Edward C. Ting

A plastic-fracture model for concrete

Abstract The paper summarizes recent efforts in formulating an elastic-plastic-fracture model for the finite-element analysis of concrete structures. Based on the geometrical considerations, a four-parameter fracture (or yielding) criterion was proposed which embraces some of the simpler existing models. Isotropic elastic and anisotropic elastic behaviors were proposed for the initial loading and the post-failure behaviors. A plastic model displaying mixed hardening was proposed to describe material behaviors between the initial yielding and the fracture failure. Incremental stress-strain relationships were derived based on the associated flow rule and Zieglers kinematic hardening rule. Three different types of failure modes were considered. A simple crushing coefficient was defined based on a dual criterion to identify the crushing type, the cracking type and the mixed type of failure. Material parameters required for each element of the plastic-fracture model were determined. An important feature of the paper is that matrix formulations for all the constitutive equations were derived and are available for finite-element implementations.

A general algorithm for moving mass problems

An algorithm is developed to solve the classical problem of the dynamic response of a finite elastic beam supporting a moving mass. An illustrative example is given. The results are shown to compare very well with experimental results.

Fundamentals of a Vector Form Intrinsic Finite Element: Part II. Plane Solid Elements

In the second article of the series, the vector form intrinsic finite element is extended to formulate plane solid elements, a three-node triangular element and a four-node isoparametric element. Also, conceptual differences of the intrinsic element and traditional element based on variational formulation are discussed.

Fundamentals of a Vector Form Intrinsic Finite Element: Part III. Convected Material Frame and Examples

In the third article of the series, a convected material frame is used to develop an incremental analysis procedure to calculate motions with large deformation and large displacement. Five numerical examples are given. The first three illustrate some numerical problems in explicit finite element that are resolved in the present approach. The other two demonstrate the stability and convergence of the method.

Dynamic response of plates to moving loads: Finite element method

Abstract An algorithm based on a finite element approach has been developed to study the transient response of plates with arbitrary boundary conditions and subjected to moving loads. Thin plate theory is assumed for the plate model and no restriction is placed on the loading conditions. The algorithm accounts for the complete dynamic interactions between the moving loads and the plate. Therefore, the method can be applied to the general moving mass problems and also to the simplified moving force and static problems. The accuracy of the algorithm is verified by comparing the numerical results obtained from the finite element method with the exact solutions and with other available numerical and experimental results. The results indicate that there are three frequency ranges that must be looked into: a subcritical region, a critical region, and a supercritical region. The dynamic deflection varies in each region. The mass inertia of the vehicle is more pronounced in the third region, where the deflection propagates in a wave-like manner.

A unified numerical approach for thermal stress waves

Abstract A unified numerical approach is introduced for the analysis of thermal stress waves. The algorithm is derived from the concept of heat displacement and a variational formulation in Lagrangian form. The objective of the paper is to demonstrate that by using the unified approach an existing computer code for isothermal finite element stress analysis can easily be modified to extend its capability to solve thermal stress problems. Numerical examples are given for the Danilovskayas problems in dynamic thermoelasticity using a plane analysis computer code. It shows that the unified approach is particularly suitable for the study of thermally-induced waves including thermomechanical coupling effects.

DYNAMIC RESPONSE OF PLATE TO MOVING LOADS: STRUCTURAL IMPEDANCE METHOD

Abstract An algorithm based on a structural impedance approach has been developed to study the transient response of plates with arbitrary boundary conditions and subjected to moving loads. Thin plate theory is assumed for the plate model and the algorithm places no restrictions on the loading conditions. The algorithm accounts for the complete dynamic interactions between the moving loads and the plate. Therefore, the method can be applied to the general moving mass problems and to the simplified moving force and static problems. The accuracy of the algorithm is verified by comparing the results obtained from the structural impedance method (SIM), in the case of moving force solutions, with the available exact solutions and with other numerical results. The dynamic deflections obtained from the moving mass solutions are compared with available experimental results. Parametric analyses over a wide spectrum of velocities and mass ratios indicate that the inertial effect on dynamic deflections is pronounced when the vehicle is traveling at high speed.

A finite element formulation for thermal stress analysis. Part I: Variational formulation

Abstract This paper deals with the development of a variational principle which can be used for solving problems related to the thermoelastic behavior of solids and is the first of the two part series. The formulation is based on the introduction of a new quantity defined as heat displacement and related to temperature in the same manner as the mechanical displacement is related to strain. The introduction of such a quantity allows the heat conduction equations to be written in a form equivalent to the equation of motion, and the equations of coupled thermoelasticity to be written in a unified form. The obtained equations are used to write a variational formulation which, together with the concept of generalized coordinates, yield a set of differential equations with the time as the independent variable. These equations can be used to formulate a finite element solution for thermoelastic problems. This is done in the second part.

A complete formulation of inertial effects in the guideway-vehicle interaction problem

This paper contains a new algorithm for the solution of the dynamic displacement of an elastic guideway (single and multiple-span) as it interacts with a vehicle with an air cushion suspension. Illustrative examples are given comparing the solutions for dynamic displacements of the system when the vehicle is modeled as a moving force, as a moving mass or as a true air cushion system, all inertial effects being considered.

Motion analysis of 3D membrane structures by a vector form intrinsic finite element

Abstract In this paper, a constant strain triangular membrane element, which is a new member of the VFIFE (vector form intrinsic finite element) family, is proposed to analyze space motion of arbitrary 3D membrane structures. A description of kinematics to dissect rigid body and deformation displacements, and a set of deformation coordinates for each time increment to describe deformation and internal nodal forces are provided. Similar to other members of the VFIFE family, a convected material frame and explicit time integration for the solution procedures are also adopted. Five numerical examples are presented to demonstrate the performance and applicability of the proposed element on the motion analysis of 3D membrane structures. It was found that the proposed element could go through the patch tests and gives stable, convergent and accurate results.