Microsoft Word - 2789-18238-2-ED.doc Journal of Naval Architecture and Marine Engineering December, 2009 DOI: 10.3329/jname.v6i2.2789 http://www.banglajol.info 1813-8235 (Print), 2070-8998 (Online) © 2009 ANAME Publication. All rights reserved. Received on: 12 July 2009 COUPLED DYNAMIC RESPONSE OF A THREE-COLUMN MINI TLP Anitha Joseph, Lalu Mangal and Precy Sara George Department of Civil Engineering, Thangal Kunju Musaliar College of Engineering, Kollam-691005, Kerala, India. e-mail: anithareebu@yahoo.co.uk Abstract: For the development of deepwater marginal fields, many new platform concepts and designs are on the anvil. The mini TLP is a proven concept in this regard wherein an optimized conventional TLP system economically and efficiently serves in developing small marginal deepwater reserves. Various new geometric configurations and designs of mini TLPs are reported in the literature. This paper presents a new geometric configuration which could be a better alternative to an existing configuration. A 3-column mini TLP is designed and its platform-mooring coupled dynamic behaviour is investigated and compared with an existing 4-column mini TLP. The numerical investigation is carried out for the 1:56 scaled model using a finite element computer program suitable for compliant offshore platforms. A combination wave force model with diffraction-radiation loading on large members and Morison loading on slender members is adopted for computing the non-linear dynamic response of the structure. The effects of parameters such as pretension in tethers and wave approach angle have been studied. The results obtained are compared with published results of the 4-column mini TLP. It is found that the dynamic responses of the 3-column mini TLP are close to the 4-column mini TLP with relatively higher surge and tether tension. Accounting for this in the design stage, the newly designed structure could be a promising candidate which can be used as an alternative to the 4-column mini TLP. Reducing the number of columns from four to three has added advantages in terms of cost and time during fabrication, installation and maintenance of the platform. Keywords: Deepwater structures; Coupled dynamics; Finite element method; Mini TLP; Nonlinear dynamic analysis. 1. Introduction Numerous small oil fields have been discovered in very deep seabeds. New concepts of platform construction, exploration, drilling and production are necessary for economic development of these minimal oil fields situated in deep, remote locations in hostile environment. Mini tension leg platform (mini TLP) is a proven concept towards this objective. It is evident from the literature that the study of structural behaviour and dynamic response of these platform concepts are presently being actively pursued for design optimisation. Several mini TLP designs have been discussed in the literature. These are: a downsized four column mini TLP for 1000 m water depth (Hudson et al. 1996, Hudson and Vasseur 1996); a family of concrete mini TLPs for generic applications (Logan 1996); a three column TLP for 800 m water depth, easily extendable to 1500 m under shorter development schedule with significant reduction in cost (Muren 1996); a mini TLP with vertical cylindrical hull connected to three radially tapered rectangular pontoons called SeaStar (Kibbee 1996 and Kibbee et al. 1999). The importance of coupled response analysis of offshore compliant structural systems has also been discussed in the literature. Analysis of deepwater compliant structures must address significant hull-tether coupling because the uncoupled method ignores the interaction effects between the platform hull and its tethers. The coupled nonlinear dynamic analysis of the` Seastar mini TLP in the time domain using finite element method has been reported (Sreekumar et al. 2001). The results were compared with the similar calculations based on Morison equation for wave loading as well as with experimental results using a 1:50 scale model. Kim and Sclavounos (2001) described the fully coupled response simulations of theme offshore structures in water depths of up to 10,000 feet. Bhattacharya et al. (2003) presented a detailed finite element methodology for A. Joseph, L.Mangal and P.S. George / Journal of Naval Architecture and Marine Engineering 6(2009)52-61 Coupled dynamic response of a three-column mini TLP 53 the analysis of coupled dynamics of mini TLPs and the nature of hull-tether coupling and its physical modeling principles have been brought out. Joseph et al. (2004) reported detailed experimental and numerical investigations on the coupled dynamic behaviour of a 4-column mini TLP with special attention to hull-tether coupling. Numerical investigation using several wave force models and validation with experiments identified the best suited wave force model, which is a combination of potential theory based wave loading on the hull- column entity and Morison-type wave loading on the slender cantilevering arms and tethers. Liagre and Niedzwecki (2006) presented the non-linear coupled dynamic response of a deepwater mini TLP considering non-linear stiffness, quadratic damping, surge-pitch and sway-roll coupling. In addition, behaviour of hydrodynamic added-mass and damping coefficient was simulated using an industry standard diffraction- radiation software package. The results obtained were used for modelling the local offshore environment, numerical simulation and model test verification of the platform response characteristics. Chen et al. (2006) compared numerical results with measurements for a mini TLP. They considered only Morison wave loading. Joseph et al. (2007) presented the design details of a 3-column mini TLP based on an existing 4-column mini TLP and carried out its numerical analysis with Morison equation alone for the wave force model Thus the importance of coupled analysis and combined wave force modelling is underscored in the literature. Several innovative designs and interesting geometrical configurations also are reported aiming towards savings and advantages in terms of material, time and cost, applicable to marginal deepwater sites. Numerous marginal oil fields have been discovered in very deepwater all around the world. For the economic development of these deepwater minimal fields, optimized new platform concepts is necessary. Based on the critical assessment of the literature and the motivation outlined above, the scope of the paper is a new mini TLP design which could have favourable dynamic response along with advantages in terms of cost, material and time. 2. Design Details of the Model The new geometrical configuration is arrived at as a part of a screening of alternative mini TLP concepts. The geometric parameters are designed with reference to the 4-column mini TLP model. The design is done by keeping the draft, the total weight, the weight displacement and the vertical centre of buoyancy same as that of the 4-column model. The model geometry and construction details of the 1:56 scaled model (Froude modeling) of the 3-column mini TLP are given in Fig. 1. Table 1 shows detailed data of both models. The principal parts of the newly designed mini TLP model are the large pontoon, three slender columns, the upper and lower decks and three cantilevering trusses to which the tendons are attached. The pontoon consists of a 400 mm diameter PVC cylinder of height 232 mm with closed bottom and top ends and provides most of the buoyancy. Three 75 mm diameter columns extend vertically upwards from the top surface of the pontoon to support the lower and upper decks. The still water level is at the level