Lazarus etzis Tenek

Postbuckling performance of the TRIC natural mode triangular element for isotropic and laminated composite shells

We present the computational performance and the achieved accuracy of the TRIC flat triangular shell element for nonlinear postbuckling analysis of arbitrary isotropic and composite shells. The element is based on the natural mode finite element method, which allows a convenient description of the current position of the structure. These natural modes are assigned to a convective coordinate system which follows the element during deformation within the framework of an Eulerian motion. With respect to this coordinate system the natural modes are additive. Numerical examples verify the accuracy, computational efficiency and the potential of the TRIC element in predicting the postbuckling behaviour of shells. Natural energy measures inform us about the energy allocation during nonlinear deformation and the interplay of the separate energy components.

BEC : A 2-node fast converging shear-deformable isotropic and composite beam element based on 6 rigid-body and 6 straining modes

Abstract We present a 2-node isotropic and composite shear-deformable beam element in space—the element BEC. The formulation is based on the natural mode finite element method whereby the 12 Cartesian degrees of freedom (6 per node) are transformed to 6 natural rigid-body and 6 natural straining modes which describe the elements kinematics. Only a sparse 6 × 6 natural stiffness matrix needs to be formed while congruent transformations, performed on the computer, transform the natural stiffness to the local and global Cartesian coordinates with significant impact on computational efficiency and economy. Initial load due to temperature is also given. In addition, simplified and partly simplified geometrical stiffnesses are established which permit the study of nonlinear phenomena such as buckling and large displacements. Throughout the formulation no locking or any other parasitic phenomena were encountered. Although a general formulation is adopted, the model is applied here to a solid beam section. The theory is implemented in our structural analysis code SANI (Structural Analysis and Information). Following validation with reference solutions, applications are made to isotropic and composite beams, frames and three-dimensional composite beam structures. The theory presented indicates a new direction in finite element analysis and structural mechanics in general.

A multilayer composite triangular element for steady-state conduction/convection/radiation heat transfer in complex shells

Abstract Our latest study presents the theoretical formulation and computer implementation of a three-node six degrees of freedom multilayer flat triangular element intended for the study of the temperature fields in complex multilayer composite shells. Inherent in the formulation, in this first introductory and self-consistent systematic study, are the three modes of heat transfer, namely conduction, convection and radiation, the latter introducing in our theoretical model strong nonlinear effects. In the present discourse, all nonlinear terms are strictly due to radiation; the material properties are assumed independent of temperature but this in no way restricts the generality of the basic theory. The formulation is based on a first-order thermal lamination theory which assumes a linear through-the-thickness temperature variation. The following features are uniquely implemented in the computer model: 1. (1) Exact integration of all matrices including the highly nonlinear radiation matrix 2. (2) Exact integration of all derivative (Jacobian) matrices for efficient nonlinear analysis 3. (3) Geometrical generality achieved by an arbitrarily oriented inexpensive flat shell element 4. (4) Compatibility with structural elements 5. (5) Computational efficiency and simplicity A predictor-corrector scheme in the form of the Newton-Raphson method is adopted for the solution of the stead-state nonlinear problem. Numerical examples, ranging from simple panels to complex anisotropic shells substantiate the theoretical formulation and show the potential of the present laminated triangular element in the computer simulation of temperature effects in complex geometries.

On Chaotic Oscillations of a Laminated Composite Cylinder Subject to Periodic Application of Temperature

Abstract In the present study, we explore and confirm the chaotic behaviour of a laminated composite cylinder subjected to a rapid periodic heat load. The laminated cylinder comprises eight layers of carbon–epoxy material and is supported by end diaphragms. The analysis is performed using the natural-mode finite element method. An irregular signal and an attractor is obtained. Takens method is used to reconstruct the attractor. For the time series, the largest Lyapunov exponents and the correlation dimension are computed. Various tests are performed in order to distinguish chaos from noise. Thus the proof for the existence of chaos is formally established

Dynamic collapse of critically stressed isotropic and composite cylinders

The present study is concerned with the dynamic collapse of cantilever isotropic and composite cylinders. The cylinders are initially subjected to critical compressive loads at the free edge. A small increase in these critical loads is then dynamically applied in the form of a sinusoidal excitation using the first natural frequency of the system. The results show that there exists a small time period whereby small dynamic excitations take place. Following this short time period, sudden large dynamic displacements occur which cause the collapse of the structure. This phenomenon takes place very near to the buckling load. An implicit unconditionally stable time scheme is applied to trace the dynamic behaviour of the structure. The effect of the excitation frequency on the response is also assessed.

Composite plate and shell element

Shells are used in many modern structures because of their efficiency and economy, their ability to retain their form, and because of other features stemming from their reaction to certain loads. Their shape allows certain membrane stress systems to develop parallel to their tangential plane and become prime carriers of the deformation. Indeed the analysis of many thin shells is solely based on the membrane theory of shells which neglects their bending rigidity. On the other hand, bending becomes important in the presence of rapidly changing loads (e.g. concentrated loads, line loads etc.), near edge constraints, near discontinuities in the shell geometry and in nonlinear deformations. The development of a general membrane and bending theory as well as related numerical implementations are subjects of intense research efforts which aim at providing deeper understanding of the mechanics of load carrying. The literature on this subject has been growing at a rapid pace over the last decades.

Nonlinear analysis of anisotropic shells

In the presence of large deflections, bifurcations, and load and displacement limit points, the analysis of arbitrary anisotropic shells requires the adoption of incremental and iterative procedures. In many cases the load-displacement curves may exhibit unstable branches followed by stable equilibrium paths. The true response is dynamic in nature. However, a full dynamic analysis is impractical and expensive. Thus in most cases a fully static solution or a combined static and dynamic solution is performed. The latter must be able to predict and pass critical limit points and predict collapse loads. The state of the art in current solution algorithms is given by Papadrakakis [80] and Crisfield [81].

Natural modes for finite elements

In the natural mode method we express the deformation u(x, y, z) at any point in a finite element as a linear combination of the nodal cartesian displacements r e n n

A brief history of FEM

mathop ulimits_{(3x1)} (x,y,z) = mathop Climits_{(3xn)} (x,y,z)mathop {{r_e}}limits_{(nx1)}