New method for ship finite element method preprocessing based on a 3D parametric technique
Yan-Yun Yu ÆYan Lin ÆZhuo-Shang Ji
Received:19November 2008/Accepted:1May 2009/Published online:23June 2009ÓJASNAOE 2009
Abstract A new method for ship finite element method (FEM)preprocessing is presented as well as its program development.The method is applicable for all kinds of ships at different levels,such as a whole ship,cargo hold parts or detailed structures.The 3D parametric technique is used when creating ship structures,which improves the modeling efficiency greatly and makes the model easy to modify.A 3D geometric constraint solver is developed to solve the constraint system of the parametric model.A meshing procedure is presented to automatically convert the parametric structure model into a finite element model,by which high quality mesh is generated in the stress concentrated area.It also becomes possible to create finite element models for different levels from the same structure model.Using this method,the engineers avoid much of the complex and laborious work of FEM preprocessing,which consumes a very significant amount of time in finite ele-ment analysis,and can pay more attention to post-pro-cessing.This method has proved to be practical and highly efficient by several engineering trials.Keywords Ship ÁFEM ÁParametric ÁPreprocessing Á
Modeling
1Introduction
With the gradual perfection of finite element method (FEM)theory and the development of computer hardware and software,finite element analysis (FEA)is playing a more and more important role in ship design,management and safety assessment.Preprocessing is the foundation of all types of ship FEA,such as static analysis,modal analysis,buckling analysis,etc.,and is one of the most important factors that affect the accuracy and validity of the FEA results.
There are three characteristics of ship structure which make preprocessing a complex and laborious job.First,the number of structural members is huge.For example,there are tens of thousands of structural members for a 20000DWT bulk carrier,none of which are exactly the same and so cannot simply be copied.Second,the topological rela-tionship between the structure members is complex,which means one member is connected with several other mem-bers and must be changed if any of the related members changes.Third,the hull surface is an irregular surface connected by many structural members,which makes it very difficult to generate a correct finite element model of high quality.In the conventional method for ship FEA,preprocessing often occupies 90%of the whole time,while post-processing consumes less than 10%.In the early design stages,a ship’s structure must often be modified according to the FEA result,which results in the modifi-cation of the finite element model;typically repeating this process several times.The engineers must devote time to do this repetitive work rather than focussing on the structure analysis itself,where their skills are needed.Obviously,preprocessing is the bottleneck of ship FEA,so improving the efficiency of preprocessing can yield important gains for engineering practice.
This work is sponsored by ‘‘Liaoning BaiQianWan Talents Program’’.Y.-Y.Yu (&)ÁY.Lin
State Key Laboratory of Structural Analysis for Industrial Equipment,Dalian University of Technology,116023Dalian,China
e-mail:dlutxiaoyu@yahoo.com.cn
Y.-Y.Yu ÁY.Lin ÁZ.-S.Ji
Ship CAD Engineering Center,Dalian University of Technology,116023Dalian,China
J Mar Sci Technol (2009)14:398–407DOI 10.1007/s00773-009-0058-1
Kawamura and Kim made great improvements to the meshing algorithm of ship structures,but still,when the geometry of the ship structures changes,the modification of theirfinite element model is very difficult.Yu et al.[4] put forward a method based on OOP for hull structure FEM preprocessing which creates a parametric structure model (PSM)and modifies thefinite element model by changing the parametric model.However,Yu’s method was program parametric,which means the relationships of the structure are written in the program;this made his method poor in universality.
Aiming at these problems,a FEM preprocessing method for ship FEA based on a3D parametric technique is pro-posed along with its program development.In this method, the ship PSM is created using a3D CAD technique,and then the structuredfinite element model(SFEM)is created automatically based on PSM.
2Ship FEA procedure based on parametric preprocessing
Figure1is theflowchart of ship FEA based on parametric preprocessing.First,a PSM is created by the engineer.the PSM contains four parts,which are the geometry of the structure,the relationships of the structure,the physical properties(such as beam section or plate thickness),and the material properties.As the PSM is created and all the parameters are properly specified,the remaining work is automatically done by the program.Second,by solving the geometry constraint system,the constraint satisfaction structure model(CSSM)is obtained.Third,by splitting the plates in CSSM into panels,the plate panel structure model (PPSM)is created.Finally,by meshing all the panels of PPSM and setting the mesh properties inherited from PSM, the SFEM is generated.If the structure needs modification according to the FEA results,the engineer only needs to modify the parameters of the PSM.The PSM is driven by the parameters,and the SFEM will change automatically according to the PSM.
