A nonlinear finite element analysis of an ice-strengthened ship shell structure

Finite element method is used to study the nonlinear behaviour of an ice-strengthened ship shell structure. The main object is the plastification and collapse of a frame. The plastic limit load for this frame is determined using the calculated load-deflection curve. The results of the finite element analysis are compared with well-known formulas of plastic design and also with experimental results. The finite element program used in the analysis is ADINA.     

Three dimensional singular element

The finite element method has become a powerful tool for computation of stress intensity factors in fracture mechanics. The simulation of singular behavior in the stress field is accomplished using “quarter points,” following the methods of Barsoum[1] and Henshell-Shaw[2]. The analysis has also been extended to cubic elements [3] and transition elements [4]. However, these concepts cannot be easily extended to three dimensional cases without additional conditions. Progress has been hampered firstly due to a variety of possible shapes the element may possess near the singular edge of the crack, and secondly due to the complexity of algebraic expressions that have to be manipulated.

In the present investigation we extensively used MACSYMA[5], a large symbolic manipulation program at MIT, thereby alleviating some of these difficulties. A simple condition between mid-side nodes has been derived which simulates the proper singular behavior along the crack.

In the investigation we first study a simple collapsed brick element. This is then generalized to a curved crack front. A few results are derived which can be used to compute the stress intensity factors. The concept of the transitional element has also been outlined. The stability of singular element has been discussed. Some of these ideas have been applied to a specific problem with unusual crack geometry. The analysis was carried out using ADINA on VAX machine. ADINA was implemented on VAX by W. E. Lorensen.     

On the analysis of creep stability and rupture

The analysis of problems involving creep material failure and creep buckling is considered. Creep buckling analyses are presented for some columns. A finite element creep rupture analysis of a rotating disc is performed and the results are compared with other solutions. Calculations are also reported for titanium notched tensile specimens and the numerical results are compared with experimental creep investigations, in which micrographs have been taken to study the rupture mechanisms.

All numerical solutions have been carried out using ADINA in which a creep-damage material law and the updated-Lagrangian-Jaumann formulation for the thermo-elastic-plastic and creep material model were implemented.     

Numerical simulation of shrinkage and creep in patch-repaired axially loaded reinforced concrete short columns

This paper presents numerical results obtained from finite element simulations of the time-dependent behaviour of moderately loaded patch-repaired reinforced concrete short columns. Patch repair is a structural concrete repair method in which damaged concrete is replaced with one of a wide range of materials. Relative to the concrete substrate, the patch repair materials used in this study had different properties, such as the elastic modulus, shrinkage and creep. A priori, it would appear that simple theory such as the engineer's theory of bending cannot be used to quantify the behaviour of the patch-repaired member. Experimental evidence needed to clarify such issues remains scarce. The finite element simulations performed in this study indicate that shrinkage and creep cause the progressive shedding of the load carried by the patch repair to the concrete substrate. Finite element results compare favourably with the predictions of the engineer's bending theory. Relative to test results some qualitative agreement is observed though there is significant quantitative deviation.     

Use of ADINA in soil mechanics with case studies for excavations

The reliability and the variety of mathematical procedures related to incremental solution strategies for the nonlinear analysis as well as the general availability of the ADINA code make this latter particularly well adapted for soil and rock mechanics. These materials, especially the soils, have indeed a marked nonlinear strain-stress behaviour. These qualities are somewhat counterbalanced by the relative lack of constitutive laws applicable to soil however.

The first part of this paper deals with the general and practical use of ADINA in soil and rock mechanics.

The second presents, as case study, an ADINA use for the evaluation of the deformations around excavations in clayey soils. With the classical methods of geomechanics, it is not possible to determine these deformations correctly. Only the use of the FEM with nonlinear constitutive laws for ground performance and possibly considering also the pore pressure allows for the good evaluation of these deformations. Two very large excavations have been analysed in this way and it was possible to compare the results of the computation with many in situ observations.     

Bifurcation, pre- and post-buckling analysis of frame structures

A procedure is developed for investigating the stability of complex structures that consist of an assembly of stiffened rectangular panels and three-dimensional beam elements. Such panels often form one of the basic structural components of an aircraft or ship structure. In the present study, the stiffeners are treated as beam elements, and the panels between them as thin rectangular plate elements, which may be subject to membrane and/or bending and twisting actions.

