Optimal design of steel and composite vessels with tube branch joint
Abstract
This paper presents a unified methodology of combining heuristic fuzzy design and FEM verification to design optimally vessels with a branch joint. This method is applicable to steels and composites. Background for this study is the recognized need for constructing vessels with branch tubes needed for processing liquids and gases with minimal ecological and maintenance problems. The methodology of fuzzy optimum design is used. The goals and constrains are expressed in a consistent formulation. First, design variables like wall thickness are defined discretely within ranges. Then decision variables are formulated like cost and safety factors. The total goal is maximization of the end user satisfaction on the design. It is product of satisfaction functions of decision variables. The stresses are calculated by reasonable free body models and notch factors. Two steels are studied, a basic low strength steel (LS) and a high strength steel (HS). At low pressure p=0.1 MPa the LS vessel is 4.2 times more satisfactory than the HS vessel. At higher pressure p=1 the LS vessel is 0.4 times less satisfactory than HS vessel. An analytical stress result agrees reasonably with FEM results at a test pressure. The optimal choice depends not only on economics and technology but also on the societal and environmental changes and megatrends. This methodology can be used to explore novel concepts.
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Introduction
This study is motivated by the recognized global need for constructing vessels with branch joints needed for processing liquids and gases with minimal ecological problems. Cylindrical vessels with elliptical ends are reasonable choices.
Customers require a reliable lifetime of tens of years with minimal initial cost, maintenance and still stand costs. These goals can be formulated and solved by applying heuristic fuzzy optimum design with FEM verification.
There are many choices for vessel materials. All materials are composite from macro to microstructural level. In certain corrosive loadings fiber reinforced composites (FRP) are a competitive choice to highly alloyed steel and in others not. In this task a reasonable selection of steel and composite materials are options.
Composites for structural engineering are commonly made by combining materials from five commonest material groups, metals, ceramics glasses, plastics and polymers. Even only two components one can obtain many useful combinations of the properties. The one with largest volume fraction is called matrix. Others can be in form of fibres, platelets and globular forms.
The fibre reinforced plastics are designed to combine the strength of strong fibres in desired direction, chemical, static and fatigue strength, impact, environmental and thermal endurance. Composite material design is discussed by [1] (Agarwal, Broutman, 1990), by [2] (Barbero, 1990) and [3] (Swanson, 1997). A novel generalized failure criterion is proposed by [4] (Knops, 2008). Now a modified criterion is developed.
Conclusion
The main conclusions of the present study can be summarized as follows
A§ The motivation to this study is to develop a methodology for obtain optimal concepts vessels with tube branches
B§ Thedesign variables are
The material options are metal and non-metals.
The geometrical options are wall thicknesses
C§ Using the methodology of unified fuzzy design the goals and constraints are defined by the same formulation.
Satisfactory cost and factors of safety and other decision variables are obtained using few discrete design variable selection options
D§ Next satisfaction functions are defined for each decision variables. Then the design goal is to maximize their product.
E§In the present study the low strength and high strength steels are competitive choices with strong and weak properties.
The total satisfaction was product of costs satisfaction and technical satisfaction.
The total satifaction for LS steel is Ptot (LS)= Pcost(LS) Ptech(LS)
The total satifaction for HS steel is Ptot (HS)= Pcost(HS) Ptech(HS)
At low pressure p=0.1 MPa Ptot(LS)/ Ptot(HS) = 4.2: 1
At high pressure p=1 MPa Ptot(LS)/ Ptoo(HS) = 0.4 :1
Technical satisfaction behaviours differ with HS and LS vessels
At low pressure p = 0.1 the ratio Ptech(LS)/ Ptech(HS) = 2.69 / 0.86 = 3.1:1
At moderate p = 0.5 and at p=1 the ratio Ptech(LS)/ Ptech(HS) = 0.5/1.7 =0.3:1
A possible explanation is the following
At low pressure p = 01MPa the strength properties of HS are underutilised and satisfaction is low
At higher pressures the good strength properties of HS can be better utilized by using thicker walls
F§ the optimality of the concept obtained by analytical optimization is verified by FEM models.
G§The present methodology will be used in future to explore new innovation concepts of various materials which are needed in the near future.