Committee II.1: Quasi-Static Response
Authors: Underwood James , Alley Erick , Andric Jerolim , Boote Dario , Gao Zhen , Van Hoeve Ad , Jelovica Jasmin , Kawamura Yasumi , Kim Yooil , Liu Jianhu , Malenica Sime , Remes Heikki , Samanta Asokendu , Woloszyk Krzysztof , Yang Deqing 
Published: April 2023

Committee Mandate
Concern for the quasi-static response of ship and offshore structures, as required for safety and serviceability assessments. Attention shall be given to uncertainty quantification of quasi-static load and response analysis approaches, and their limitations, including exact and approximate methods for derivation of different acceptance criteria.

Introduction
In the design of ship and offshore structures, Naval Architects and Structural Engineers require access to a wide range of analysis methods to successfully progress from concept brief through to a production ready design, that will safely operate for the duration of its service life.
Significant development in computational analysis techniques have occurred over the preceding decades, coupled with increased availability of high-performance computing; however, computationally intensive methods regularly do not fit the requirements of a design team, particularly in the early design phases. Whilst some quasi-static methods may have arisen at times of lesser computational capabilities, quasi-static analysis methods remain relevant, providing an appropriate balance between accuracy and speed, often having an ability to provide a quick result based on minimal input data, facilitating rapid design iteration.
In ship and offshore structures, the loading, whether local or global, is predominantly caused by a dynamic motion that is cyclic or oscillating, for example the wave loading of a ship hull girder in a seaway, the sloshing loading due to the motions of fluid in a tank, the loading on a deck or equipment foundation, etc. True dynamic analysis of such scenarios is complex and time consuming to undertake, and often can’t be successfully completed until the structural design details are in a progressed state. Therefore, quasi-static methods implementing a simplified approach that resembles the scenario, whether through a defined loading or to induce a seemingly equivalent structural response, have been developed. Not all loading scenarios can be suitably represented by quasi-static methods, particularly where loading is complex or structural response of the individual parts of the system may interact. However, where a quasi-static method can be implemented to develop a structure with sufficient reserve to facilitate safe operation, the benefits to the design process can be significant.
In structural response analysis, a method may be considered to be quasi-static where the effects of structural dynamics (structural inertia and damping) may be neglected. In this regards the time component, or time derivatives, may be neglected. To adopt a quasi-static method, the true time dependant loading must be sufficiently slow in relation to the structural response not to coincide with resonant response frequencies. Due to this ‘slow’ progression, during analysis the system may be considered to be in static equilibrium at all time instances.
These points are true for many quasi-static analyses, where loading may be through incremental application of force or displacement to a structure, and static equilibrium of the system is achieved before the next increment is applied. Therefore, time associated with the loading is only implied and not explicitly included in the assessment. In other words, the structural responses at any time instant will be only determined by the loads at that time instant, and the structural responses have no memory effect.
Whilst the applied loading may be incremental, it need not be entirely linear, and in the same regard the structural response also need not be linear. For example, the loading and response could be coupled, such that as the structure deforms the load is iterated to reflect the new state of the system. However, in the application of quasi-static methods, the relative accuracy and therefore suitability of the method should always be considered.
Quasi-static analysis covers a broad spectrum of methods from hand calculations to finite element analysis (FEA) and may even combine methods such as computational fluid dynamics (CFD). The methods may be used directly for structural assessment, or as part of broader method, such as the input to a reliability analysis or optimisation routine, or to derive a peak stress or stress sequence for fatigue assessment. For this reason, there may be perceived overlap between this and other ISSC committees. However, this committee has specifically focussed the presented report around methods that are quasi-static in nature, including where the topics, such as fatigue, ultimate and accidental limit states, that are covered in depth from a different perspective by other ISSC Technical Committees.