Conformal transition structure of superstructure and broadside of ship and design method

Abstract

The invention provides a conformal transition structure of a superstructure and a broadside of a ship and a design method.The conformal transition structure is arranged at the connecting position of the root of the end side of the superstructure and the broadside and comprises a thickened broadside wall plate and a superstructure wall plate, the broadside wall plate and a ship broadtop strake are conformal, the upper end of the broadside wall plate is basically aligned with a main deck, and the lower end of the superstructure wall plate is aligned with the main deck. The upper building wall plate is connected with the side wall plate, the upper building wall plate and the upper building side plate are conformal, and the lower end of the upper building wall plate is basically aligned with the main deck; a semicircular corner opening is formed in the portion, at the root of the superstructure end side, of the superstructure wall plate, and the lower edge of the corner opening is smoothly connected with the upper end of the side wall plate. According to the conformal transition structure, the semicircular corner openings are adopted to reduce stress concentration of the transition area, the stress concentration of the transition area can be greatly reduced, the deck space utilization rate can be increased, the appearance continuity of a ship can be guaranteed, and the radar reflection area of the whole ship can be controlled easily.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of ship structure design, in particular to a conformal transition structure of a ship superstructure and a side and a design method. BACKGROUND

[0002] In the design of the ship structure, in order to reduce the degree of the superstructure participating in the total longitudinal strength of the ship body, the strong superstructure is usually divided into multiple light superstructure structures, and there are two common superstructure division schemes. The first one is to divide the strong superstructure by using a telescopic joint, each superstructure is rigidly connected with the main ship body, and a reinforcing plate made of the same material as the main ship body is embedded on the lower end side wall of the telescopic joint, the thickness of the reinforcing plate is 2 times the thickness of the outer side wall plate of the superstructure, the length is 500mm on both sides of the telescopic joint, and the height is not less than 200mm, but this connection type cannot reduce the stress concentration at the root of the superstructure, but rather increases the structure weld in the high stress area, which is prone to fatigue cracking, and this arrangement can greatly increase the open area between the superstructure and the side, reduce the superstructure cabin area on the deck, and the space utilization rate on the deck is low.

[0003] The second one is to use a circular or elliptical arc transition type at the connection between the superstructure and the deck, which can improve the utilization rate of the deck space on both sides of the superstructure and realize partial conformal design. However, the length of the transition area should be 1.5 times the height of the superstructure, which leads to a large open area between the light superstructures, making it difficult to set up a telescopic joint, and causing the appearance of the superstructure connection area to be discontinuous, increasing the radar reflection area of the ship. SUMMARY

[0004] In view of the above defects in the prior art, a conformal transition structure of a ship superstructure and a side and a design method are provided, which can greatly reduce the stress concentration in the transition area, improve the deck space utilization rate, and ensure the continuity of the ship appearance, which is conducive to controlling the radar reflection area of the whole ship.

[0005] The technical scheme adopted by the present application to solve the above technical problems is as follows: A conformal transition structure of a ship superstructure and a side, which is arranged at the connection between the end side root of the superstructure and the side, comprises a thickened side wall plate and a superstructure wall plate, the side wall plate is conformal with the ship side top plate, the upper end of the side wall plate is basically aligned with the main deck, the superstructure wall plate is connected with the side wall plate, the superstructure wall plate is conformal with the superstructure side plate, and the lower end of the superstructure wall plate is basically aligned with the main deck; the superstructure wall plate is provided with a semicircular corner opening at the end side root of the superstructure, and the lower edge of the corner opening is smoothly connected with the upper end of the side wall plate.

[0006] According to the technical scheme, the thickened wall plate is arranged between the upper building wall plate and the side wall plate, the thickened wall plate comprises an upper protruding part connected with the upper building wall plate above the main deck and a lower supporting part connected with the side wall plate below the main deck, an arc opening is arranged on the upper protruding part, and the arc opening is a component part of the corner opening.

[0007] According to the technical scheme, the height of the arc opening of the upper protruding part of the thickened wall plate is at least one fourth of the height of the whole corner opening.

[0008] According to the technical scheme, a semicircular wall plate is arranged in the corner opening, and a transition gap is arranged between the semicircular wall plate and the corner opening.

[0009] According to the technical scheme, the side wall plate and the upper building wall plate are provided with reinforcing materials, and the semicircular wall plate is fixedly connected with the upper building wall plate and the upper protruding part of the thickened wall plate through a plurality of continuously arranged reinforcing ribs.