of the columns (Fig. 1) such that the draft in tethered condition is 598 mm (which is same as that of 4-column TLP model). Therefore the water plane area consists of the three columns (Awp= 3×4418 = 13253 mm 2). The three tendon-supporting cantilevered trusses, each of length 246 mm consisting of two 40 mm diameter horizontal PVC tubes and two 32 mm diameter inclined PVC tubes, extend radially from the pontoon’s circumference, at an angle of 120º from each other. PVC flats of size 80 mm  50 mm  20 mm (with a 10 mm diameter hole drilled centrally for receiving the tendon assembly) connect the ends of each pair of horizontal truss members. For model tether: Young's modulus is 0.457  1011 N/m2, cross- sectional area is 4.04 mm2, and mass density is 0.0317 kg/m. The weight of model (W) without ballast (additional weight) is 17.882 kg (= Wmin). At design draft of 598 mm, the weight displacement (∆) of the model is 37.84 kg. Two tether pretension levels were used in experiments, Tt/∆ = 0.26 (Tt = W = 9.84 kg; W = 28 kg, ballast = 10.06 kg, W/Tt = 2.85) and Tt/ = 0.17 (Tt = W = 6.43 kg; W = 31.41 kg, ballast = 13.47 kg, W/Tt = 4.88). Steel ballast weights could be used to achieve desired model weight. The condition with W/Tt ratio of 2.86 is in the range of typical TLP designs. The two tether pretension levels can be achieved by varying the weight of the model, by inserting the ballast in the three columns. The percentage difference of weight displacement of the present model from that of 4-column model is 1.96. The percentage difference of the water plane area is 5.9 and that of the total weight of the model is 0.65. All these values are sufficiently low so that results of the present model could be compared with published results of the 4-column mini TLP. A. Joseph, L.Mangal and P.S. George / Journal of Naval Architecture and Marine Engineering 6(2009)52-61 Coupled dynamic response of a three-column mini TLP 54 Fig. 1. Three-column mini TLP model (scale 1:56) Table 1: Model Data Parameter 3-column mini TLP 4-column mini TLP Displacement () 37.84 kg 38.6 kg Weight (W) Tt/=0.26 28.6 kg 28 kg Tt/=0.17 32 kg 31.41 kg Total tether pretension (Tt) Tt/=0.26 10 kg 9.84 kg Tt/=0.17 6.56 kg 6.43 kg Water depth 4.3 m 4.3 m Draft 598 mm 598 mm Height of pontoon 232 mm 232 mm Diameter of cylindrical pontoon 400 mm 400 mm Water plane area of hull (Awp) 13253 mm 2 12469 mm2 Moment of area of water plane (Iwp) 53.37×106 mm 4 140.5×106 mm4 Diameter of columns 75 mm 63 mm Length of tether (Lt) 3.6 m 3.6 m Vertical centre of gravity (VCG) from keel W = 18 kg 429 mm 450 mm W = 28.6 kg 295 mm 310 mm W = 32 kg 280 mm 292 mm Vertical centre of buoyancy 159 mm 157 mm The tethers of the present model is taken as the same as that for the 4-column model. They are strand type twisted steel wire ropes of 3 mm outer diameter comprising of six strands of seven threads each (i.e. a total of 42 threads). Diameter of each thread is 0.35 mm and hence its c/s area is 0.0962 mm2. On this basis, the cross section area (A) of the steel wire is 420.0962 = 4.04 mm2. Mass density of the tether (t) is 0.0317 kg/m, so that the total mass of one tether is 0.03173.6 = 0.114 kg, which is negligible compared to the platform mass. The value of Young's modulus is E = 0.4571011 N/m2. Tether 400  pontoon (D1) 75  column (D2) Deck 610610 32  (D3) 5 9 8 (D ) 48 2 3 57 3 66 2 32 1 2 5 Z X 246 Z Y Y X 1 2 3 (a) Elevation X-Z (b) Elevation Y-Z (c) Plan A. Joseph, L.Mangal and P.S. George / Journal of Naval Architecture and Marine Engineering 6(2009)52-61 Coupled dynamic response of a three-column mini TLP 55 The damped natural periods of vibration of the mini TLP model (Table 2) reveal that the surge, sway and yaw (soft modes) frequencies lie much below while the heave, roll and pitch (stiff modes) frequencies lie above the