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This is an open access article distributed under the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

As a proof of concept, the GADT is applied to a widely used benchmark problem. The dimensional truss optimization benchmark problem has well documented global and local minima. The GADT is shown to outperform several published solutions. Subsequently, the GADT is deployed onto three-dimensional structural design optimization for offshore wind turbine supporting structures.

The design problem involves complex least-weight topology as well as member size optimizations. The GADT is applied to two popular design alternatives: tripod and quadropod jackets.

The two versions of the optimization problem are nonlinearly constrained where the objective function is the material weight of the supporting truss. The considered design variables are the truss members end node coordinates, as well as the cross-sectional areas of the truss members, whereas the constraints are the maximum stresses in members and the maximum displacements of the nodes.

These constraints are managed via dynamically modified, nonstationary penalty functions. The structures are subject to gravity, wind, wave, and earthquake loading conditions.

The results show that the GADT method is superior in finding best discovered optimal solutions. Introduction and Background Offshore structures offer presumably the greatest level of sophistication and difficulty in the analysis, design, and construction stages.

This is due to multitude of complexities introduced by the offshore locations. The entailed unique conditions such as underwater currents, surface waves and wind, and seabed soil can often become problematic quickly.

Such conditions introduce additional factors to the design challenge, such as extreme temperatures and rough weather conditions, marine growth, fatigue, corrosion, marine vessel impact, and interaction with aeroelastic and hydrodynamic loads.

These conditions need to be thoughtfully taken into consideration due to the long and short term effects that can compromise the structure. The intricacy of the design and analysis process multiplies when earthquake loads are factored in.

However, it is recommended to account for all loads simultaneously except for seismic loads, based on the potential occurrence combinations [ 1 , 2 ]. Therefore, seismic effects are not typically considered to occur at the same time as other loads [ 3 ].

The considered combinations of different loads and their influence on the design of offshore structures are further elaborated on in a later section. The size, type, and configuration of the members supporting offshore structure, for instance, may produce a significant influence on marine growth size, which poses a consequent impact on hydrodynamic drag forces. The resulting effects of nonlinearities associated with fluid-structure interaction may be too significant for a thoughtless dismissal in the design phase [ 4 ].

Furthermore, the interaction between the soil, foundation, and the structure is crucial phenomenon to be studied for the development of enhanced structural system designs supporting offshore wind towers [ 5 — 10 ]. A common simplified approach to the complex process of offshore structural design is the use of uncoupled load effects [ 11 — 13 ]. The justification of the above simplified method in fatigue analysis is attributable to the following: a material and geometric nonlinearities are not significant structural fatigue responses, b wind and wind-induced currents and waves can be assumed as stationary and independent processes, and c soil stress levels are moderate to presume linear behavior under wind and sea wave loading [ 14 ].

Employing such approach allows for the advantageous implementation of simple soil-structure interaction behavior. Devising optimal designs that satisfy multiple performance criteria, such as minimizing cost and maximizing efficiency, is arguably one of the most influential factors in modern structural design.

Member-level local optimization techniques are routinely used to identify design quantities for acceptable structural performance. Within this framework, several optimization techniques have been utilized in the past [ 15 ].

In the presence of multiple optima and nonsmooth constraints in the design variable space, it is difficult to obtain a set of optimum values using member-level optimization formulations. This shortcoming inspired researchers to explore using the relatively new and innovative evolutionary-based optimization techniques.

Many structural optimization problems involve problem-specific constraints applicable to the solutions limiting the feasible search space. In these types of problems, it is challenging to adapt traditional optimization techniques to handle constraints. One of the most popular constraint handling methods is by incorporating penalty functions due to the relative simplicity and ease of implementation. Topology optimization was used by many researchers to generate alternative structural design concepts for benchmark wind turbine blades.

In these studies, the focus is alternative structural layout for wind turbine blades with the aim of improving its design, minimizing weight, and, ultimately, wind energy cost reduction e. Potentially significant cost savings that result from optimized structural designs encourage the incorporation of efficient optimization techniques. However, determining the optimal structural shape and weight of the supporting system is not a trivial task.

The complexity is increased due to the mathematical description of loads aeroelastic [wind], hydrodynamic, and seismic , the many variables describing the geometry, the nonsmooth objective function, and the constraints that have to be satisfied.

This study presents the implementation of the GADT to achieve superior optimization. The capabilities of the presented optimization tool are demonstrated on a well-established optimization benchmark problem known for being challenging with known global and multiple local minima. Finally, the GADT tool is used to solve two typical least-weight design problems for offshore wind turbine supporting structures through topology and member size optimization.

The algorithm is coded using the MATLAB [ 36 ] commercial software package and its GA libraries, while the structural analysis and design for the different topology and loading configurations is performed using the SAP [ 37 ] commercial software package.

Primary Loads on Offshore Structures 2. Hydrodynamic Loads Sea Waves and Currents Hydrodynamics [the kinematics of the water particles] is a very sophisticated branch of applied science that has been studied extensively.

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As a Recommended Practice RP document, it contains technical descriptions and instruction, rather than truly prescriptive requirements. API welcomes highly specialized inspectors, welding engineers, metallurgists and other professionals across the entire petrochemical industry to obtain the API Welding Inspection and Metallurgy certification as a validation of their profound knowledge of welding processes and metallurgy.

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Api rp 2a 2014 pdf free download

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The determination of acid volume is complicated and is generally based on field experience or using rules of thumb.The results show that the GADT method is superior in finding best discovered optimal solutions. Dalda Ka Dastarkhwan Category: I did not have good luck with this recipe.

The shear and normal stiffnesses of the interface element were set to ten times the equivalent stiffness of the surrounding soil as recommended in the FLAC3D manual [ 39 ].

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What happens after inspection? Parsons, M. Figure 5: Effect of bedrock depth on the lateral load-displacement curve at the pile head. Numerous researchers have proposed different p-y curves with considerations for soil types, loading type static or cyclic , and water conditions saturated or unsaturated soil.

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