Practical aspects of frequency-domain identification of dynamic models of marine structures from hydrodynamic data

The motion response of marine structures in waves can be studied using finite-dimensional linear-time-invariant approximating models. These models, obtained using system identification with data computed by hydrodynamic codes, find application in offshore training simulators, hardware-in-the-loop simulators for positioning control testing, and also in initial designs of wave-energy conversion devices. Different proposals have appeared in the literature to address the identification problem in both time and frequency domains, and recent work has highlighted the superiority of the frequency-domain methods. This paper summarises practical frequency-domain estimation algorithms that use constraints on model structure and parameters to refine the search of approximating parametric models. Practical issues associated with the identification are discussed, including the influence of radiation model accuracy in force-to-motion models, which are usually the ultimate modelling objective. The illustration examples in the paper are obtained using a freely available MATLAB toolbox developed by the authors, which implements the estimation algorithms described.

A Matlab toolbox for parametric identification of radiation-force models of ships and offshore structures

This article describes a Matlab toolbox for parametric identification of fluid-memory models associated with the radiation forces ships and offshore structures. Radiation forces are a key component of force-to-motion models used in simulators, motion control designs, and also for initial performance evaluation of wave-energy converters. The software described provides tools for preparing non-parmatric data and for identification with automatic model-order detection. The identification problem is considered in the frequency domain.

Joint identification of infinite-frequency added mass and fluid-memory models of marine structures

This paper addresses the problem of joint identification of infinite-frequency added mass and fluid memory models of marine structures from finite frequency data. This problem is relevant for cases where the code used to compute the hydrodynamic coefficients of the marine structure does not give the infinite-frequency added mass. This case is typical of codes based on 2D-potential theory since most 3D-potential-theory codes solve the boundary value associated with the infinite frequency. The method proposed in this paper presents a simpler alternative approach to other methods previously presented in the literature. The advantage of the proposed method is that the same identification procedure can be used to identify the fluid-memory models with or without having access to the infinite-frequency added mass coefficient. Therefore, it provides an extension that puts the two identification problems into the same framework. The method also exploits the constraints related to relative degree and low-frequency asymptotic values of the hydrodynamic coefficients derived from the physics of the problem, which are used as prior information to refine the obtained models.

Inclusion of tapered tubes in enhancing the crash performance of automotive frontal structures

This paper treats the design and analysis of an energy absorbing system. Experimental tests were conducted on a prototype, and these tests were used to validate a finite element model of the system. The model was then used to analyze the response of the system under dynamic impact loading. The response was compared with that of a similar system consisting of straight circular tubes, empty and foam-filled conical tubes. Three types of such supplementary devices were included in the energy absorbing system to examine the crush behavior and energy absorption capacity when subjected to axial and oblique impact loadings. The findings were used to develop design guidelines and recommendations for the implementation of tapered tubes in energy absorbing systems. To this end, the system was conceptual in form such that it could be adopted for a variety of applications. Nevertheless, for convenience, the approach in this study is to treat the system as a demonstrator car bumper system used to absorb impact energy during minor frontal collisions.

Time- vs. frequency-domain identification of parametric radiation force models for marine structures at zero speed

The dynamics describing the motion response of a marine structure in waves can be represented within a linear framework by the Cummins Equation. This equation contains a convolution term that represents the component of the radiation forces associated with fluid memory effects. Several methods have been proposed in the literature for the identification of parametric models to approximate and replace this convolution term. This replacement can facilitate the model implementation in simulators and the analysis of motion control designs. Some of the reported identification methods consider the problem in the time domain while other methods consider the problem in the frequency domain. This paper compares the application of these identification methods. The comparison is based not only on the quality of the estimated models, but also on the ease of implementation, ease of use, and the flexibility of the identification method to incorporate prior information related to the model being identified. To illustrate the main points arising from the comparison, a particular example based on the coupled vertical motion of a modern containership vessel is presented.