There are two key technologies for this parametric preprocessing method,which are the research emphasis of this paper.First,how to realize parameterization,or in other words,how to define and create a PSM.Section3of this paper describes this parameterization mechanism in detail.Second,how to generate an SFEM from the PSM, which requires meshing the3D structure model to get the finite element model consisting of nodes and elements. Section4discusses how to create PPSMs of planar plates, and Section5discusses how to create PPSMs of shell plates.Section6shows how to generate the SFEM from PPSMs.
3Parametric structure model
A parametric structure model is a structure model defined by constraints,parameters,and necessary geometry.Con-straints,which are used to preserve the relationships of the structures,will be maintained and solved automatically by the system once they are specified.Parameters,which are the primary dimensions of the ship,could,together with the constraints,drive the structure model.Only the necessary geometry data is required when defining a structural member,while the other data are generated from the related members and will be updated automatically if the relative members are changed.
The ship structures mainly consist of stiffened plates, which are plates with accessories such as stiffeners, brackets and openings—plates are the foundation of the structure.There are two types of parameterization in a PSM.One is the plates’parametric modeling,which cre-ates and maintains the structure solely with regard to the plates.Plate parameterization is described in3.1and3.2. The other is accessories parametric modeling as described in3.3,which applies to what is inside a plate and manages the shape or position of the plate accessories.
3.1Plate parameterization
The objective of parametric design is tofind the model that satisfies all the given constraints.The core algorithm of parametric design is geometric constraint solving(GCS). The geometry of a ship plate is a bounded plane,which can be decomposed into two independent parts,the base plane and the curve boundary.The base plane,which can be expressed with equations or transformation of
another Fig.1Flowchart of ship FEA based on a3D parametric technique
plate’s base plane,is the plane on which the plate lies.For example,in the structure shown in Fig.2,the base plane of the double bottom plate DB_BTM is described as Z =2000,and the 1730mm off-center girder GR_1730is described as GR_CEN offsetting 1730mm.The boundary is used to define the border of the plates.For instance,the boundary of DB_BTM is SHELL_ENG,GR_1730,plane X =29#and plane X =39#.
As stated above,both the base plane and the boundary of each plate are defined with dimensions,equations or transformations of other plates.If the dimensions or equations change,the objective of the GCS system is to find the plate geometries,which are the bounded planes that satisfy all the requirements.
3.2Geometric constraint solver for plates Definition a.
Prepositive entity If the calculation of e 2depends on e 1directly or indirectly,then e 1is a prepositive entity of e 2.
b.Closed constraint If e 1and e 2are prepositive entities to
each other,then e 1and e 2make up a closed constraint.The geometries of plates in PSM are simple,but the plates are large in number,so much so that it is impossible to solve the GCS system with the traditional GCS algo-rithms.According to the features of a ship PSM,a 3D geometric constraint solver is developed under the premise that closed constraints are avoided in the modeling stage.This geometric constraint solver can find the CSSM of plates efficiently.
As the base plane and the boundary are relatively independent,the GCS system of plates is divided into two subsystems,which are the base plane GCS system and the
boundary GCS system.On this basis,the algorithm for the 3D solver is as follows.(1)
PL ={(p 1,b 1),…,(p n ,b n )}is the plate set of all the plates in the PSM,where n is the number of the plates,p i is the plate base plane and b i is the plate boundary (1B i B n ).
(2)
Find the base plane construction sequence Q ={q 1,q 2,…,q n },where q i [PL (1B i B n )and the base plane of q j is not the prepositive entity of the base plane of q i ,(i \\j B n ).
(3)
Calculate the geometry of the base planes for all plates.There are no closed constraints on the base planes,so the base plane of q 1should not depend on any other plane.If all of {q 1,…,q i -1}(1\\i B n )are calculated,then q i can be calculated from {q 1,…,q i -1},for q i does not depend on any of {q i ?1,…,q n },which are undetermined.
(4)
Find the boundary construction sequence S ={s 1,s 2,…,s n },where s i [PL (1B i B n )and the base plane of s j is not a prepositive entity of the base plane of s i ,(i \\j B n ).
