Analysis Of Thin-walled Structures Research Articles

Dynamic instability and free vibration analysis of thin-walled structures with arbitrary cross-sections

Dynamic instability and free vibration analysis of thin-walled structures with arbitrary cross-sections

Analysis-suitable unstructured T-splines: Multiple extraordinary points per face

Analysis-suitable T-splines (AST-splines) are a promising candidate to achieve a seamless integration between the design and the analysis of thin-walled structures in industrial settings. In this work, we allow multiple extraordinary points per face, i.e., we remove the restriction of preceding works that required extraordinary points to be at least four rings apart from each other. We do so by mathematically showing that AST-splines with multiple extraordinary points per face are linearly independent and their polynomial basis functions form a non-negative partition of unity. This extension of the subset of AST-splines drastically increases the flexibility to build geometries using AST-splines; e.g., much coarser meshes can be constructed around small holes. The AST-spline spaces detailed in this work have C1 inter-element continuity near extraordinary points and C2 inter-element continuity elsewhere. For the convergence studies performed in this paper involving second- and fourth-order linear elliptic problems with manufactured solutions, we have not found any drawback caused by allowing multiple EPs per face in either the first refinement levels or the asymptotic behavior. To illustrate a possible isogeometric framework that is already available, we design the B-pillar and the side outer panel of a car using T-splines with the commercial software Autodesk Fusion360, import the control nets into our in-house code to build AST-splines, and import the Bézier extraction information into the commercial software LS-DYNA to solve eigenvalue problems. The results are compared with conventional finite elements and good agreement is found between AST-splines and conventional finite elements.

Large deflection and post-buckling of thin-walled structures by finite elements with node-dependent kinematics

In the framework of finite elements (FEs) applications, this paper proposes the use of the node-dependent kinematics (NDK) concept to the large deflection and post-buckling analysis of thin-walled metallic one-dimensional (1D) structures. Thin-walled structures could easily exhibit local phenomena which would require refinement of the kinematics in parts of them. This fact is particularly true whenever these thin structures undergo large deflection and post-buckling. FEs with kinematics uniform in each node could prove inappropriate or computationally expensive to solve these locally dependent deformations. The concept of NDK allows kinematics to be independent in each element node; therefore, the theory of structures changes continuously over the structural domain. NDK has been successfully applied to solve linear problems by the authors in previous works. It is herein extended to analyze in a computationally efficient manner nonlinear problems of beam-like structures. The unified 1D FE model in the framework of the Carrera Unified Formulation (CUF) is referred to. CUF allows introducing, at the node level, any theory/kinematics for the evaluation of the cross-sectional deformations of the thin-walled beam. A total Lagrangian formulation along with full Green–Lagrange strains and 2nd Piola Kirchhoff stresses are used. The resulting geometrical nonlinear equations are solved with the Newton–Raphson linearization and the arc-length type constraint. Thin-walled metallic structures are analyzed, with symmetric and asymmetric C-sections, subjected to transverse and compression loadings. Results show how FE models with NDK behave as well as their convenience with respect to the classical FE analysis with the same kinematics for the whole nodes. In particular, zones which undergo remarkable deformations demand high-order theories of structures, whereas a lower-order theory can be employed if no local phenomena occur: this is easily accomplished by NDK analysis. Remarkable advantages are shown in the analysis of thin-walled structures with transverse stiffeners.

Acoustic fatigue life prediction of structure based on power spectral density method

In the field of aerospace engineering, a large amount of thin shell structure is used in order to reduce the weight. These structures will be damaged by acoustic fatigue at high levels of noise and vibration loads. Acoustic fatigue analysis of thin walled structure is a very important part of the aircraft structure design. Simulation and analysis of three different fixation methods for random acoustic loads of thin-walled structure of aluminium alloy were introduced in this article. A method of power spectral density (PSD) was calculated for sound pressure level respectively in the band limited white noise 145 dB, 148 dB, 151 dB combined with fatigue damage theory based on linear length of the sound. The length of the 7075 Aluminium alloy material is 300 mm, and the thickness is 1.5 mm. The results show that: in the case of different ways of holding, the maximum stress suffered by the aluminium alloy thin sheet appeared at the constraint location, and this position is dangerous position for structural fatigue where will first be destroyed by random loads. Under random acoustic loads, the strain cloud of aluminium alloy thin sheet structure is the same with the first vibration mode, so the random vibration response was most effected by the first modal. Acoustic fatigue of the different sound pressure level was calculated by using the method of PSD and Miner linear damage rule.