practical range of wave frequencies. Table 2: Comparison Natural periods of vibration and damping ratios of the mini TLP model (Tt/Δ = 0.26,  = 0) Degree of freedom Natural period (s) Damping ratio Surge, sway 10.600 0.040 Heave 0.115 0.129 Roll, Pitch 0.130 0.118 Yaw 3.630 0.274 3. Coupled Response Analysis The dynamic response of the model is investigated using nonlinear finite element method in the time domain. The underwater hull of the mini TLP comprises of three sets of slender columns and cantilevering arms as well as a hydro-dynamically compact pontoon with a slender tether system providing the compliance. So a wave force model with diffraction-radiation loading on the pontoon-column unit and Morison loading on slender members was adopted for computing the non-linear dynamic response of the structure. For evaluating wave forces on hydrodynamically transparent (slender) members, Morison equation is generally used. Depending on the Keulegan-Carpenter (KC) numbers of various members, drag coefficient (Cd) values ranging from 0.5 to 0.76 and inertia coefficient (Cm) values ranging from 2.2 to 2.3 were selected from experimental values given in Chakrabarti (1987). The hydrostatic parameters used in the numerical analysis are heave stiffness = 43.34 N/m, pitch stiffness (= roll stiffness) = 0.01524 Nm/rad. To carry out linear diffraction-radiation analysis of the scaled model a cylindrical fluid domain of diameter approximately five times that of the larger diameter (400mm) hull is selected. The finite element mesh of the fluid domain with horizontal seabed boundary has 12702 nodes and 11442 eight-noded brick elements. The diffraction-radiation analysis is carried out using a finite element code which has been extensively used in a variety of problems yielding frequency-dependent added mass and radiation damping coefficients and first order wave forces (Sathyapal, 2001). Second order dampers have been used at the radiation boundary. In the context of the nonlinear dynamic analysis, the added mass matrix is modeled by a 3D global coupled mass element and the radiation damping matrix is modeled by a 3D global coupled damper element, locating both at the CG of the hull. To carry out the nonlinear dynamic analysis, a finite element code for the nonlinear time domain simulation of dynamic response based on updated Lagrangian formulation considering both hull-tether coupling and coupling between six platform degrees of freedom is used. The dynamic equilibrium equation is solved in the time domain using the incremental-iterative Newmark-Beta algorithm (Sreekumar, 2001). The finite element model is presented in Fig. 2. It comprises of 39 nodes, 62 beam elements, 3 spring elements, 7 mass elements and 180 equations. There are 4 beam elements per tether, 16 in pontoon, 2 each per cantilevering truss, 3 in columns below SWL, and 15 above the SWL representing the columns and the upper and lower decks. Table 3 shows the diameters for hydrodynamic calculations for the different sets of elements (1 to 7 marked in the basic FE model in Fig. 2). The three dimensional beam elements are modelled such that (i) the mass distribution should match with the overall mass of 17.882 kg of the mini TLP model (ii) the VCG should match with 450 mm, as in the case of the 4-column mini TLP model. Six 3D coupled mass elements (at the top and bottom nodes of the pontoon column elements) model the ballast (lumped mass) for varying the pretension values. Effect of two tether pretensions of 26 % and 17 % and two wave approach angles 0º and 60º are studied. The tether nodes at the seabed are given fixed boundary conditions. Being a compliant structure, the large displacements are of interest than the structural deformation of the platform. So the elastic tethers are modelled as beam elements with their true