(5)
Calculate the bounded plane of each plate by simultaneous solution of its base plane and its boundary.The base plane is calculated in (3),so the undetermined part of the plate is the boundary.As there are no closed constraints in the boundary,the boundary of s 1should not depend on any other plate.Using the same principle as in calculating the base plane in (3),the bounded planes for the plates are calculated in sequence of s 1,s 2,…,s n .
Figure 3gives the constraint solving process.The most important and the most difficult steps are (2)and (4),which are how to find the base planes’construction sequence and the boundaries’construction sequence.There are several methods by which to obtain the construction sequence for the constructive geometric constraint solver.Most of these methods are based on graph theory,and the GCS system is expressed as a graph,by analysis of which the constructive sequence is created.Because of the space complexity of the 3D problem,the plate parametric system cannot be solved with those methods.So a sequence searching
algorithm,
Fig.2The structure of the engine room bottom Parametric Plate model Boundaries construction sequence
Base planes
Construction sequence Base planes
Plate geometry
Sequential solution
Geometric constraint solving Boundary GCS system
Base plane GCS system
base planes definition boundaries definition
which is suitable for the plate geometric constraint solver,is proposed as follows:(1)
Let A =[A 1,…,A n ],where A i is the set of the prepositive entities of e i (1B i B n ).F ={f 1,…,f n }is the flag list;f i indicates if e i is accessed.Set f i =0(1B i B n ).R is the resulting list that stores the entities in construction sequence.(2)
Procedure seek_sequence (e i )
If f i is equal to 1then return ;Set f i =1;
For each entity e k in A i Call seek_sequence (e k );Append e i to R .return ;(3)For each entity e i (1B i B n ),call seek_sequence (e i ).
(4)
Calculation complete.R is the construction sequence.
This sequence searching algorithm is based on recur-sion,which is not easy to read but highly efficient in practice.Each entity is accessed only once after seeking,so this algorithm is suitable for large scale GCS problems.Here is an example of a plate parametric model con-straint satisfaction problem.By changing the double bot-tom height and the side girder position of the structure in Fig.2,a new structure that satisfies all the given con-straints will be created by this method,as shown in Fig.4.3.3Plate accessories parameterization
The plate’s accessories are defined with constraints,and will be changed automatically if the plates are modified.There are three kinds of constraints for accessories:
(1)
Subordinate constraint,by which the accessories are subordinate to the plate.These constraints ensure that the accessories will be moved,copied and deleted along with the plate to which they are subordinate.(2)
Boundary constraint.The accessories take the plate as a boundary,and should be extended or trimmed according to the plate.
(3)
Distance constraint.The distance between the acces-sories and the plate boundary satisfy certain equations.
An example is given to show how these constraints work.Figure 5is the drawing of a ship 31#floor under the engineer room.Copy it from 31#to 30#,and 30#floor is created as shown in Fig.6,where the thin curves are the original structure and the thick are the ones updated according to the constraints.The constraints work as follows.
The plate of the 30#floor is generated by the algorithm stated in 3.2.The stiffeners,openings and brackets are subordinate to the floor by subordinate constraints,so they move to 30#together with the plate.There are boundary constraints between the stiffeners and the floor,so the stiffeners are trimmed to suit the floor geometry.A dis-tance constraint is defined between the side opening and the floor border,which changes the vertical position of the opening as required.As a result of these constraints,all the accessories are changed automatically according the designer’s intension,as shown in Fig.6.3.4Parameters of PSM
Parameter driving is an important feature of parametric design.In a ship PSM,a parameter is a generalized concept which includes more meaning than in the
traditional
Fig.4Structure satisfying all the given constraints
(1)Hull surface.Hull surface is considered as a general-
ized parameter.The modification or replacement of the hull surface would lead to the update of all the structures connected to the hull surface.
(2)Frame space and longitudinal space.The position of a
large number of structural members are defined using frame space or longitudinal space rather than the real coordinate.These members will be changed if frame space or longitudinal space is modified.
(3)Major structure positions.The major structure posi-
tions,such as double bottom height,double shell width,and platform height,determine the positions of the corresponding structures.
The parameters,which are the dominant factors of the structure,drive the structural model to vary over a large range.The constraints maintain the relation of the structure members automatically.The parameters and the constraints make PSM easy to create and also easy to modify
A constraint satisfaction structure model is created by the above two stages of parameterization,which are the plate parameterization and the accessories parameterization.
