Thermal stress analysis of a ship with independent tanks

In this thesis, thermal stress analysis of an asphalt carrier is performed. With the conventional tanker designs, it is not safe to carry the cargoes either at high temperatures, such as asphalt, or at very low temperatures, such as LNG. In case these were to be carried directly with conventional designs, the heat transfer across the ship's hull will cause thermal stresses, which may affect the safety of the vessel during its voyage. If temperature gradients that occurs on the ship's hull are very steep, then thermal stresses cannot be neglected. The other critical point when working with thermal stresses is the temperature dependent material properties. With high temperature, it is often experienced that the strength parameters drop significantly. On the other hand, with low temperatures, material may become brittle which may cause initiation of fractures. Due to these reasons, ships with independent tanks were designed to replace conventional tanker designs when the cargo temperature is a significant parameter in the design. Independent tanks have no additional contribution on the strength of the vessel. They are responsible for carrying their own mass, as well as the mass of the cargo they are carrying. Independent tanks are attached to the hull by means of supports with low thermal conductivity and high compressive strength. Thermal properties of these supports are critical in nature for lowering the heat transfer between the tank and the vessel. However, the other mode of heat transfer occurs at the medium between the tank and the hull via convection. Hence, independent tanks are isolated. In case of asphalt carriers, rock wool is a common material for this purpose. When the isolation of the tank is complete, the calculations may be performed based on the assumption that the heat transfer only occurs via supports. In this thesis, thermal stresses due to heat transfer via these supports will be investigated as per rules by DNV-GL. Firstly, general information about independent tanks and the loads they are experiencing during their lifetime will be explained. The loads are divided into four categories as follows: static loads, functional loads, environmental loads and accidental loads. Thermal loads are considered as a functional load. In order to prevent thermal stresses, independent tanks are allowed to expand and contract freely with respect to their support locations. Support locations can be considered as pivot point while calculating final dimensions of the independent tanks. Considering the movements of the ship, four different types of supports are designed. Each type of support operates separately to react ship's movements on different degree of freedom. After brief description of independent tanks and loads that are carried, the linear theory of plates will be investigated as they are the most common structural members in naval architecture. Based on small displacement assumption of the linear theory, bending effects and in-plane effects will be investigated separately. This assumption will later lay foundation in development of finite element model of plates. Before proceeding with thermoelasticity theory, discussion on heat transfer in a solid medium is provided. Theory is built upon Fourier's Law and heat equation. In this thesis, steady-state heat transfer problem is considered as the investigated condition of the ship is operational conditions. Hence, time-transient problem is omitted. The ULEPSI interface material consists of several layers with each layer having different thermal and mechanical properties. From heat transfer point of view, these interface materials experiences one-dimensional heat transfer as the heat transfer occurs only through the thickness of the these parts. Thermal properties of these interface materials are idealized by use of single equivalent conductivity coefficient. Equivalent thermal conductivity coefficient is calculated by thermal resistance analogy. Thermoelasticity theory is explained briefly and then its application on plates is investigated. In linear theory, materials are assumed to be isotropic and homogeneous. Based on Kirchhoff's hypothesis, bending and membrane mathematical models are prepared separately. In plates, thermal stresses may occur in two modes; first type of thermal stresses occur due to temperature distribution through the thickness of the plate which results in form of thermal bending moments. In case the plate is considerably thin, temperature distribution across the thickness is simplified as a linear distribution. The second mode of thermal stresses occur on the plate is because of the temperature distribution on the midplane. This mode causes contractions and expansions of midplane. If the plate is not constrained, the plate will deform freely. Thus, staying in its initial stress free-state. However, in most uses, the plate will be constrained in some way which will prevents its free expansion or contraction. Hence, the in-plane forces on the plane mid-surface will cause stresses. In both cases, thermal load will not cause shear deformation on the plate. Although generalized thermoelasticity theory provides time-transient formulation for deformations coupled with temperature changes, under steady state conditions with slow rate of deformations, coupling term can be neglected. Coupling term includes both the temperature effects and inertia effects. With this assumption, generalized thermoelastic equation is simplified and can be solved in two steps. First step is to solve steady state heat transfer problem in order to obtain final temperature distribution. Later, this temperature distribution is mapped as input for the calculation of initial strains due to thermal loads and then structural problem is solved under given mechanical loads and boundary conditions. This method is also called uncoupled approach. Thermal stress investigation on this thesis employed finite element method which is a very powerful numerical tool in engineering calculations. Although many physical phenomena can be explained with partial differential equations, most of the time they are not feasible to be used for complex geometrical sets. Finite element method discretizes continuous domain into finite number of elements. Each element has number of nodes depending on its geometrical dimensions as well as order of its shape functions, which establishes its internal deformation characteristics among its nodes. By use of this method, problem of partial differential equation is converted into a problem of a simpler linear equation system. Before application of this method on an example asphalt carrier by use of a commercial software ANSYS, finite element model of a plate under both mechanical and thermal loads are formulated. Stiffness matrix is composed as sum of stiffness matrix of plate bending element and plane-stress element. This approach is due to small displacement assumption of the linear theory. For the formulation of the bending element, non-conforming MZC element shape functions are used. As for the plane-stress element, bilinear shape functions are used. For derivation of stiffness matrix and force vector for an element minimum potential energy principle is applied to general energy equation. These formulations are initially generated for general physical coordinate system. However, in order to apply numerical integration scheme, physical coordinates of the element are mapped into natural coordinate system. Thus, Gauss integration scheme then employed easily. Calculation of terms in stiffness matrix and force vector is performed on MATLAB platform. After, initial development of the theoretical background, thermal stress analysis of an asphalt carrier is performed in ANSYS Workbench software. Due to nature of the structural design of the ship and the loads, only one half of the ship is modeled. This allowed us to lower total node count of the finite element model by application of symmetry boundary conditions. Geometric model of the ship is modeled with 2D surface geometries and then meshed with flat shell elements. Considering the total temperature change of the structure and the deformation, uncoupled thermal stress analysis is performed. For the calculation on this thesis, first, steady-state thermal analysis is performed in order to obtain final temperature distribution across the ship's hull. Afterwards, these temperature results were transferred into structural analysis as nodal loads and no mechanical loads were considered on the analysis. The model consists of one cargo tank and half of the pump room. In order to understand effect of interface material on temperature distributions and thermal stresses on the hull, two finite element models are prepared. First model is prepared with ULEPSI interface material and then in order to prepare second model, material properties of ULEPSI is changed to material properties of steel. Boundary conditions of the both models are kept the same. As a result of the analyses, great changes in temperature distributions and stresses are observed at some of the components of the hull with respect to different interface materials. As for the independent tanks, stresses are found to be considerably low with some local high stresses. These stresses are due to geometrical design of the tank's bottom structure and can be avoided with minor structural modifications. However, stresses that are observed on the hull are due to non-uniform temperature distribution at the bottom structure. Although, ULEPSI interface material helps greatly in reducing thermal stresses by lowering the rate of heat transfer from independent tank to hull, the distribution of supports at inner bottom is equally important. High stresses are observed at locations where different types of supports are located closely. General deformation behavior of the bottom structure is very similar to the deformation of plate with different temperatures on its faces. Since the temperature difference is considerably high between bottom plating and inner bottom plating, bottom structure bends around lateral axis. This deformation shape is very important as it may cause separation between the tank and the hull. These separations will lead non-uniform distribution of forces at supports during ship's voyage which may cause local high stresses. Therefore, it is recommended to use an iterative approach for establishing ideal locations for supports at initial design stage of the ship.