[0010] The application further provides a design method of a conformal transition structure of a ship superstructure and a side, comprising the following steps: S1, a ship finite element model is established, boundary conditions and loads are set, and stress distribution at a connection position of the superstructure and a main ship body is calculated; S2, a range of the conformal transition structure is determined according to stress gradient variation of a stress concentration area, and a grid model of a superstructure side plate, a ship side top plate and an accessory structure in the corresponding area in the ship finite element model is deleted; wherein the range of the conformal transition structure comprises a lower side length L1, an upper side length L2, a left side height H1 and a right side height H2; S3, geometric parameters of the conformal transition structure are induced according to geometric characteristics of the conformal transition structure, and a finite element submodel of the conformal transition structure is automatically established by using a program language; wherein the geometric parameters of the conformal transition structure comprise a side wall plate thickness t1, an upper building wall plate thickness t2, a thickened wall plate length L3, a thickened wall plate height H3 and a thickened wall plate thickness t3, a thickened wall plate height H4 exceeding the main deck, and a corner opening radius r; S4, a connection relationship between the conformal transition structure submodel and the ship finite element model is defined, automatic assembly of the conformal transition structure submodel and the ship finite element model is realized, geometric parameters of the conformal transition structure are modified, and a calculation model of different schemes is updated by using parameterized modeling and automatic connection relationship; S5, the calculation model of different schemes is loaded for calculation, simulation results are extracted, and whether the requirements are met is checked; if yes, an optimal design scheme is output; if no, the geometric parameters of the conformal transition structure are modified, the calculation model is updated, and recalculation and checking are performed; S6, setting the semicircular wall plate and the reinforcing rib in the calculation model of the optimal design scheme obtained in step S5, checking the strength of the semicircular wall plate and the reinforcing rib, and judging whether the requirements are met; if yes, outputting the design parameters of the entire conformal transition structure and completing the structure design; if no, modifying the parameters of the semicircular wall plate and the reinforcing rib and rechecking the strength.

[0011] According to the technical scheme, in step S1, the ship finite element model includes a main hull and a superstructure, and the ship finite element model at least includes the entire cabin section where the conformal transition structure is located and each half of the adjacent cabin sections in the length direction.

[0012] According to the technical scheme, in step S4, when the conformal transition structure submodel and the ship finite element model are assembled, the connection parameters are set according to the actual welding type and the welding leg height.

[0013] According to the technical scheme, in step S6, the calculation model is simplified, the semicircular wall plate only bears the action of wave splash water pressure, the reinforcing rib divides the semicircular wall plate into multiple panel grids, and the local strength of the multiple panel grids and the reinforcing rib is checked respectively.

[0014] According to the technical scheme, the panel grid is a rectangular absolutely rigid plate that is freely supported according to two parallel edges, rigidly fixed according to the third edge, and completely free according to the fourth edge, and the local strength is checked; the reinforcing rib is a single-span beam that is rigidly fixed at both ends on a rigid support and bears uniform load, and the local strength is checked.

[0015] The present application has the following beneficial effects: 1. The transition structure of the present application is conformal with the superstructure side wall and the ship topside strake, adopts a semicircular corner opening to reduce stress concentration in the transition area, can greatly shorten the range of the transition area, reduce the difficulty of design and manufacture of the expansion joint, increase the width of the superstructure and the cabin area, ensure the continuity of the ship appearance, and is conducive to controlling the radar reflection area of the entire ship.

[0016] 2. The conformal transition structure proposed in the present application does not increase the number of structural welds in the stress concentration area, reduces the risk of fatigue cracking, and improves the safety of the structure.

[0017] 3. The present application uses parameter induction and parameterized modeling method to greatly reduce the workload of finite element modeling in the multi-scheme iteration process, can quickly complete the structure design, and improve the design efficiency. BRIEF DESCRIPTION OF DRAWINGS

[0018] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the following will briefly introduce the drawings needed to be used in the embodiments. It should be understood that the following drawings only show some of the embodiments of the present application, and therefore should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can also be obtained without creative labor.