Geometrically nonlinear Hessian eigenmode decomposition for local stability analysis of thin-walled structures

A nonlinear geometric formulation based on position and unconstrained vector is originally proposed to evaluate the local stability of thin-walled members. The Hessian is decomposed into linear and geometric equivalent installments. As the Hessian matrix exhibits a definite positive quadratic form, stability condition for large displacements requires that the Hessian matrix positivity be verified at each load small steps. This condition must be established by evaluating the smallest eigenvalue signal at the critical point imminence. The positional finite element method is formulated from a total Lagrangian reference. The mechanical system equilibrium is guaranteed by the total potential energy stationary principle. The constitutive law of Saint–Venant–Kirchhoff is obtained from the linear relationship between the second Piola–Kirchhoff stress tensor and Green–Lagrange deformation tensor. Some examples demonstrate the applicability of the methods.

A new approach to the identification of distortion modes of thin-walled structures based on plate/shell theory

In this paper, a new approach to identify cross-section deformation modes is presented and utilized in the establishment of a high-order beam model for dynamic analyses of thin-walled structures. Towards this end, a systematic procedure to extract cross-section in-plane vibration shapes for a thin-walled cross-section is developed based on elastic plate/shell theory. Then the distortion shapes are separated from vibration shapes by removing the components of classic modes involved with the minimum value problem of 2-norm. Sequentially, curve fitting method is utilized to approximate the distortion shape functions along the cross-section midline. It should be noticed that these distortion modes are arranged in hierarchy consistent with the order that they are identified and the number of distortions to be identified depends on the required model precision. Based on this, Hamilton's principle is applied to formulate the dynamic governing equations of the beam by constructing its displacement field with the linear superposition of the cross-section mode shapes including distortions. Numerical examples are also presented to validate the new approach and to demonstrate its efficiency in the reproduction of three-dimensional behaviours of thin-walled structures in dynamic analyses.

A Simplified Approach to Identify Sectional Deformation Modes of Thin-Walled Beams with Prismatic Cross-Sections

In this paper, a simplified approach to identify sectional deformation modes of prismatic cross-sections is presented and utilized in the establishment of a higher-order beam model for the dynamic analyses of thin-walled structures. The model considers the displacement field through a linear superposition of a set of basis functions whose amplitudes vary along the beam axis. These basis functions, which describe basis deformation modes, are approximated from nodal displacements on the discretized cross-section midline, with interpolation polynomials. Their amplitudes acting in the object vibration shapes are extracted through a modal analysis. A procedure similar to combining like terms is then implemented to superpose basis deformation modes, with equal or opposite amplitude, to produce primary deformation modes. The final set of the sectional deformation modes are assembled with primary deformation modes, excluding the ones constituting conventional modes. The derived sectional deformation modes, hierarchically organized and physically meaningful, are used to update the basis functions in the higher-order beam model. Numerical examples have also been presented and the comparison with ANSYS shell model showed its accuracy, efficiency, and applicability in reproducing three-dimensional behaviors of thin-walled structures.

Thermal modeling and analysis of thin-walled structures in micro milling

The numerical analytical model has been developed to predict the thermal effect with respect to thin walled structures by micro-milling. In order to investigate the temperature distribution around micro-edge of cutter, it is necessary to considering the friction power, the shearing power, the shear area between the tool micro-edge and materials. Due to the micro-cutting area is more difficult to be measured accurately, the minimum chip thickness as one of critical factors is also introduced. Finite element-based simulation was employed by the Advantedge, which was determined from the machining of Ti-6Al-4V over a range of the uncut chip thicknesses. Results from the proposed model have been successfully accounted for the effects of thermal softening for material.