stiffness while arbitrarily high values are used for the rigid platform. A. Joseph, L.Mangal and P.S. George / Journal of Naval Architecture and Marine Engineering 6(2009)52-61 Coupled dynamic response of a three-column mini TLP 56 Fig. 2. Finite element model of mini TLP Table 3: Diameters of beam elements for hydrodynamic calculation Element set Description of member Diameter (m) Structural area of cross section (m2) 1 Tether 0.003 4.040910-06 2 Horizontal cantilevering arm 0.0566 8.503810-04 3 Sloping cantilevering arm 0.0453 3.445710-04 4 Pontoon - central member 0 4.036210-03 5 Submerged column 0 2.07710-03 6 Column above SWL 0.075 6.785810-04 7 Deck and other pontoon members 0 1.2509610-03 4. Results and Discussion The results of the diffraction-radiation analysis are added mass [], radiation damping coefficients [], diffraction force components {F} and their phases for unit wave amplitude. The analysis is carried out for frequencies ranging from 0.36 Hz to 2.5 Hz. Figure 3 shows that the surge added mass for the 3-column mini TLP is 12.5 % lower than that of 4-column mini TLP (for a wave frequency of 1.2 Hz). The sway added mass for the 3-column mini TLP is 11 % lower than that of 4-column mini TLP (for a wave frequency of 1.2 Hz). The heave added mass for the 3-column mini TLP is 10 % lower than that of 4-column mini TLP (for a wave period of 1.6 Hz). Roll added inertia of the 3- column mini TLP is 10 % higher and Pitch added inertia of 3-column mini TLP is 9 % higher than that of the 4- column mini TLP (for a wave frequency of 1.2Hz). 4#3D-beam elements in one tether Node with constraints Beam element Y X Z P B O S S S 1 2 3 4 6 7 7 7 7 7 7 7 7 7 5 39 nodes 62 elements A. Joseph, L.Mangal and P.S. George / Journal of Naval Architecture and Marine Engineering 6(2009)52-61 Coupled dynamic response of a three-column mini TLP 57 Fig. 3. Comparison of added mass of mini TLP models. Figure 4 shows that all damping coefficients, except heave, are higher for the 3-column mini TLP model. Surge and sway damping coefficients are 60 % higher, heave damping coefficient is 55 % lesser, and roll as well as pitch damping coefficients are 45 % higher for the 3-column mini TLP (for a wave frequency of 1.2 Hz) compared to the 4-column mini TLP. The reduction in the case of 4-column mini TLP could be attributed to the cancellation by interference from the reflected waves from the four columns and supporting frames, whereas for a 3-column mini TLP, the interference is only from three columns and supporting frames resulting in an increase of waves passing out of the radiation boundary thus increasing the radiation damping. In Fig. 5 the diffraction force components as well as their phases for unit wave amplitude (for  = 0) are compared with that of 4-column mini TLP. Surge force is 13 % and heave force is 21 % higher for 3-column mini TLP (for a wave frequency of 0.8 Hz). Pitch moment is almost same for both the models For both the models, sway force, Roll moment and yaw moment vanish for  equal to 0 and hence not shown.. The plots 12 16 20 24 28 0.4 0.8 1.2 1.6 2 f (Hz) 3 column mini TLP 4 column mini TLP μ 1 1 (k g ) 12 16 20 24 28 0.4 0.8 1.2 1.6 2 f (Hz) μ 2 2 (k g ) 12 16 20 24 28 0.4 0.8 1.2 1.6 2 f (Hz) μ 3 3 (k g ) 0 1 2 3 4 5 0.4 0.8 1.2 1.6 2 f (Hz) μ 4 4 (k g m 2 ) 0 1 2 3 4 5 0.4 0.8 1.2 1.6 2 f (Hz) μ 5 5 ( k g m 2 ) 0 1 2 3 4 5 0.4 0.8 1.2 1.6 2 f (Hz) μ 6 6 (k g m 2 ) -10 -5 0 5 0.4 0.8 1.2 1.6 2 f (Hz) μ 1 5 (k g m ) -10 -5 0 5 10 0.4 0.8 1.2 1.6 2 f (Hz) μ 2 4 (k g m ) Surge added mass Sway added mass Heave added mass Pitch added mass Roll added mass Yaw added mass Coupled added mass Coupled added mass A. Joseph, L.Mangal and P.S. George / Journal of Naval Architecture and Marine Engineering 6(2009)52-61 Coupled dynamic response of a three-column mini TLP 58 show that