4Creating PPSMs for planar plates
It is very important that the elements in SFEM are asso-ciated correctly with the connection of the structure members in CSSM,and that’s why PPSM is introduced.In the SFEM,there is no connection information between elements except by using common edges or common nodes as topology.So if two plates are connected,the mesh on their intersection line must be the same.This requirement is simple,but can be difficult to satisfy,which is the reason why the preprocessing of ship FEMs is laborious and complex.
A plate panel structure model,which consists of plate panels,is the transitional model from CSSM to SFEM.A panel is a panel of plates,the boundary of which is the theoretical curve(stiffener theoretic curve or plates boundary curve),and there is no other theoretical curve within a panel.All plates exist as panels in PPSM,and common edges or common vertexes of panels replace the connection relationship among the structures in CSSM. Definition
a.Vertex degree.In a undirected connected graph,the
number of the edges associate with a vertex is called the vertex degree.
b.Loop.A loop is a subgraph in which all vertex degrees
are equal to two.c.The least loop.L is a loop in a connected graph,which
consists of vertexes V L={v1,…,v m}and edges
E L={e1,…,e n}.Subgraph G L={V L,E L}.If all the
vertexes’degrees of G L are two,then L is called the least loop.
d.The most loop.The loop that contains all the edges and
vertexes of a connected graph is called the most loop.
e.Bridge.The edge that is on none of the loops in a
connected graph is called the bridge.
As shown in Fig.7,G1is a connected graph with9 vertexes and12edges.There are4least loops in G1, and the most loop is the one that contains all the vertexes and edges.G2is a graph with10vertexes and 12edges.There are2bridges in G2as shown in the figure.
4.1Procedure for creating a PPSM
Given a plate PL in CSSM,the PPSM of PL is created by the following four steps.
(1)Get the plates set S P,which consists of all the plates
that intersect with PL.Get the intersections of PL with each plate in S P,and save the intersections in curve set S IC.Append the theoretical curves of all the stiffeners to S IC.
(2)In S IC,get all intersection points of the curves to each
other,and save them in set S PP.Then split all the curves in S IC with points in S PP,and the resulting curve segments set S CS is created.
(3)Taking the points in S PP as vertexes,and curves in S CS
as edges,an undirected connected graph G=(V,E) can be created.Here G is called the relation graph.G stores the topology between the points and the curves.
The procedure is shown in Fig.8.
Every panel in the PPSM corresponds to a least loop of G;therefore,we can solve the problem of creating a PPSM by searching the least loop of G.
Among the above three steps,thefirst and the second step are easy because there are mainly about space curve intersections,which is well known in theory.The third step is the most complex one,which is how tofind all the least loops for the relation graph.Fu[5]developed an
algorithmsearching the least loop with a direction factor,which is suitable for small scale relation graph with liner edge.Fu’s method is not suitable for creating a PPSM,though, because the relation graph is too large with all kinds of edges such as line,arc,spline,polyline,etc.An improved least loop searching method is proposed which is able to create PPSM quickly and accurately.
4.2Panel searching algorithm
Finding all the panels is the key problem of creating a PPSM.An algorithm of least loop searching in an undi-rected connected graph is presented which can help in searching all the panels of the PPSM.The panel searching process is as follows.
(1)Create the adjacency matrix M n9n,where n is the
number of the vertexes.M i,j(1B i B n,1B j B n) denotes not only whether there is an edge between vertex i and j,but also how many remaining times the corresponding edge has to be searched.For each element in M corresponding to an edge in G,it is important to assume that there should be no more than one edge between two arbitrary vertexes.
Like the deepfirst search(DFS)strategy,when the searching is completed,each edge should be searched twice,so M i,j is initially set to2if there is an edge between node i and j,otherwise it is set to0.Because there may be up to thousands of vertexes in a PPSM,M is too large to be stored and accessed.Therefore,a sparse matrix is used for M,and the corresponding algorithm of sparse matrices is used for calculation.
(2)Search the most loop.In this algorithm,the most loop
must be searched before the least loops,as the elements in M are modified when searching the most loop,which is the precondition of the least loop search.
The search begins with V0,the X coordinate and Y coordinate of which are the maximal among all the ver-texes.E0is thefirst edge to be searched,which is the edge associated with V0with the minimal angle to the X coor-dinate.If an edge is searched,the corresponding element in M should be decremented by1.