The main objective of the study is the determination of the critical buckling loads and the generation of the complete force-deformation behavior of such structures within a specified load range, based on the use of a computer program developed for this purpose. The present formulation can trace through the postbuckling or post limit behavior whether it is of an ascending or descending type. A limit load extrapolation technique is automatically initiated within the computer program, when the stability analysis of an imperfect or laterally loaded structure is being carried out.

The general approach to the solution of the problem is based on the finite element method and incremental numerical solution techniques. Initially, nonlinear strain-displacement relations together with the assumed displacement functions are utilized to generate the geometric stiffness matrices for the beam and plate elements. Based on energy methods and variational principles, the basic expressions governing the behavior of the structure are then obtained. In the incremental solution process, the stiffness properties of the structure are continuously updated in order to properly account for large changes in the geometry of the structure.

The computer program developed during the course of this study is referred at as GWU-SAP, or the George Washington University Stability Analysis Program.     

Modeling of travelling-loads and time-dependent masses with ADINA

The conception and construction of new rail vehicles like the magnetic-field monorail with a maximum speed of 400 km/hr require more detailed investigations about the dynamic behaviour of the train and the railway line. The problem to be analyzed is the dynamic behaviour of a beam subjected to travelling loads and masses with constant and non-uniform speed.

The paper contains the following topics: —Modification of ADINA to handle travelling-load-problems with user-subroutines; —Modification of ADINA to handle problems with time dependent mass-distributions; —Comparison of ADINA results with an analytical solution; —Influence of mass and speed; —Influence of the different terms of the equations of motion.     

Elasto-plastic contact stress analysis of joints subjected to cyclic loading

Rigorous elastic-plastic finite element analysis of joints subjected to cyclic loading is carried out. An incremental-iterative algorithm is developed in a modular form combining elasto-plastic material behaviour and contact stress analysis. For the case of the interference fit, the analysis sequentially carries out insertion of the pin and application of the load on the joint, covering possible initiation of separation (and/or yielding) and progressively the receding/advancing contact at the pin-plate interface. Deformations of both the plate and the pin are considered in the analysis. Numerical examples are presented for the case of an interference fit pin in a large plate under remote cyclic tension, and for an interference fit pin lug joint subjected to cyclic loading. A detailed study is carried out for the latter problem considering the effect of change in contact/separation at the pin-plate interface on local stresses, strains and redistribution of these stresses with the spread of a plastic zone. The results of the study are a useful input for the estimation of the fatigue life of joints.     

Fracture mechanics J-integral calculations in thermo-elasto-plasticity

A finite element post-processor has been developed to calculate an incremental plasticity-based J-integral for fracture mechanics evaluations. The post-processor accounts for elastic-plastic deformations and thermal strains. The ADINA finite element computer program, with minor modifications by Babcock and Wilcox, was used with the Ramberg-Osgood stress-strain law and provides through its “porthole” files the required results of stresses, strains, displacements, and elastic and plastic strain energies.

The numerical results of the post-processor indicate that the thermal J-integral, which consists of a line integral for the isothermal case and an additional area integral for the thermal effect, can be considered path-independent even in the presence of plastic and thermal strains.     

An application of ADINA to the solution of fluid-structure interaction problems

ADINA is employed to solve the lowest natural frequencies and corresponding mode shapes of a plate and turbine blade when submerged in water. Finite element solution parameters such as integration order of elements, mass matrix, flow around edges, and other modelling considerations are reported. The performance of the present solution algorithms and comparisons with experimentally obtained results are also presented.

The experience reported can be useful for the analysis of problems involving an elastic structure immersed in an acoustic fluid (exterior problems) and problems involving an acoustic fluid within elastic structures (interior problems).     