the phase angles in surge and sway are independent of wave approach angle. Also, the phases of surge and sway are identical for both 3-column and 4-column mini TLPs. Fig. 4. Radiation damping coefficients of mini TLP models. The results of the non-linear dynamic analysis are presented in Fig. 6 and Fig. 7 in the form of response amplitude operators (RAO). From Fig. 6 it is seen that the surge response, which is the only major motion response is more for the 3-column mini TLP i.e., a maximum of 20 % increase (for a wave period of 1.5 s, Tt/Δ = 0.17). The heave response is small and is almost same for both the structures. The maximum value is less than 2 mm for wave amplitude of 1 m. The pitch response also is small but higher for 3-column model. The maximum value is less than 0.17o against 0.11o per unit wave amplitude for the 4-column mini TLP. It is evident from Fig. 7 that the dynamic tether tension is higher for the 3-column model, the maximum being 94 N per unit wave amplitude (for a wave period of 1.5 s, Tt /Δ = 0.17) against 60 N for the 4-column mini TLP. 0 5 10 15 20 0.4 0.8 1.2 1.6 2 f (Hz) β 2 2 (N s/ m ) 0 5 10 15 20 0.4 0.8 1.2 1.6 2 f (Hz) β 3 3 (N s/ m ) -0.5 0 0.5 1 1.5 2 0.4 0.8 1.2 1.6 2 f (Hz) β 4 4 ( N s m ) 0 5 10 15 20 0.4 0.8 1.2 1.6 2 f (Hz) 3 column mini TLP 4 column mini TLP β 1 1 (N s/ m ) -0.5 0 0.5 1 1.5 2 0.4 0.8 1.2 1.6 2 f (Hz) β 5 5 (N s m ) -0.5 0 0.5 1 1.5 0.4 0.8 1.2 1.6 2 f (Hz) β 6 6 (N s m ) -8 -4 0 4 8 0.4 0.8 1.2 1.6 2 f (Hz) β 1 5 ( N s ) -8 -4 0 4 8 0.4 0.8 1.2 1.6 2 f (Hz) β 2 4 (N s ) Surge Sway Heave Roll Pitch Yaw Coupled (Surge-pitch) Coupled (Sway-roll) A. Joseph, L.Mangal and P.S. George / Journal of Naval Architecture and Marine Engineering 6(2009)52-61 Coupled dynamic response of a three-column mini TLP 59 Fig. 5. Diffraction force components and their phases. Parametric studies reveal almost similar observations for tether pretension values of Tt /Δ = 0.17 and 0.26 which show that the chosen pretension levels which are in the practical range do not affect the dynamic response appreciably. For a change of wave approach angle from 0º to 60º, it is observed that there is considerable decrease in responses for surge and pitch while, the heave and tether responses shows little change. But the resultant horizontal displacement in the direction of the wave is the same as that for θ = 0º. 5. Conclusion The study thus shows that there is no drastic change in the dynamic response of the proposed 3-column mini TLP compared to the 4-column mini TLP. The increase in the case of surge and tether tensions is expected as the number of tethers is reduced to three from four, and can be taken into account while designing the structure. As its dynamic responses are found to be close, the 3-column structure can be considered as an alternative to the 4-column mini TLP. Reducing the number of columns from four to three has added advantages in terms of cost and time during fabrication, installation and maintenance of the platform. 0 100 200 300 400 500 0.4 0.8 1.2 1.6 2 f (Hz) 3 column mini TLP 4 column mini TLP fd 1/ a ( N /m ) 0 100 200 300 400 500 0.4 0.8 1.2 1.6 2 f (Hz) fd 3/ a ( N /m ) 0 100 200 300 400 500 0.4 0.8 1.2 1.6 2 f (Hz) fd 5/ a ( N m /m ) -200 -100 0 100 200 0.4 0.8 1.2 1.6 2 f (Hz) P ha se ( de gr ee s) -200 -100 0 100 200 0.4 0.8 1.2 1.6 2 f (Hz) p h as e (d eg re e) -200 -100 0 100 200 0.4 0.8 1.2 1.6 2 f (Hz) p h as e (d eg re es ) Surge Surge Heave Heave Pitch Pitch A. Joseph, L.Mangal and P.S. George / Journal of Naval Architecture and Marine Engineering 6(2009)52-61 Coupled dynamic response of a three-column mini TLP 60 Fig. 6. Surge, heave and pitch responses. Fig. 7. Dynamic tether tension responses. Acknowledgement The authors thankfully acknowledge the support from Department of Ocean Engineering, Indian Institute