Shape optimization of structures under earthquake loadings

The optimum design of structures under static loads is well-known in the design world; however, structural optimization under dynamic loading faces many challenges in real applications. Issues such as the time-dependent behavior of constraints, changing the design space in the time domain, and the cost of sensitivities could be mentioned. Therefore, optimum design under dynamic loadings is a challenging task. In order to perform efficient structural shape optimization under earthquake loadings, the finite element-based approximation method for the transformation of earthquake loading into the equivalent static loads (ESLs) is proposed. The loads calculated using this method are more accurate and reliable than those obtained using the building regulations. The shape optimization of the structures is then carried out using the obtained ESLs. The proposed methodologies are transformed into user-friendly computer code, and their capabilities are demonstrated using numerical examples.     

Reliability analysis of brittle structures under random loadings

A method for the reliability analysis of brittle structures subjected to random loads is proposed. The method is based on the weakest-link hypothesis and Weibull statistics for brittle materials. Initial flaws with a given expected size are assumed to be distributed at random with a certain density per unit volume. Basic concepts in random vibration theory and fracture mechanics are utilized in evaluating stress statistics, crack propagation and strength degradation. A structure fails when the stress intensity at any flaw reaches a critical value for rapid crack propagation. The failure of the structure is modeled as the first exceedance in random vibration theory. The effects of multi-vibration modes on the failure probability of the structure are included in the formulation. The evaluation of stress distribution and the computation of failure probability can be accomplished in a finite element analysis. Numerical examples on the evaluation of lifetime reliabilities of structures are given to demonstrate the feasibility of the proposed method.     

Computations of refractory lining structures under thermal loadings

Refractory linings are used to protect the exterior metallic part of some vessels containing very hot fluids. They are submitted to high thermomechanical loading that can lead to cracking. A local approach is first presented in order to analyse the refractory lining as a 3D domain. A smeared crack model is used to compute the damage in the refractory. Comparison with experiments on a refractory wall containing metal parts is performed in order to validate the 3D numerical computations. Some type of refractorised vessels (e.g. some steel ladles) can directly be analysed from this 3D modelling. Since some other refractorised vessel contains a very large number of metallic parts (such as tubes or anchors), it cannot be possible to compute such a global structure with this 3D analysis. Consequently, an approach has been developed based on a two-layer shell equivalent to the lining including the metallic casing with tubes and the refractory. The thermal and mechanical parameters of the model are identified with an inverse method, using results of 3D calculations performed with the local model defined previously. An experimental validation is made by a bending test, performed on a large refractory lining specimen. In the case of a cyclone of coal-fired power plant, the equivalent shell permits to compute the damage of the refractory in the global structure.     

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.     

Structural optimization with fatigue and ultimate limit constraints of jacket structures for large offshore wind turbines

The purpose of the research presented in this paper is to develop and implement an efficient method for analytical gradient-based sizing optimization of a support structure for offshore wind turbines. In the jacket structure optimization of frame member diameter and thickness, both fatigue limit state, ultimate limit state, and frequency constraints are included. The established framework is demonstrated on the OC4 reference jacket with the NREL 5 MW reference wind turbine installed at a deep water site. The jacket is modeled using 3D Timoshenko beam elements. The aero-servo-elastic loads are determined using the multibody software HAWC2, and the wave loads are determined using the Morison equation. Analytical sensitivities are found using both the direct differentiation method and the adjoint method. An effective formulation of the fatigue gradients makes the amount of adjoint problems that needs to be solved independent of the amount of load cycles included in the analysis. Thus, a large amount of time-history loads can be applied in the fatigue analysis, resulting in a good representation of the accumulated fatigue damage. A reduction of 40 % mass is achieved in 23 iterations using the CPLEX optimizer by IBM ILOG, where both fatigue and ultimate limit state constraints are active at the optimum.     

Modeling historical fecal coliform loadings to large European rivers and resulting in-stream concentrations

Information on fecal coliform (FC) concentrations in European rivers is scarce. The objective of this study was to identify hotspots of water pollution in Europe and provide information on the different FC sources and their contributions to the loads that lead to concentrations in rivers. Model simulations were carried-out with the large-scale water quality model WorldQual to assess the calculated loads regarding to its associated sources and to further estimate the related in-stream concentration. For the year 1995, model results indicated that FC loadings were higher in central Europe with 500 to above 2000 10¹⁰ cfu km⁻² a⁻¹ than in northern and eastern Europe where loadings ranged between 0 and 200 10¹⁰ cfu km⁻² a⁻¹. Major sources of FC loadings are domestic sewage, followed by scattered settlements (private treatment), urban surface runoff and manure application. Concentrations showed similar regional patterns as loadings, with high concentrations in central Europe and low concentrations in northern and eastern Europe.     