Post-buckling behavior of thin steel plates using computational models

Thin plates loaded in plane will buckle at very small loads, and due to unavoidable out-of-plane imperfections, the theoretical buckling load cannot be observed experimentally. If the plate is adequately supported along its boundaries, it will be able to carry a much higher load than the theoretical buckling load.Computational models can be used to study the post buckling behaviour of thin plate structures up to failure. Failure of such structures is usually due to large out-of-plane deflections, yielding, and rupture. Therefore, the computational model should include the effects of geometric and material nonlinearities. In this paper, the nonlinear finite element analysis program NONSAP and ANSR-III were modified and used in the analysis. Since these programs did not include the suitable elements and material properties to conduct the subject study, new elements and new material properties were added to the programs. In particular, a thin shell element was added and the solution routines were modified to improve its accuracy and efficiency.The modified programs were used on a Super Computer to calculate the post buckling strength of stiffened and unstiffened plates subjected to uniaxial compression, and plates subjected to in plane bending or shear. Crippling of plates subjected to in-plane or eccentric edge compressive loads was also examined. The results from the computational models were compared with test results and reasonable agreements were obtained. A computational model was developed for a multi-story thin steel plate shear wall subjected to cyclic loading and the results from the model were compared with experimental results, and again agreement was achieved.     

Nonlinear vibration of cord-reinforced composite shells

This paper discusses ADINA finite element incremental formulations for nonlinear static and dynamic analysis of materials with nonlinear constitutive equations. The formulations are applied to axisymmetric problems of cord reinforced composites using the ADINA computer program. Numerical results on natural frequencies and mode shapes of cord reinforced inflatable toroidal shells are presented for axisymmetric modes of excitation.     

The concept of fracture mechanics applied to the progressive failure of structural members

Because of the imperfections inherent in all real materials and because of possible overloads, a structure which is thought to be capable of safely carrying its design load may suddenly fail. A flaw may grow from its initial size at design stress levels to a size intolerable to the structure. If the flaw is undetected before it reaches the critical size, a catastrophic failure may result.

An approximate method of analysis is suggested in this work. Refinements involving special treatment of stress singularities may be added if desired. The basic idea is that a structure or structural member is considered to be an assemblage of finite parts (as in finite element approaches). When, for one cause or another, one of these parts fails, it is considered to lose its effectiveness in the structure completely. A structure with no redundancy in its design would collapse immediately if the loads were held constant. In a structure which has been designed with some redundancy (as with panels, beams, etc), the effect of successive failure or portions on the integrity of the overall structure can be analyzed.

In this report, calculations of the loss of load carrying capacity and of stiffness of a particular structure are presented as an example of the approach. The discrete parts into which the structure is divided for the analysis are allowed to fail one-at-a-time. The compliance of the structure increases as the individual failures progress. The purpose of the research was to develop a structural toughness term involving the rate of increase of compliance with volume of material failed. It was anticipated that the point of instability of the structure could be related to the toughness. However, the limited computations do not permit generalization of the results of this report to other structures or loadings. To accomplish a general definition of structural toughness requires additional research.     

Analysis of offshore structures with ADINA

The paper describes a developed version of the ADINA program, suitable for analysis of slender structures exposed to wave, current and wind action. The forces are calculated up to instantaneous water level using the non-linear Morison equation. The program includes several different current and wave theories, with arbitrary flow-directions.

The program is general and flexible. Comparisons are made with a number of special written programs. Future development is outlined.     

Nonlinear static analysis of end-fittings for GFRP-prestressing rods

This contribution affords an insight into a current research project about end fittings for pretensioned GFRP rods. The purpose of the present paper is to show that the ADINA-FE-program can be modified by the user at reasonable expense for the analysis of structures and materials whose properties cannot be reproduced adequately by the original version of the program. For the analysis of anchorage elements for pretensioned GFRP rods a modified elastic-plastic material model for 2/D-elements and a bond-link-element have been added to the program maintaining completely its modular structure. The modifications are explained and the stiffness matrix for the bond-link-element is derived. With this modified program different types of end fittings are analyzed with special regard to bond between the GFRP rod and the surrounding synthetic resin material. A comparison of the results of the FE-analysis shows good correspondence to test data.     

Interactive modeling system for bridges

The modeling system described in this paper was developed in conjunction with the computer program called STACRB that was developed in the CURT research project at the University of Pennsylvania. In essence, the STACRB program utilized the method of finite elements to analyze the static behavior of horizontally curved and straight aligned bridge structures.

