VIII Congreso Internacional de Investigación REDU

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Análisis modular de la estructura en GRP de una embarcación planeadora para servicio interislas en Galápagos

Modular analysis of the GRP structure of a planing craft for Galápagos interisland service

Desarrollo tecnológico y procesos energéticos

Palabras clave
Modular analysis, finite elements, dynamic equilibrium, planing craft


The analysis of a complex structure is commonly performed using discretization, transforming the equilibrium differential equations into a system of algebraic equations, with large number of unknowns. For adequate description of high gradient regions, these large number of unknowns requires significant computational time. To reduce the number of computer operations, a module of the structure may be considered, reducing the number of unknowns for the region of interest.
A drawback of modular analysis is the selection of appropriate conditions on its boundaries. The common recommendation is to apply results from the model of the structure with a coarse finite element discretization, at the boundaries of the segment. However, this requires modelling the entire ship hull. Another complexity arises when the system is not in static equilibrium, due to the acting forces which produce accelerations of the system.


In the present work it is proposed to develop a finite element modular analysis of the structure of a Galápagos interisland service planing boat, in dynamic equilibrium, for the evaluation of its structural integrity using results of the hull bending as a beam.


First, dynamic response accelerations in the vertical plane are calculated considering weight and hydrodynamic pressure on the hull bottom. Then, the hull bending assumed as a beam of variable section is calculated in quasi-static equilibrium, considering the acceleration of hull segments. Finally, the load per unit length, combining weight, inertial effect and hydrodynamic force are integrated to calculate the bending moment distribution and the deflection of the hull considered as a beam.
Then, two hull modules are discretized applying the finite element method, one from the stern to analyze the influence of the outboard motor weights, and another from the midsection, with high hydrodynamic pressure on the bottom. Construction material for the model is glass fiber reinforced plastic laminates with some elements with wood cores. Boundary conditions for each module are geometrical on the left and natural on the right side, ensuring uniqueness of solutions. Internal forces are applied as concentrated forces in the structure main elements. Also, distributed loads are applied to each segment: bottom pressure and effective weight with inertial effect. For the case of the aft module, propeller thrust is also considered.

Principales Resultados

First, results are used to confirm the equilibrium of each module obtained with the hull beam model. Then, results of the aft module allow to analyze in detail the stresses in the motor bolt fixing holes, with values in the laminate and in the wooden core of the transom below permissible ones. In the central module, results also confirm acceptable stress levels for the operating speed considered.


The developed process allows to analyze in detail areas of high stress concentrations, employing a reasonable computational time. Representing internal forces with a discrete number of forces on longitudinal elements avoids to have local bending stresses on plate elements. From the FEM results, stress levels obtained let determine that the vessel structure could be redesigned with savings in material costs while maintaining its structural integrity.