentrations; fatigue failure thus becomes the most critical failure mode for a fastening element itself or the region around it under fluctuating stresses. A designer should seek the ways of increasing fatigue strength of a joint to ensure the safety of the whole structure. Resistance spot welding is the most preferred method to join metal sheets. The design variables for spot‐weld joints affecting their strengths are basically sheet thickness, spot‐weld nugget diameter, number of spot welds and the joint type as exemplified in tensile shear (TS), modified tensile shear (MTS), coach peel (CP) and modified coach peel (MCP) specimens. In this study, the effects of these parameters on the fatigue life of spot‐weld joints have been investigated. For this purpose, one of the most reliable fatigue assessment models, Coffin–Manson approach, was used. In order to accurately determine the stress and strain states, a nonlinear finite element analysis was carried out taking into account plastic deformations, residual stresses developed after unloading and contacting surfaces. The results provide designers with some guidelines to foresee the impact of design changes on fatigue strength of spot‐weld joints.     

One point quadrature shell elements: a study on convergence and patch tests

One point quadrature shell elements are being widely used in the numerical simulation of shell structures, including sheet forming, because essentially of their computational efficiency. Nowadays, the purpose of using one point quadrature shell elements is not only related to computational efficiency but also because these elements have shown to be simultaneously robust and accurate in the simulation of complex sheet metal forming processes. The main objective of this work is to study the convergence behavior of different one-point quadrature shell elements and their ability to pass the membrane and bending patch tests. For comparison purposes, two new elements include a new formulation for the membrane strain field in order to further improve the membrane behavior of the element developed in previous work of (in Cardoso et al. Comput Meth Appl Mech Eng 191:5177, 2002). The original convective membrane strains of Cardoso et al. (Comput Meth Appl Mech Eng 191:5177, 2002) (in the stabilization matrices only) are thus replaced by new membrane strains, constructed directly at the co-rotational coordinate system (located at the element’s center). It is thus proved that with this new membrane formulation the elements pass now all the patch tests but, for warped (or curved) element geometries, their accuracy is not as good as the original element of (Cardoso et al. in Comput Meth Appl Mech Eng 191:5177, 2002) based on the convective coordinate system. In the numerical results presented in this paper, comprehensive comparison and discussion of these formulations are made for well known linear benchmark examples.     

Energy and momentum conserving elastodynamics of a non‐linear brick‐type mixed finite shell element

The paper presents aspects of the finite element formulation of momentum and energy conserving algorithms for the non‐linear dynamic analysis of shell‐like structures. The key contribution is a detailed analysis of the implementation of a Simó–Tarnow‐type conservation scheme in a recently developed new mixed finite shell element. This continuum‐based shell element provides a well‐defined interface to strain‐driven constitutive stress updates algorithms. It is based on the classic brick‐type trilinear displacement element and is equipped with specific gradient‐type enhanced strain modes and shell‐typical assumed strain modifications. The excellent performance of the proposed dynamic shell formulation with respect to conservation properties and numerical stability behaviour is demonstrated by means of three representative numerical examples of elastodynamics which exhibit complex free motions of flexible structures undergoing large strains and large rigid‐body motions. Copyright © 2001 John Wiley & Sons, Ltd.     

Finite deformation formulation of a shell element for problems of sheet metal forming

An elastic-plastic thin shell finite element suitable for problems of finite deformation in sheet metal forming is formulated. Hill's yield criterion for sheet materials of normal anisotropy is applied. A nonlinear shell theory in a form of an incremental variational principle and a quasi-conforming element technique are employed in the Lagrangian formulation. The shell element fulfills the inter-element C ¹ continuity condition in a variational sense and has a sufficient rank to allow finite stretching, rotation and bending of the shell element. The accuracy and efficiency of the finite element formulation are illustrated by numerical examples.     

A reduced integration solid‐shell finite element based on the EAS and the ANS concept—Large deformation problems

In this paper we address the extension of a recently proposed reduced integration eight‐node solid‐shell finite element to large deformations. The element requires only one integration point within the shell plane and at least two integration points over the thickness. The possibility to choose arbitrarily many Gauss points over the shell thickness enables a realistic and efficient modeling of the non‐linear material behavior. Only one enhanced degree‐of‐freedom is needed to avoid volumetric and Poisson thickness locking. One key point of the formulation is the Taylor expansion of the inverse Jacobian matrix with respect to the element center leading to a very accurate modeling of arbitrary element shapes. The transverse shear and curvature thickness locking are cured by means of the assumed natural strain concept. Further crucial points are the Taylor expansion of the compatible cartesian strain with respect to the center of the element as well as the Taylor expansion of the second Piola–Kirchhoff stress tensor with respect to the normal through the center of the element. Copyright © 2010 John Wiley & Sons, Ltd.