Stochastic response of offshore towers to random sea waves and strong motion earthquakes

Presented is a stochastic method of analysis of offshore towers subjected separately to random sea waves and to strong motion earthquakes. The Pierson-Moskowitz wave height spectrum is used along with linear wave theory to define a stationary random sea state as caused by wind generated surface waves. A zero mean ergodic Gaussian process of finite duration is used to characterize horizontal ground acceleration caused by strong motion earthquakes. For each type of loading, full fluid structure interaction effects are included in stochastic analysis. Numerical results for 4 representative deep water towers having heights of 475, 675, 875 and 1,075 feet are presented. Particular emphasis is placed on the maximum or extreme values of total transverse shear and total overturning moment versus elevation above the base of each tower. The results of the earthquake analysis are compared with corresponding design code values and the role of ductility is briefly discussed.     

A new modal correction method for linear structures subjected to deterministic and random loadings

In the general framework of linear structural dynamics, modal corrections methods allow improving the accuracy of the response evaluated with a reduced number of modes. Although very often neglected by researchers and practitioners, this correction is particularly important when strains and stresses are computed. Aimed at overcoming the main limitations of existing techniques, a novel dynamic modal acceleration method (DyMAM) is presented and numerically validated. The proposed correction involves a set of additional dummy oscillators, one for each dynamic loading, and can be applied, with a modest computational effort, to discrete and continuous systems under deterministic and random inputs.     

On the application of an element-by-element lanczos solver to large offshore structural engineering problems

Iterative methods for solving large sets of linear equations have been used as an alternative to direct methods of solution since the early beginning of numerical analysis. The conjugate gradient method (CCM), one of the most widely used, seeks a solution that minimizes the potential energy of the finite element assemblage. Recently, the use of Lanczos algorithm for the solution of large sets of linear equations has been re-examined. Lanczos biorthogonalization procedure is an oblique projection method that provides a solution approximation whose residual is orthogonal to a Krylov subspace. It has been shown that Lanczos and CGM share several properties but the former has the advantage of not being necessary to compute the approximated solution at each iteration. Jacobi preconditioning can also be employed in order to accelerate convergence. The Lanczos procedure was implemented using an element-by-element (EBE) scheme. The applications spread over typical offshore engineering problems encompassing regular and irregular meshes. These problems are normally ill-conditioned when compared with continuum problems. For all the analyses addressed the element-by-element Lanczos procedures presented outstanding computational efficiency.     

Hydrodynamic structures of droplets engineered in rectangular micro-channels

This paper reports on numerical simulations of the hydrodynamics inside droplets in rectangular micro-channels. Two- and three-dimensional simulations are performed thanks to a finite-volume/front-capturing method. Droplet interface deformation and velocity fields inside both droplets and continuous phase can then be followed. This study leads to important results about droplet deformation and inner streamlines for mass and heat transfer studies. More particularly, the capillary number seems to have a great influence on the liquid/liquid flow hydrodynamics and this impact on film thickness and slip velocity is quantified through correlations.     

A large deformation elastic-plastic dynamic analysis of square plate and spherical shell subjected to shock loadings

Based on Bathe's methodology and Yuan's formulation, a large deformation elastic-plastic transient dynamic finite element method is proposed for shock loading dynamic analysis on simple local structure, such as square plate and spherical shell. The verification of the adopted method shows good agreement with related literature. The proposed method is then extended to study strong shock loading problems on local structure. The displacement/acceleration time histories with plastic zone spread phenomenas are shown in several interesting figures.     

Fully stressed design of passive controllers in framed structures for seismic loadings

This paper addresses the optimal design problem of added damping in framed structures. Interstory performance indices for linear and nonlinear structures are chosen and restricted to allowable values under the excitation of an ensemble of realistic ground motion records. Optimality criteria are formulated based on fully stressed characteristics of the optimal solution, and a simple analysis/redesign procedure is proposed for attaining optimal designs. Results of four examples presented compare well to those obtained using formal gradient-based optimization.     

Integrated simulation framework for the process planning of ships and offshore structures

Recently, requests for accurate process planning using simulation have been increasing in many engineering fields, including the shipbuilding industry. To date, designers of shipyards have developed in-house simulation systems or used commercial systems such as the QUEST by Dassault system when requests for the simulation of process planning have occurred. However, these methods have some limitations. First, it requires a lot of time to develop a new in-house simulation system. In addition, it is hard to reuse previously developed systems when developing a new one and it is also hard for these to satisfy the various needs of shipyards effectively.     