Hybrid frequency–time domain models for dynamic response analysis of marine structures

Time-domain models of marine structures based on frequency domain data are usually built upon the Cummins equation. This type of model is a vector integro-differential equation which involves convolution terms. These convolution terms are not convenient for analysis and design of motion control systems. In addition, these models are not efficient with respect to simulation time, and ease of implementation in standard simulation packages. For these reasons, different methods have been proposed in the literature as approximate alternative representations of the convolutions. Because the convolution is a linear operation, different approaches can be followed to obtain an approximately equivalent linear system in the form of either transfer function or state-space models. This process involves the use of system identification, and several options are available depending on how the identification problem is posed. This raises the question whether one method is better than the others. This paper therefore has three objectives. The first objective is to revisit some of the methods for replacing the convolutions, which have been reported in different areas of analysis of marine systems: hydrodynamics, wave energy conversion, and motion control systems. The second objective is to compare the different methods in terms of complexity and performance. For this purpose, a model for the response in the vertical plane of a modern containership is considered. The third objective is to describe the implementation of the resulting model in the standard simulation environment Matlab/Simulink.

Second-order elastic finite element analysis of structures using a single element per member

Finite element frame analysis programs targeted for design office application necessitate algorithms which can deliver reliable numerical convergence in a practical timeframe with comparable degrees of accuracy, and a highly desirable attribute is the use of a single element per member to reduce computational storage, as well as data preparation and the interpretation of the results. To this end, a higher-order finite element method including geometric non-linearity is addressed in the paper for the analysis of elastic frames for which a single element is used to model each member. The geometric non-linearity in the structure is handled using an updated Lagrangian formulation, which takes the effects of the large translations and rotations that occur at the joints into consideration by accumulating their nodal coordinates. Rigid body movements are eliminated from the local member load-displacement relationship for which the total secant stiffness is formulated for evaluating the large member deformations of an element. The influences of the axial force on the member stiffness and the changes in the member chord length are taken into account using a modified bowing function which is formulated in the total secant stiffness relationship, for which the coupling of the axial strain and flexural bowing is included.

Three-dimensional hydrogen-bonded structures in the hydrated proton-transfer salts of isonipecotamide with the dicarboxylic oxalic and adipic acid analogues

The structures of the 1:1 hydrated proton-transfer compounds of isonipecotamide (piperidine-4-carboxamide) with oxalic acid, 4-carbamoylpiperidinium hydrogen oxalate dihydrate, C6H13N2O+·C2HO4-·2H2O, (I), and with adipic acid, bis­(4-car­bam­oylpiperidinium) adipate dihydrate, 2C6H13N2O+·C6H8O42-·2H2O, (II), are three-dimensional hydrogen-bonded constructs involving several different types of enlarged water-bridged cyclic associations. In the structure of (I), the oxalate monoanions give head-to-tail carb­oxy­lic acid O-HOcarboxyl hydrogen-bonding inter­actions, forming C(5) chain substructures which extend along a. The isonipecotamide cations also give parallel chain substructures through amide N-HO hydrogen bonds, the chains being linked across b and down c by alternating water bridges involving both carboxyl and amide O-atom acceptors and amide and piperidinium N-HOcarboxyl hydrogen bonds, generating cyclic R43(10) and R32(11) motifs. In the structure of (II), the asymmetric unit comprises a piperidinium cation, half an adipate dianion, which lies across a crystallographic inversion centre, and a solvent water mol­ecule. In the crystal structure, the two inversion-related cations are inter­linked through the two water mol­ecules, which act as acceptors in dual amide N-HOwater hydrogen bonds, to give a cyclic R42(8) association which is conjoined with an R44(12) motif. Further N-HOwater, water O-HOamide and piperidinium N-HOcarbox­yl hydrogen bonds give the overall three-dimensional structure. The structures reported here further demonstrate the utility of the isonipecotamide cation as a synthon for the generation of stable hydrogen-bonded structures. The presence of solvent water mol­ecules in these structures is largely responsible for the non-occurrence of the common hydrogen-bonded amide-amide dimer, promoting instead various expanded cyclic hydrogen-bonding motifs.

Coordination polymeric structures in the sodium salt of 4-chloro-3-nitrobenzoic acid and the sodium and potassium salts of 4-nitroanthranilic acid