Let V i be the current vertex,E i be the current edge,and Es be the set of active edges incident to V i.Active edge means an edge that has been searched less than twice,so its corresponding element in M is1or2.The next edge E i?1is the one with minimal direction angle to E i among Es.Here, the direction angle is the angle of two edges’tangent line at V i.The next vertex is the other end of E i?1.
When V0is searched again,the most loop search is completed,and the searched edges comprise the most loop in sequence.
(3)Search the least loop.The least loop search algorithm
is similar to the most loop search algorithm.The difference is that,when V i and E i are searched,the next edge E i?1is the one with the maximal direction angle to E i,not the minimal.
Repeat the least loop search,until all the elements in M are zero,which means the least loop search is completed. Now panels can be created according to all the least loops.
(4)The relation graph may not satisfy the requirements
of the above least loop search algorithm,so the following improvement should be takenfirst:In a PPSM,any beam or bracket,the end of which is not on the edge of the structure,will lead to a bridge in relation graph G.The bridge will not be included in any loop and will be ignored in the least loop search.
So a virtual edge,which starts from the isolating end of the bridge and ends in the nearest panel edge,is added to help the bridge to be included in a loop.
After that,the structure can be modeled correctly.
There may be panels with only two curves in the PPSM, in which case the corresponding least loop has only two edges in relation graph G,such as the plate in Fig.9,where P2is a panel with only two curves.There should not be more than two edges between two vertexes,so the relation graph for such a PPSM does not meet criteria.
The Fig.8Relation graph creation procedure
following measures are taken to solve this problem:Before creating M ,we should find all edges between the ends of which there are other edges,such as the edges relative to curve C 1or C 6in Fig.9.Insert a vertex in the middle of each edge,which splits each edge into two edges,and then a new relation graph without this problem is created.Then M is created based on the newly created graph.After the least loop search,the inserted vertexes will be removed and the split edge will be merged.
With these improvements,the panel searching algorithm is effective for all kinds of planar plates.
Figure 10is the flowchart for the above panel searching algorithm.With this algorithm,a PPSM for any complex PSM can be created with high efficiency.Figure 11is the PPSM for the structure shown in Fig.2created by this algorithm,where different colors indicate different panels.
5Creating PPSMs for surface plates
Section 4describes the algorithm for creating PPSMs for planar plates.The relation graph for a planar plate is a planar graph,while the one for a surface plate is a space graph.So this algorithm cannot be used to create a PPSM for surface plates.However,it would be available for surface plates with the following improvements.
Though the hull surface is complex,it can be split into several monotonic surfaces.A monotonic surface is a surface for which a project plane can be found,and if two curves on the surface have no intersections,the projections of them on the project plane do not intersect with each other.
Surface Ss in Fig.13is the fore part surface of the ship shown in Fig.12.Ss can be projected along direction Vp onto plane P with the intersection curve segments S CS ,and the projection is Sp .Any two non-crossing curves on Ss
have no intersection on Sp ,which means this surface is a monotonic surface.A planer relation graph can be created for Sp ,and all the panels for Sp can be searched with the algorithm described in 4.2.Any space panel on Ss corre-sponds to a planar panel on Sp .When all the panels on Sp are searched,the panels on Ss can be found correspond-ingly,as shown in Fig.14.As all the panels are found,the PPSM for the surface plate is created.
This is a general algorithm to create a PPSM for dif-ferent kinds of shell plates,including shell plates with bulbous bow and bulbous stern.And it is suitable for a shell plate with inclined structures such as inclined longitudinal or inclined stringer,which greatly increase the modeling difficulty for the traditional preprocessing
method.
Fig.10Flow chart to find all the
panels
Fig.11PPSM created by least loop search
algorithm
6.1Creating the SFEM by meshing PPSMs
A structurefinite element model can be divided into two parts.One is the mesh,which consists of nodes and ele-ments;the other is the properties,which includes the physical property and the material property.The mesh of the SFEM is created by meshing the panels in the PPSMs, under the premise of uniformly meshing on the common edge of adjacent panels.For a simple geometry such as the panels in a PPSM,the meshing algorithm is quite mature [2,6–9],and so will not be discussed in this paper.The advancing front mesh algorithm is used to mesh the panels, and quadrilateral elements are generated as far as possible.
