Kai-Uwe Schröder

POSTBUCKLING OF COMPRESSIVELY LOADED IMPERFECT COMPOSITE PLATES: CLOSED-FORM APPROXIMATE SOLUTIONS

In this paper, closed-form approximate solutions for the geometrically nonlinear behaviour of rectangular laminated plates with flexural orthotropy under longitudinal compression are presented. Based on the governing Marguerre-type differential equations postulated for imperfect plates, two plate configurations are discussed in detail, representing important application cases in practical engineering work. The first configuration is a laminated plate that is simply supported at all four edges (the so-called SSSS plate), while for the second configuration clamped unloaded longitudinal edges are considered (denoted as the SSCC plate). For both plate configurations, rather simple closed-form approximations in the form of trigonometric shape functions are employed for the description of the out-of-plane postbuckling plate deflections. Based on the chosen shape functions, the compatibility condition with respect to the in-plane strains is fulfilled exactly, while the out-of-plane equilibrium condition for a deflected plate element is not, but is solved using a Galerkin-type formulation instead. Eventually, very simple closed-form solutions for all postbuckling state variables (deflections, in-plane edge displacements, and effective widths) are derived that can be used very conveniently in engineering practice. The high accuracy of the presented analysis methods is established by comparison with the results of other authors.

Numerical static and dynamic analyses of improved equivalent models for corrugated sandwich structures

ABSTRACT In order to further improve the accuracy of the equivalent models of the trapezoidal corrugated core, a 3D homogenization method based on a representative unit cell (RUC) has been developed to obtain a complete set of equivalent properties, which also investigates the influences of the elastic modulus in the thickness direction and different RUCs on the equivalent models that were rarely considered in previous studies. Then free vibration analysis is conducted to further validate the present homogenized models by comparing with the corresponding actual corrugated sandwich structures. Finally, parametric studies are carried out to investigate the influence of the corrugation height and trough angle on the equivalent properties and natural frequencies. Results show that sufficient accuracy of the present homogenized models can be easily obtained by choosing suitable profile geometries and high-quality meshes. Furthermore, the effects of corrugation height and trough angle both play a vital role in the equivalent properties and dynamic behavior of corrugated sandwich structures. Several conclusions are drawn, which may be useful for designing such kinds of sandwich cored structures in the applications.

Sizing strategy for stringer and orthogrid stiffened shells under axial compression

ABSTRACT Thin-walled stiffened shell structures are used in primary structures of space launcher vehicles. These structures are prone to buckling and thus fail due to a loss of structural stability. Generally, it has to be distinguished between two major modes of instability for stiffened shell structures: a global buckling of the entire structure and a local buckling of skin fields, longitudinal and circumferential stiffeners. Due to the large number of variables when designing stiffened shell structures, their preliminary design is a demanding task. To allow an efficient preliminary design, sizing strategies can be developed. For this purpose, analytical methods, which allow to assess the local and global instability of stiffened shell structures, are employed. In this article, sizing strategies based on efficient analytical methods are introduced and applied to identify suitable designs of stringer stiffened and orthogrid stiffened shell structures. To study the imperfection sensitivity of stringer and orthogrid stiffened shell structures, numerical computations are performed using the single perturbation load approach and mode shape imperfections. Finally, weight strength curves are derived for stringer and orthogrid stiffened shell structures.

Efficient and Robust Shell Design of Space Launcher Vehicle Structures

Space launcher vehicles consist of thin-walled shell structures which are prone to buckling and often are sensitive towards geometrical imperfections. Even small deviations of the shell from the perfect structure which still are within manufacturing tolerances, result in a tremendous decrease of load carrying capacity. To account for geometrical imperfections in an early design phase, empirical knock-down factors or theoretical approaches can be applied. In this paper, it is shown that the design of imperfection sensitive shell structures with unknown geometric imperfections may not lead to robust designs for the existing empirical and theoretical design methods. In contrast to unstiffened structures and grid stiffened shell structures, which are imperfection sensitive, it is known that the influence of imperfections during an early design phase of ring frame stringer stiffened shells is negligible when the post-buckling regime of the skin fields is exploited. Frame stringer stiffened structures can be designed in a robust manner, using efficient analysis methods, as imperfection tolerant structures; but, existing methods to size ring frame stiffeners of space launcher vehicles shell structures do not mandatorily lead to reliable and light designs. In this contribution a novel method for the efficient design of ring frame stringer stiffened shells is presented. The suggested approach is based on the explicit description of the mechanical behavior of the ring frame stiffeners at the onset of panel instability. Together with existing sizing methods for stringer stiffened shell panels the suggested approach allows for robust designs of ring frame stringer stiffened shells. The application of the novel method to size ring frames reveals that the minimum stiffness requirements are satisfied likewise with regard to existing methods; whereby, the lightweight potential is not mandatorily exploited using existing methods.