The structures of the hydrated sodium salts of 4-chloro-3-nitrobenzoic acid {poly[aqua(μ4-4-chloro-3-nitrobenzoato)sodium(I)], [Na(C7H3ClNO4)(H2O)]n, (I)} and 2-amino-4-nitrobenzoic acid {poly[μ-aqua-aqua(μ3-2-amino-4-nitrobenzoato)sodium(I)], [Na(C7H5N2O4)(H2O)2]n, (II)}, and the hydrated potassium salt of 2-amino-4-nitrobenzoic acid {poly[μ-aqua-aqua(μ5-2-amino-4-nitrobenzoato)potassium(I)], [K(C7H5N2O4)(H2O)]n, (III)} have been determined and their complex polymeric structures described. All three structures are stabilized by intra- and intermolecular hydrogen bonding and strong π–π ring interactions. In the structure of (I), the distorted trigonal bipyrimidal NaO5 coordination polyhedron comprises a monodentate water molecule and four bridging carboxylate O-atom donors, generating a two-dimensional polymeric structure lying parallel to (001). Intra-layer hydrogen-bonding associations and strong inter-ring π–π interactions are present. Structure (II) has a distorted octahedral NaO6 stereochemistry, with four bridging O-atom donors, two from a single carboxylate group and two from a single nitro group and three from the two water molecules, one of which is bridging. Na centres are linked through centrosymmetric four-membered duplex water bridges and through 18-membered duplex head-to-tail ligand bridges. Similar centrosymmetric bridges are found in the structure of (III), and in both (II) and (III) strong inter-ring π–π interactions are found. A two-dimensional layered structure lying parallel to (010) is generated in (II), whereas in (III) the structure is three-dimensional. With (III), the irregular KO7 coordination polyhedron comprises a doubly bridging water molecule, a single bidentate bridging carboxylate O-atom donor and three bridging O-atom donors from the two nitro groups. A three-dimensional structure is generated. These coordination polymer structures are among the few examples of metal complexes of any type with either 4-chloro-3-nitrobenzoic acid or 4-nitroanthranilic acid.

Hydrogen-bonded two- and three-dimensional polymeric structures in the ammonium salts of 3,5-dinitrobenzoic acid, 4-nitrobenzoic acid and 2,4-dichlorobenzoic acid

The structures of the ammonium salts of 3,5-dinitrobenzoic acid, NH4+ C7H3N2O6- (I), 4-nitrobenzoic acid, NH4+ C7H4N2O4- . 2H2O (II) and 2,4-dichlorobenzoic acid, NH4+ C7H3Cl2O2- . 0.5H2O (III), have been determined and their hydrogen-bonded structures are described. All salts form hydrogen-bonded polymeric structures, three-dimensional in (I) and two-dimensional in (II) and (III). With (I), a primary cation-anion cyclic association is formed [graph set R3/4(10)] through N-H...O hydrogen bonds, involving a carboxyl O,O' group on one side and a single carboxyl O-atom on the other. Structure extension involves both N-H...O hydrogen bonds to both carboxyl and nitro O-atom acceptors. With structure (II), the primary inter-species interactions and structure extension into layers lying parallel to (0 0 1) are through conjoined cyclic hydrogen-bonding motifs: R3/4(10) [one cation, a carboxyl (O,O') group and two water molecules] and centrosymmetric R2/4(8) [two cations and two water molecules]. The structure of (III) also has conjoined R3/4(10) and centrosymmetric R2/4(8) motifs in the layered structure but these differ in that he first involves one cation, a carboxyl (O,O') as well as a carboxyl (O) group and one water molecule, the second, two cations and two carboxyl O-groups. The layers lie parallel to (1 0 0). The structures of the salt hydrates (II) and (III) reported in this work, giving two-dimensional layered arrays through conjoined hydrogen-bonded nets provide further illustrations of a previously indicated trend among ammonium salts of carboxylic acids, but the anhydrous three-dimensional structure of (I) is inconsistent.

Revolute joint approach to model joint mechanism in water-filled road safety barriers

Portable water-filled road barriers (PWFB) are roadside structures placed on temporary construction zones to separate work site from traffic. Recent changes in governing standards require PWFB to adhere to strict compliance in terms of lateral displacement and vehicle redirectionality. Actual PWFB test can be very costly, thus researchers resort to Finite Element Analysis (FEA) in the initial designs phase. There has been many research conducted on concrete barriers and flexible steel barriers using FEA, however not many was done pertaining to PWFB. This research probes a new technique to model joints in PWFB. Two methods to model the joining mechanism are presented and discussed in relation to its practicality and accuracy. Moreover, the study of the physical gap and mass of the barrier was investigated. Outcome from this research will benefit PWFB research and allow road barrier designers better knowledge in developing the next generation of road safety structures.