The modeling system communicates with the user through a problem oriented language. The commands in this language allow the user to define the parameters that characterize the structure, modify an already existing structure, or inquire about the results of analysis already completed for a structure. The commands are entered in free format and are executed interpretively, thus allowing the user to communicate with the system in a conversational mode. The user may also enter the command on punched cards and execute the routine as a non-conversational batch job. The modeling system can be used to either control the analysis or operate independently from it. In the former case, the modeling system synthesizes the structure, then calls on the STACRB program to analyze it. When the analysis is completed, the control is returned to the modeling system to interpret the results of the analysis according to the commands supplied by the user. In the latter case, the results from the modeling procedure alone are punched onto cards which may subsequently be inputed to the analysis routine.

The modeling system also includes facilities for graphical displays of components of the designed structure such as structure geometry and element discretization or results of analysis such as nodal deflections, reactions and element stresses. The displays may be produced either on the line printer for conversational purposes or on a CALCOMP plotter.

The overall increased efficiency introduced by the modeling system in the analysis/design cycle of a bridge structure is quite significant.     

钢筋混凝土空心高桥墩非线性极限承载力分析

为了得到一高50m的钢筋混凝土空心桥墩极限承载力,基于ANSYS软件,采用8节点等参单元SOLID65,考虑几何非线性、材料非线性以及结构的初始缺陷等因素,对桥墩进行了极限承载力全过程分析,得到了结构的极限荷载、荷载-变形曲线及裂缝的分布。分析结果表明,高桥墩的非线性因素明显,在计算中应充分考虑。á     

A finite element model for the nonlinear analysis of reinforced and prestressed masonry walls

A materially nonlinear layered finite element model is proposed for the analysis of reinforced and/or prestressed masonry wall panels under monotonie loadings in the plane and/or out of the plane, capable of evaluating both the serviceability load and the ultimate load. An orthotropic incrementally linear relationship and equivalent uniaxial concept are used to represent the behaviour of masonry under biaxial stresses while a uniaxial bilinear elasto-plastic model with hardening is employed for rebar and the so-called ‘power-formula’ is adopted to describe the stress-strain relationship of prestressing steel.

After cracking, the smeared coaxial rotating crack model is adopted and tension stiffening, reduction in compressive strength and stiffness after cracking, and strain softening in compression are accounted for. The modified Newton-Raphson iteration method is employed to ensure convergency of non linear solution.

The proposed finite element model has been tested by a comparison with experimental data available in literature, both for reinforced and prestressed wall panels. The analysis of results shows good agreement between the values obtained by the proposed model and those obtained experimentally.     

Analysis of the hexcan of a fast breeder reactor with a through crack

Application of the finite element method to the problem involving a superficial crack in a hexcan of a fast breeder reactor is discussed.

The aim is to calculate the stress intensity factor of the hexcan with a through crack in the static and dynamic case, loaded with internal pressure. In the dynamic fracture the crack is considered both fixed and propagating. The structure is discretized with shell elements of 6 and 8 nodes available in the ADINA Code.     

Optimal dimension-exchange token distribution on complete binary trees

Load balancing on a multi-processor system involves redistributing tasks among processors so that each has roughly the same amount of work to perform. The token-distribution problem is a static variant of the load balancing problem for the case in which the workloads in the system cannot be divided arbitrarily; i.e., where each token represents an atomic element of work. A simple, scalable method for distributing tokens over a distributed-memory parallel architecture is the so-called dimension-exchange approach, which is based on the repetitive application of an extremely simple and scalable local exchange protocol. The behaviour of this approach depends heavily on the topology of the interconnection network.

This paper presents an analysis of dimension-exchange algorithms for token distribution on the complete binary tree. We show that for the complete binary tree of height H, and any initial distribution for which the discrepancy in workloads is greater than H tokens, the dimension-exchange method will eventually reduce the discrepancy to at most H. Furthermore, we show that the rate of this convergence to H is worst-case optimal. These results are the first to establish that dimension-exchange techniques lead to optimal algorithms for finitely-divisible load balancing on a tree-connected network.