Geometrical nonlinear analyses of thin-walled structures with free surface using XFEM

Geometrical nonlinear analyses of thin-walled structures with free surface using XFEM

Free vibration analysis of reinforced thin-walled plates and shells through various finite element models

This article deals with free vibration analysis of thin-walled structures reinforced by longitudinal stiffeners using refined one-dimensional (1D) models.The 1D theory, which is used in the present article, has hierarchical features and it is based on the Carrera Unified Formulation (CUF). The displacement field over the cross section is obtained by means of Taylor (TE) or Lagrange (LE) expansions. Finite element (FE) method is applied along the beam axis to obtain weak form solutions of the related governing equations. The obtained results are compared with those from classical finite element formulations based on plate and shell (2D), beam (1D), and solid (3D) elements that are available in commercial software. When solid formulation is used to build the FE solutions, stringers and skin are modeled with only 3D elements while, in the 2D-1D FE models, shell and beam elements are used for skin and stringers, respectively. Three benchmark problems are analyzed: a flat plate, a curved panel, and a thin-walled cylinder. When TE models are used, different orders of expansion, N, are considered, where N is a free parameter of the formulation. As far as Lagrange expansions are concerned, four-node (LE 4) and nine-node (LE 9) elements are used to build different meshes on the cross section. The results show that the present 1D models are able to analyze the dynamic behavior of complex structures and can detect 3D effects as well as very complex shell-like modes typical of thin-walled structures. Moreover, the 1D-CUF elements yield accurate results with a low number of degrees of freedom.

Selective mass scaling and critical time-step estimate for explicit dynamics analyses with solid-shell elements

Explicit integration is often used in highly nonlinear finite element structural dynamics simulations. However, explicit time integration is stable only if the used time-step is smaller than a critical threshold, which can be shown to depend on the smallest geometrical dimension of the finite elements in the mesh. This aspect is particularly critical when solid-shell elements are used for the analysis of thin walled structures, since the small thickness can lead to unacceptably small time-steps. A selective mass scaling technique, based on a linear transformation of the element degrees of freedom, is proposed in this paper to increase the size of the critical time-step without affecting the dynamic response. An analytical procedure is also developed for the computation of the element highest eigenfrequency and estimate of the critical time-step size. The computational effectiveness and accuracy of the proposed methodology is tested on the basis of numerical examples.

A software package for computer-aided design analysis of thin-walled structures from composite materials

An algorithm of analyzing the design parameters for a thin-walled wing from composite material based on the efficient distribution of structural material between load-carrying elements is described. We consider the problems of convergence acceleration for the iteration design analysis. Also presented are the examples of determining the design parameters for a superlight aircraft wing and the rational parameters of the filler in the form of a three-dimensional rod structure.

New Finite Element for Analysis of Thin-Walled Structures

The analysis of thin-walled structures has been discussed by many theoreticians who produced seminal works. Unfortunately, these studies are based on mathematical formulations which are not easy to understand by the majority of engineers because the background provided by the undergraduate schools does not cover the solution of complex differential equations or the use of area coordinates in the calculation of cross-section properties. Accordingly, practicing engineers are often at a loss in problems involving nonlinear differential equations or the meaning of an elusive mechanical action called bimoment in the evaluation of longitudinal stresses caused by warping torsion. On the other hand, present day formulations should take advantage of the availability of computers that can easily handle the matrix relations on which the finite element analysis is based. This work presents a new finite element that allows the evasion of the aforementioned complexities. The main novelty is the discussion of a nonnodal...

A new beam element for analyzing geometrical and physical nonlinearity

Based on Timoshenko’s beam theory and Vlasov’s thin-walled member theory, a new model of spatial thin-walled beam element is developed for analyzing geometrical and physical nonlinearity, which incorporates an interior node and independent interpolations of bending angles and warp and takes diversified factors into consideration, such as traverse shear deformation, torsional shear deformation and their coupling, coupling of flexure and torsion, and the second shear stress. The geometrical nonlinear strain is formulated in updated Lagarange (UL) and the corresponding stiffness matrix is derived. The perfectly plastic model is used to account for physical nonlinearity, and the yield rule of von Mises and incremental relationship of Prandtle–Reuss are adopted. Elastoplastic stiffness matrix is obtained by numerical integration based on the finite segment method, and a finite element program is compiled. Numerical examples manifest that the proposed model is accurate and feasible in the analysis of thin-walled structures.