Impact and energy absorption of portable water-filled road safety barrier system fitted with foam

Portable water-filled barriers (PWFBs) are roadside appurtenances that are used to prevent errant vehicles from penetrating into temporary construction zones on roadways. A numerical model of the composite PWFB, consisting of a plastic shell, steel frame, water and foam was developed and validated against results from full scale experimental tests. This model can be extended to larger scale impact cases, specifically ones that include actual vehicle models. The cost-benefit of having a validated numerical model is significant and this allows the road barrier designer to conduct extensive tests via numerical simulations prior to standard impact tests Effects of foam cladding as additional energy absorption material in the PWFB was investigated. Different types of foam were treated and it was found that XPS foam was the most suitable foam type. Results from this study will aid PWFB designers in developing new generation of roadside structures which will provide enhanced road safety.

Effect of crack depth and specimen width on fracture toughness of a carbon steel in the ductile-brittle transition region

The effects of crack depth (a/W) and specimen width W on the fracture toughness and ductile±brittle transition have been investigated using three-point bend specimens. Finite element analysis is employed to obtain the stress-strain fields ahead of the crack tip. The results show that both normalized crack depth (a/W) and specimen width (W) affect the fracture toughness and ductile±brittle fracture transition. The measured crack tip opening displacement decreases and ductile±brittle transition occurs with increasing crack depth (a/W) from 0.1 to 0.2 and 0.3. At a fixed a/W (0.2 or 0.3), all specimens fail by cleavage prior to ductile tearing when specimen width W increases from 25 to 40 and 50 mm. The lower bound fracture toughness is not sensitive to crack depth and specimen width. Finite element analysis shows that the opening stress in the remaining ligament is elevated with increasing crack depth or specimen width due to the increase of in-plane constraint. The average local cleavage stress is dependent on both crack depth and specimen width but its lower bound value is not sensitive to constraint level. No fixed distance can be found from the cleavage initiation site to the crack tip and this distance increases gradually with decreasing inplane constraint.

Effect of constraint on ductile crack growth and ductile-brittle fracture transition of a carbon steel

Ductile-brittle fracture transition was investigated using compact tension (CT) specimens from -70oC to 40oC for a carbon steel. Large deformation finite element analysis has been carried out to simulate the stable crack growth in the compact tension (CT, a/W=0.6), three point-point bend (SE(B), a/W=0.1) and centre-cracked tension (M(T), a/W=0.5) specimens. Experimental crack tip opening displacement (CTOD) resistance curve was employed as the crack growth criterion. Ductile tearing is sensitive to constraint and tearing modulus increases with reduced constraint level. The finite element analysis shows that path-dependence of J-integral occurs from the very beginning of crack growth and ductile crack growth elevates the opening stress on the remaining ligament. Cleavage may occur after some ductile crack growth due to the increase of opening stress. For both stationary and growing cracks, the magnitude of opening stress increases with increasing in-plane constraint. The ductile-brittle transition takes place when the opening stress ahead of the crack tip reaches the local cleavage stress as the in-plane constraint of the specimen increases.

Experimental study on creep and shrinkage of high-performance ultra-lightweight cement composite of 60 MPa

Creep and shrinkage behaviour of an ultra lightweight cement composite (ULCC) up to 450 days was evaluated in comparison with those of a normal weight aggregate concrete (NWAC) and a lightweight aggregate concrete (LWAC) with similar 28-day compressive strength. The ULCC is characterized by low density < 1500 kg/m3 and high compressive strength about 60 MPa. Autogenous shrinkage increased rapidly in the ULCC at early-age and almost 95% occurred prior to the start of creep test at 28 days. Hence, majority of shrinkage of the ULCC during creep test was drying shrinkage. Total shrinkage of the ULCC during the 450-day creep test was the lowest compared to the NWAC and LWAC. However, corresponding total creep in the ULCC was the highest with high proportion attributed to basic creep (≥ ~90%) and limited drying creep. The high creep of the ULCC is likely due to its low elastic modulus. Specific creep of the ULCC was similar to that of the NWAC, but more than 80% higher than the LWAC. Creep coefficient of the ULCC was about 47% lower than that of the NWAC but about 18% higher than that of the LWAC. Among five creep models evaluated which tend to over-estimate the creep coefficient of the ULCC, EC2 model gives acceptable prediction within +25% deviations. The EC2 model may be used as a first approximate for the creep of ULCC in the designs of steel-concrete composites or sandwich structures in the absence of other relevant creep data.