Erez Gal

Geometrically nonlinear analysis of shell structures using a flat triangular shell finite element

SummaryThis paper presents a state of the art review on geometrically nonlinear analysis of shell structures that is limited to the co-rotational approach and to flat triangular shell finite elements. These shell elements are built up from flat triangular membranes and plates. We propose an element comprised of the constant strain triangle (CST) membrane element and the discrete Kirchhoff (DKT) plate element and describe its formulation while stressing two main issues: the derivation of the geometric stiffness matrix and the isolation of the rigid body motion from the total deformations. We further use it to solve a broad class of problems from the literature to validate its use.

Geometrically nonlinear three-noded flat triangular shell elements

Abstract This paper provides a novel approach to the geometrically nonlinear analysis of shells by deriving the geometric stiffness matrix by load perturbing the linear equilibrium equations in their finite element formulation. Rotations are considered as finite, and rigid body motion is elegantly removed to result in pure elastic deformations that enable stress retrieval via linear constitutive relations. Simple three-noded triangular elements that have proven successful in linear analysis will thus transform to powerful nonlinear elements.

Geometric Stiffness of Space Frames Using Symbolic Algebra

This paper is concerned with the derivation of the geometric stiffness matrix for space frames. Symbolic algebra is used to calculate the gradient of the member force vector that defines, in global coordinates, the geometric stiffness matrix. Members of solid cross-sections with no warping are considered. The independent nodal variables are the common position coordinates of the member ends. An additional independent variable, which cannot be related to the position coordinates, is the angle of twist at one end of each member. Since the angle of twist is defined locally, its effect on the stiffness matrix is found separately and then transformed to the global coordinates. The advantages of the present approach are its explicitness in derivation and clear physical insight. Finally, the geometric stiffness matrix is implanted into an existing 3D nonlinear frame analysis program. For the analytical, numerical and experimental benchmark examples studied, the present results appear to be in good agreement with the results available in the literature.

THREE-DIMENSIONAL NON-PRISMATIC BEAM-COLUMNS

This paper is concerned with three-dimensional straight beam-columns with no warping whose cross sections vary along the axis in a uniform manner with respect to the principal directions. The basic four coupled differential equations governing the behavior of 3D beam-columns are first rederived using the method of perturbations. These equations are reformulated to include varying cross sections. Finally, a 6 × 6 stiffness matrix (which is sufficient to describe 3D behavior) is computed by solving the equations 6 times for a sequence of appropriate discontinuities. The finite difference method is employed for that purpose. Timoshenkos closed form solution for the buckling load of a tapered column is chosen for comparison with that obtained by the proposed formulation. Effects of twist are also presented.

High-Rate Time-Dependent Displacement Gage for HE Field Tests

A dynamic gage, capable of continuously measuring high-rate displacements of structures, has been developed and tested by the research team of the Protective Technologies Research & Development Center (PTR&DC) of the Faculty of Engineering Sciences of the Ben-Gurion University of the Negev. The gage, which was originally developed in order to monitor the time-dependent displacements of concrete slabs subjected to explosion-generated blast wave impacts, can be used to monitor the displacement of any structure that is exposed to high-rate dynamic loads. The displacement gage is based on a torsion tube, twisted by a long flexure element that is connected to the measured point or structure. The twist of the torsion tube is monitored by strain gages. The displacement gage was tested in the impact pendulum laboratory of the PTR&DC, and will be used in high explosive (HE) field tests.

BUCKLING AND STRESS SOFTENING OF BEAM-COLUMNS UNDER COMPLEX THREE-DIMENSIONAL LOADING

This paper is concerned with buckling and stress softening of beam-columns under axial compression, biaxial bending and torsion. Members with no warping whose cross sections vary along the axis in a uniform manner with respect to the principal directions are also considered. The basic four coupled differential equations governing the behavior of three-dimensional beam columns are reformulated to include varying cross sections. A 12 × 12 stiffness matrix is assembled by solving the equations 6 times (which is sufficient to describe 3D behavior) for a sequence of appropriate discontinuities using the finite difference method. Two sets of curves are then computed. One set displays interaction diagrams that highlight the stress softening of beam stiffnesses. The other set of curves displays the buckling compressive load of a rectangular cantilevered beam under a variety of tri-directional moments (two bending moments and one twisting moment).

Practical Thermal Multi–Scale Analysis for Composite Materials–Mechanical-Orientated Approach

ABSTRACT This paper describes a thermal multi-scale formulation for composite materials based on a mechanical homogenization approach. The presented formulation evaluates the effective macroscopic thermal conductivity of the composite materials and also the microscopic heat flux field by scaling down to the micro-scale level. The effective thermal conductivity of the composite materials was calculated by applying the homogenization theory over the unit cell. The uniqueness of the presented multi-scale analysis related to the elastic problems solved at the microscopic scale (unit cell). This method has the advantage of applying periodic boundary conditions and uniform macroscopic temperature gradient over the unit cell. The proposed thermal multi-scale analysis was verified and its efficiency was demonstrated on large scale problem.

Blast Waves Caused by Internal Explosion in Ammunition and Explosive Facility: Vulnerability and Protection Alternatives

Internal explosion in an ammunition and explosive (A&E) facility might cause the most dangerous consequences. The blast can spread to all parts of the facility harming personnel in different levels. High pressure can cause lethality due to lung damage. It might also cause building collapse mainly of the structure’s elements right aside the explosion that might turn into debris and rubbels. The secondary fragments of nearby equipment (connected or unconnected) might fly with high velocity. Shock wave moving through the structure and the ground might cause people to be overturned or to fall down with possible injuries or fatalities.

Transient Thermal Multiscale Analysis for Rocket Motor Case: Mechanical Homogenization Approach

This paper describes a mechanical homogenization approach to the application of a multiscale formulation for a transient heat transfer problem. The presented formulation evaluates the effective macroscopic thermal properties of composite materials and, by scaling down to the microscale level, provides the microscopic heat flux field by solving elastic problems at the microscopic scale (unit cell). This novel method has the advantage of applying periodic boundary conditions and a uniform macroscopic temperature gradient over the unit cell, which is not easy and often not practical to achieve with heat transfer computation software. The proposed multiscale analysis is verified by various examples of composite materials, and its efficiency is demonstrated on a large-scale problem involving a solid rocket motor.