of Technology Madras, and All India Council for Technical Education (Research Promotion Scheme-2006). References Anitha Joseph, Idichandy,V.G. and Bhattacharyya, S.K. (2004): Experimental and numerical study of coupled dynamic response of a mini tension leg platform, ASME Transactions, Journal of Offshore Mechanics and Arctic Engineering, Vol. 126, pp. 18-33. doi:10.1115/1.1833358 Anitha Joseph, Lalu mangal and Anima, V. (2007): Numerical study of nonlinear dynamic response of a three column mini tension leg platform, Proc. Fourth Indian National Conf. Harbour and Ocean Engineering, NITK, Surathkal, India, pp. 307- 314. Bhattacharyya, S.K., Sreekumar, S. and Idichandy, V.G. (2003): Coupled dynamics of Seastar mini tension leg platform, Ocean Engineering, Vol. 30, pp. 709-737. doi:10.1016/S0029-8018(02)00061-6 H ea ve R A O (m /m ) 0 0.002 0.004 0.006 0 0.5 1 1.5 2 2.5 3 Wave period (s) 0 0.002 0.004 0.006 0 0.5 1 1.5 2 2.5 3 Wave period (s) P it ch R A O (r ad /m ) S u r g e R A O ( m /m ) 0 0.3 0.6 0.9 1.2 0 0.5 1 1.5 2 2.5 3 Wave period (s) 3 column mini TLP 4 column mini TLP T et h er 1 T en si on R A O (N /m ) T et h er 2 T en si o n R A O (N /m ) 0 50 100 150 0 0.5 1 1.5 2 2.5 3 Wave period (s) 3 column mini TLP 4 column mini TLP 0 50 100 150 0 0.5 1 1.5 2 2.5 3 Wave period (s) 0 50 100 150 0 0.5 1 1.5 2 2.5 3 Wave period (s) T et h er 3 T en si o n R A O (N /m ) A. Joseph, L.Mangal and P.S. George / Journal of Naval Architecture and Marine Engineering 6(2009)52-61 Coupled dynamic response of a three-column mini TLP 61 Chakrabarti, S.K. (1987): Hydrodynamics of offshore structures, Computational Mechanics Limited and Springer-Verlag, New York, pp. 199-200. Chen, X., Yu Ding, Jun Zhang, Pierre Liagre, Niedzwecki, J. and Teigen, P. (2006): Coupled dynamic analysis of a mini TLP: Comparison with measurements, Ocean Engineering, Vol. 33, No. 1, pp. 93-117. doi:10.1016/j.oceaneng.2005.02.013 Hudson, W.L., Meurant, O. and Vasseur, J. (1996): Mini TLP for deep but mild waters, Journal of Offshore Technology, Vol. 4, 4, pp. 16-19. Hudson, W.L. and Vasseur, J.C. (1996): Small tension leg platform for marginal deepwater fields, Proc. Offshore Technology Conf., OTC 8046. Kibbee, S.E., John Chianis., Davies, K.B., and Sarvano, B.A. (1994): The Sea Star Tension Leg Platform, Proc. Offshore Technology Conf., OTC 7535. Kibbee, S., Leverette, S.J., Davies, K.B.and Matten, R.B. (1999): Morpeth SeaStar Mini- TLP, Proc. Offshore Technology Conf., OTC 10855. Kim, S. and P.D. Sclavounos (2001): Fully coupled response simulations of theme offshore structures in water depths of up to 10,000 feet, Proc. Eleventh Int. Offshore and Polar Engineering Conf. Liagre P.F.and Niedzwecki, J. M. (2006): Estimating non-linear coupled frequency-dependent parameters in offshore engineering, Applied Ocean Research, Vol. 25, 1-19. doi:10.1016/S0141-1187(03)00029-4 Logan, B.L., S. Naylor, T. Munkejord and Nygaard, C. (1996): ‘Atlantic alliance: The next generation tension leg platform’, Proc. Offshore Technology Conf., OTC 8264. Muren, J., P. Flugstad, B. Greiner, R. D'Souza and Solberg, I.C. (1996): The 3 column TLP - A cost efficient deepwater production and drilling platform’, Proc. Offshore Technology Conf., OTC 8045. Sathyapal, S. (2001): Finite element procedures for second order steady and low frequency wave forces on elongated bodies with forward speed, Ph.D. Thesis, Indian Institute of Technology, Madras. Sreekumar, S. (2001): Analytical and experimental investigations on the dynamics of deepwater mini tension leg platforms, Ph.D. Thesis, Indian Institute of Technology, Madras. Sreekumar, S., Idichandy,V.G. and Bhattacharyya, S.K. (2001): Coupled dynamics of SeaStar mini tension leg platform using linear diffraction-radiation theory, Proc. Offshore Mechanics and Arctic Engineering Conf., 1074.