Damage Assessment in Adhesively Bonded Structures by Using SmartSHM

Adhesively bonded joints are attracting increasing interest in a wide range of industries, especially in transportation sectors (marine, automotive, aerospace), due to manifold advantages compared to conventional joining techniques such as riveting and welding. Therefore, both the design of adhesive joints as well as the assessment of possible failures in bonded structures during service life is of great concern. This paper presents a novel approach for an efficient SHM technique. The approach is presented and discussed on the basis of two different adhesively bonded applications, namely the single lap joint configuration and a one sided repair patch, which can be considered as a special case of single lap joints. The SmartSHM technique is based on the use of structural damage indicators. For single lap joints, the approach is related to the shift of the back face strain curve and its zero crossing due to crack initiation. Considering the repair patch, bending effects in longitudinal and transverse direction are investigated in 2D and 3D numerical analyses. Especially transverse bending effects show high potential for a SHM system based on two circumferential optical fiber sensors. doi: 10.12783/SHM2015/27

Modelling and analysis of piezolaminated functionally graded polymer composite structures reinforced with graphene nanoplatelets under strong electroelastic fields

This paper focuses on the electromechanical modelling and analysis of piezolaminated functionally graded polymer composites reinforced with graphene nanoplatelets considering strong electric field nonlinearities. Non-uniform distribution of reinforcement of graphene nanoplatelets is assumed along the thickness direction in multilayer polymer nanocomposites, whereas uniform dispersion GPLs in each layer is assumed. Modified Halpin-Tsai micromechanics is used to determine the effective Young’s modulus of GPLs considering the effects of geometry and dimension changes. Electro-elastic nonlinear constitutive relations are used to model the piezoelectric layers under strong applied electric fields. Through variational formulation, a finite element is derived to model and analyse the layered GPL/polymer composite structures. Various simulations are performed to study the effects of several parameters like distribution pattern and size of GPLs by applying actuation voltages to piezoelectric layers.

Elastic body impact on sandwich panels at low and intermediate velocity

This paper investigates the dynamics and failure modes during the impact of an elastic body on a sandwich structure by means of non-linear finite element analysis. The main motivation for the study is the accidental impact of a human body on the interior sandwich structure of a civil aircraft during a crash situation. The considered model is a rectangular simply supported sandwich plate that is loaded dynamically by the centric impact of a spherical body with varying stiffness. In principle, the impactor stiffness has a significant influence on the contact forces between impactor and sandwich structure, and consequently, leads to a change in the impactor deceleration and re-acceleration as well as a change in the contact duration. However, the deformation of a “softer” impactor causes a smoother load introduction. Thus, two questions arise: can the altered stress distribution change the initial failure mode of the sandwich structure? And how are the deformations and deceleration and accelerations of the elastic impactor influenced? As, particularly, the latter question is crucial to human safety in crash situations, the inertia loads exerted on the elastic impactor are evaluated in detail by standard injury criteria.

On the Application of the Limit Drawing Ratio to Complex Geometries

The initial design of a deep drawing part is a largely experience based task which is followed by a finite element simulation. If changes are to be made in the design, again these are based on the experience of the engineer. For the modern engineer it becomes increasingly harder to gain enough experience to design a deep drawing part from scratch since the different materials used today behave much differently. One step towards a synthesizing design method is the determination of what geometries can be drawn. The deep drawing product will be assembled from local geometries and connecting elements. In this work the limit drawing ratio will be defined on the example of a corner-geometry, where it can be shown, that such a local geometry can be handled independently from the global shape. This way the classic concept of the limit drawing ratio can be applied to different tool-geometries. The concept of the local limit drawing ratio is then validated on a parametric finite element simulation.

Smart Structural Health Monitoring Validated on a Simple Plate under Compressive Loading

The subject of this research is the implementation of a Smart Structural Health Monitoring based on structural analysis and its validation on the plate under compressive loading. In the given context the structural analysis provides the most probable failure mode of the structure, e.g. buckling and the stress and deformation state at failure. With this information an algorithm analyses the onset of failure and infers from these analysis results the measurement values, which have to be monitored to identify the damage. By means of this, an appropriate sensor and the optimal sensor placement are chosen. As this pre-process supports the damage identification it is referred to as Smart Structural Health Monitoring (SSHM). The potential of SSHM to optimize the damage identification process is compared to a simple Structural Health Monitoring is demonstrated with a plate under compressive loading. In an experimental setup the plate is loaded up to buckling. After buckling the loading still increases up to failure of the plate caused by the deformations in the post buckling region. With a minimum of sensors and in combination with the analysis results of the SSHM the damage of the plate is detected, located and quantified.