The properties of the SFEM are inherited from the PSM, rather than from the PPSM or the CSSM,and they are applied to the mesh automatically.As a result,if the PSM is modified,both the mesh and the properties of the SFEM will be updated automatically.
Figure15is the SFEM for the PSM in Fig.2,and Fig.16is the whole ship SFEM of a bulk carrier.
6.2Fine mesh model
Generally,in order to get accurate results,the element size should be small and the quantity of mesh should be high enough around stress concentrated areas,such as upper hopper knuckle,bracket toes,plate around openings and critical regions for special
purposes. Fig.13Projecting surface onto a
plane Fig.14PPSM for the fore hull
surface Fig.15SFEM of the engine room
bottom
Fig.16SFEM of the whole ship of a bulk carrier
In the PSM,stress concentrated areas are specified by defining smaller mesh sizes of curves or regions,and is independent of the geometry of the PSM.This information is transferred from the PSM to the PPSM,where the panel edges have different mesh sizes as required.
Mesh generation starts from the edges with smaller mesh size,and propagates outward gradually.The edges around stress-concentrated areas are meshed first,without any restriction of the existing elements,so high-quality quadrilateral elements are generated there.The existing elements should be considered when meshing the other regions,which is why the quality of the mesh in such a region is not as good as in stress-concentrated areas,even triangular elements.However,this is not very important,because a few low quality elements in areas that are not stress-concentrated areas will not affect the result of the FEA.
Figure 17is the SFEM for shell plate PPSM shown in Fig.14,with fine mesh in stress-concentrated area.6.3Creating the SFEM for different levels from the
same PSM In the initial design stage,a ship usually needs different level FEAs simultaneously,for such purposes as cargo hold strength analysis and detailed structures strength analysis.The traditional way is to separately create different finite element models for different levels,which is laborious and unnecessary.
The geometry of the fine mesh model is the same as that of the rough mesh model.The difference between these
two kinds of model is the mesh size,the mesh distribution and the mesh quantity.In PSM,the stress-concentrated areas definitions are independent of the geometry.If the stress-concentrated area definitions are ignored when cre-ating the SFEM,a rough mesh model will be created;otherwise,a fine mesh model will be generated.
As a result,the same PSM can be used for different levels of FEA preprocessing.Figure 18contrasts a fine mesh model and a rough mesh model generated from the same PSM.
7Efficiency of the approach
Using the above parametric preprocessing approach,the SFEM for the fore part structure of a bulk carrier is gen-erated,as shown in Fig.19.There are 88surface objects in the PSM,and 1914panels in the PPSM.In the SFEM,there are 28404nodes and 29275elements.
With the parametric preprocessing approach,the time to create PSM depends on the experience of the engineer.With a skillful engineer,this PSM can be created within a few hours.The time to create a PPSM from a PSM is about 3s,and meshing PPSM about 132s.While with the traditional non-parametric method,creating this FEM model may take a skillful engineer several days,or even a few weeks.
Creating the PSM,which need be done only once,takes most of the preprocessing time in this parametric approach.As the PSM is created,the time to generate the SFEM is negligible.If the structures are changed,such as replacing the hull surface,modifying the platform’s height,changing the plate thickness or the beam section,the SFEM will
be
Fig.17Fine mesh model of shell
plates
Fig.18Rough mesh model and fine mesh model generated from the same PSM
8Conclusion
The parametric preprocessing approach proposed in this paper is a universal approach that is suitable for FEA of all kinds of ships.With this parametric technique,the effi-ciency of preprocessing has been greatly improved under the condition of not decreasing the mesh quantity,espe-cially in stress-concentrated areas.The parametric model is driven by the parameters.If these parameters are changed, thefinite element model will be generated very rapidly,and then the FEA results emerge,so it is an excellent tool for ship structure optimization design,especially in the initial design stage.
If the PSM of a ship is created,it can be used for quite a lot of ships that have similar structures simply by modi-fying the parameters.Those ships may have different principal dimensions,frame spacing,hull surface,prime structure positions,plate thickness,etc.,but only one PSM is required for ships with similar structure,which means the PSM is of great universality.
In conclusion,the ship FEM preprocessing method based on this3D parametric technique is a practical engi-neering approach with good universality and high effi-ciency,by which the design or FEA of a ship becomes more effective.
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