A geometrical and physical nonlinear finite element model for spatial thin-walled beams with arbitrary section

Based on the theories of Bernoulli-Euler beams and Vlasov’s thin-walled members, a new geometrical and physical nonlinear beam element model is developed by applying an interior node in the element and independent interpolations on bending angles and warp, in which factors such as traverse shear deformation, torsional shear deformation and their coupling, coupling of flexure and torsion, and second shear stress are all considered. Thereafter, geometrical nonlinear strain in total Lagarange (TL) and the corresponding stiffness matrix are formulated. Ideal plastic model is applied to physical nonlinearity to comply with the yield rule of Von Mises and incremental relationship of Prandtle-Reuss. Elastoplastic stiffness matrix is derived by numerical integration on the basis of the finite segment method. Examples show that the developed model is feasible in analysis of thin-walled structures with high accuracy.

Elastoplastic analysis of thin-walled structures in reservoir area

In the structural design of the high pier, in order to analyze the strength and structure stability, the pier was often considered a thin-walled structure. Elastoplastic incremental theory was used to establish the model of elastoplastic stability of high pier. By considering the combined action of pile, soil and pier together, the destabilization bearing capacity was calculated by using 3-D finite element method (3-D FEM) for piers with different pile and section height. Meanwhile, the equivalent stress in different sections of pier was computed and the processor of destabilization was discussed. When the pier is lower, the bearing capacity under mutual effect of pile, soil and pier is less than the situation when mutual effect is not considered; when the pier is higher, their differences are not conspicuous. Along with the increase of the cross-sectional height, the direction of destabilization bearing capacity is varied and the ultimate capacity is buildup. The results of a stability analysis example are almost identical with the practice.

Selective mass scaling for thin walled structures modeled with tri-linear solid elements

A method for selective mass scaling in explicit finite element analyses of thin walled structures, modeled with solid elements, is introduced. The method aims at increasing the critical time step without significantly altering the dynamical response of the system. The proposed method is based on the exclusion of certain rigid body motions from the applied mass scaling by filtering the local velocity field.

Nonlinear Analysis of Thin-Walled Structures: Statics, Dynamics, and Stability. Mechanical Engineering Series

Nonlinear Analysis of Thin-Walled Structures: Statics, Dynamics, and Stability. Mechanical Engineering Series

The quadratic finite element/strip with generalized degrees of freedom and their application

This paper presents a quadratic finite element with generalized degrees of freedom (GDOF) and a quadratic finite strip with GDOF based on the principle that the local displacement fields of elements should be compatible with the global displacement field of the corresponding systems. Firstly, a global displacement field is developed using quadratic B-spline functions. Secondly, local displacement fields of elements and strips are constructed, employing multi-term interpolation polynomials of second degree. Making the local displacement fields of elements and strips be compatible with their corresponding global displacement fields, respectively, models of the finite element with GDOF and the finite strip with GDOF are accordingly generated. On the other hand, the quadratic B-spline function is convenient to derive the explicit form of characteristic equations for computing model because of its lower order, and accordingly simplifies the computation, compared with cubic and quintic spline functions. Several numerical examples demonstrate the accuracy, simplicity and versatility of the present element and strip in the analysis of thin-walled structures.

Buckling analysis of thin-walled structures: numerical developments and applications

This article is the second part of a review of recent research in buckling analysis of thin-walled structures. The first part [1] covered fundamental developments in new methods of analysis and their applications. The present review focusses on numerical developments based mainly on the finite element and finite strip methods, and applied research on specific types of thin-walled structures, including stiffened panels, girders, shear panels, and cold-formed structural members.