How to predict very large and complex crystal structures

Evolutionary crystal structure prediction proved to be a powerful approach in discovering new materials. Certain limitations are encountered for systems with a large number of degrees of freedom (“large systems”) and complex energy landscapes (“complex systems”). We explore the nature of these limitations and address them with a number of newly developed tools.For large systems a major problem is the lack of diversity: any randomly produced population consists predominantly of high-energy disordered structures, offering virtually no routes toward the ordered ground state. We offer two solutions: first, modified variation operators that favor atoms with higher local order (a function we introduce here), and, second, construction of the first generation non-randomly, using pseudo-subcells with, in general, fractional atomic occupancies. This enhances order and diversity and improves energies of the structures. We introduce an additional variation operator, coordinate mutation, which applies preferentially to low-order (“badly placed”) atoms. Biasing other variation operators by local order is also found to produce improved results. One promising version of coordinate mutation, explored here, displaces atoms along the eigenvector of the lowest-frequency vibrational mode. For complex energy landscapes, the key problem is the possible existence of several energy funnels - in this situation it is possible to get trapped in one funnel (not necessarily containing the ground state). To address this problem, we develop an algorithm incorporating the ideas of abstract “distance” between structures. These new ingredients improve the performance of the evolutionary algorithm USPEX, in terms of efficiency and reliability, for large and complex systems.     

An analysis of the effects of the leg-spacing on spectral response of offshore structures

The authors have applied a computer-based model to perform spectral analysis of jacket platforms. The analysis is carried out in a consistent manner using the finite element method. The proper estimation of the phasing effects of the ocean waves on structural responses is dependent, inter alia, on the accurate calculation of nodal forces. Using the finite element approach the vector of nodal forces can be most accurately computed taking into account the varying distributed loads along the structural members. The model, developed by the first author, calculates cross-receptances of response for all degrees of freedom that enable the phase effects due to the spatial extent of the structure to be properly accounted for. This model includes the phase effects of wave loadings on the platform and it can thus give a more accurate estimation of response spectra which are generally required for design calculations; this is far more accurate than calculating wave loadings on an equivalent cantilever as is often done.     

Computing the transmission zeros of large space structures

The transmission zeros of a large space structure are frequently computed by means of the general-purpose algorithm of A. Emami-Naeini and P. Van Dooren (1982). It is shown that careful exploitation of the special form of the equations of motion of structural dynamics leads to an algorithm that is at least 60 times as fast as this when applied to an undamped structure, and 15 times as fast for a lightly damped one     

Integrodifferential approach to solution of eddy currents in linear structures with motion

A nonstandard integrodifferential approach to computation of eddy currents in linear structures with motion is presented. Described is a general continuous 3D model of the problem, together with the possibilities of forming corresponding numerical schemes. The methodology is illustrated by two examples.     

Soil-structure interaction and effect of axial force on the dynamics of offshore structures

The offshore structures are flexible systems subjected to various types of loadings. The heavy gravitational loads on the top decks, wind and water wave pressures acting on the platforms are transferred to the soil through the piles or mat foundations. Under the vibration, the variation in the pore pressures induces additional effects on the embedded part of the piles. The effect of the soil-structure interaction on the dynamics of the structure is taken into account as the deformations of the soil caused by the motion of the structure which in turn modify the response of the structure. The effect of the axial forces, within the individual members, on the vibration of the structure is included in the formulation. The dynamic stiffness matrix of the members are developed by considering the actual mass distribution and the effect of the axial force of the members. For the members embedded into soil, the soil reactions and the skin frictions are also considered as continuously varying over the members. Therefore, the equations of motion are satisfied along any infinitesimal element of the members. The new formulation is introduced in the general purpose computer code STDYNL, then the sensitivity of the overall dynamic response of the deep water platforms to the variation of the soil characteristics and to the effect of the axial forces of the members are investigated.     

Lyapunov analysis of the approximate motion equations of flexible structures

In this paper, the effectiveness of the approximate motion equations of a flexible structure, obtained by the RitzKantorovich method, is analysed by using Lyapunov functions. The analysis, which is restricted to the case of a single flexible beam for the sake of simplicity, is carried out under the assumption that a partial dissipation is present, affecting only the first degrees of freedom of the system. By means of suitable Lyapunov functions, an overbounding estimate of the quadratic approximation error is determined as a decreasing function of the approximation order. The analysis is completed by considering the two ‘extreme’ cases: the theoretical absence of dissipation and the presence of structural dissipation, affecting all the infinite degrees of freedom.     

Task-oriented programming of large redundant robot motion

Large robots are a new domain of advanced robotics. Examples of their application fields are tasks like operations on large free-form surfaces, especially aircraft cleaning and removing paint from hulls. They are equipped with a programmable robot control comparable to a control system used for industrial robots. However, conventional teach-in methods are not able to manage the complexity of programming large redundant robot operation on free-form geometries. The Fraunhofer IPA has developed an innovative off-line programming system that allows the creation of robot motion programs which satisfy time and energy optimization criteria. This system helps to avoid collisions within the workspace and to fulfill conditions that arise from the robot kinematics and dynamics. This advanced programming system has been successfully used to generate motion programs for the world's largest mobile robot, the aircraft cleaning manipulator SKYWASH. In this context offline programs for eleven different types of aircraft have been developed.