[0019] Figure 1 Structure diagram of the conformal transition structure of the present application; Figure 2 Geometric parameter diagram of the conformal transition structure of the present application; Figure 3 Flow chart of the design method suitable for the conformal transition structure of the present application; Figure 4 Ship finite element model established in step S1 of the embodiment of the method of the present application; Figure 5 Conformal transition structure sub-models of different opening radii automatically updated in the embodiment of the method of the present application; Figure 6 Assembly diagram of the ship finite element model and the conformal transition structure sub-models in the embodiment of the method of the present application; Figure 7 Strength checking diagram of the semicircular wall plate in the embodiment of the method of the present application; Figure 8 Stress calculation result diagram of the ship finite element model established in step S1 of the embodiment of the method of the present application; Figure 9 Enlarged diagram of A in the above figure; Figure 8 Figure 10 Stress calculation result diagram of the finite element after setting the conformal transition structure in the embodiment of the method of the present application; Figure 11 Enlarged diagram of B in the above figure. Figure 10

[0020] In the figure: 1, upper building wall plate; 2, side wall plate; 3, thickened wall plate; 4, semicircular wall plate; 5, transition gap; 6, reinforcing material; 7, reinforcing rib; 8, main deck. DETAILED DESCRIPTION

[0021] In order to make the purpose, technical solutions and advantages of the embodiments of the present application more clear, the following will combine the drawings in the embodiments of the present application to clearly and completely describe the technical solutions in the embodiments of the present application. Obviously, the described embodiments are some of the embodiments of the present application, not all the embodiments. The components of the embodiments of the present application described and shown in the drawings here can be arranged and designed in various different configurations.

[0022] ​​Below, take the conformal transition structure design of the superstructure and the side of a certain ship as an example to specifically illustrate the ship superstructure and side conformal transition structure and design method proposed by the application.

[0023] As shown in Figure 1 , the conformal transition structure is arranged at the connection between the end side root of the superstructure and the side, and includes the thickened side wall plate 2 and the superstructure wall plate 1, the side wall plate 2 is conformal to the ship side top strake, the upper end of the side wall plate 2 is basically aligned with the main deck 8, the superstructure wall plate 1 is connected with the side wall plate 2, the superstructure wall plate 1 is conformal to the superstructure side plate, the lower end of the superstructure wall plate 1 is basically aligned with the main deck 8; the superstructure wall plate 1 is provided with a semicircular corner opening at the end side root of the superstructure, and the lower edge of the corner opening is smoothly connected with the upper end of the side wall plate 2.

[0024] In this embodiment, in order to further improve the strength of the connection between the superstructure and the side, a thickened wall plate 3 is arranged between the superstructure wall plate 1 and the side wall plate 2, the thickened wall plate 3 includes an upper convex part connected with the superstructure wall plate 1 above the main deck 8, and a lower supporting part connected with the side wall plate 2 below the main deck 8, an arc opening is arranged on the upper convex part of the thickened wall plate 3, and the arc opening is a component part of the corner opening, that is, the superstructure wall plate 1 and the upper convex part of the thickened wall plate 3 jointly form a semicircular corner opening. The height of the arc opening of the upper convex part of the thickened wall plate 3 accounts for at least one fourth of the height of the entire corner opening.

[0025] In this embodiment, a semicircular wall plate 4 is arranged in the corner opening, and a transition gap 5 is arranged between the semicircular wall plate 4 and the corner opening. The side wall plate 2 and the superstructure wall plate 1 are provided with reinforcing materials 6, and the semicircular wall plate 4 is fixedly connected with the superstructure wall plate 1 and the upper convex part of the thickened wall plate 3 through a plurality of continuously arranged reinforcing ribs 7.

[0026] This embodiment also provides a design method of the conformal transition structure of the superstructure and the side of a ship.

[0027] S1, a ship finite element model is established, boundary conditions and loads are set, and stress distribution at the connection between the superstructure and the main hull is calculated; In this embodiment, according to the general arrangement scheme and the geometric shapes of the main hull and the superstructure, a ship finite element model of the region where the superstructure is located is established, which includes the main hull and the superstructure, does not include any transition structure or measures for eliminating stress concentration such as rounding transition, and at least includes the entire cabin section where the conformal transition structure is located and each half of the adjacent cabin sections in the length direction.

[0028] In this embodiment, as shown in Figure 4 , the load applied on the ship finite element model is the sag bending moment load, and the part where the boundary conditions are applied is the intersection between the neutral axis of the end face of the finite element model and the longitudinal median section, and the stress distribution and deformation at the connection between the superstructure side wall and the side are calculated.

[0029] In this embodiment, Figure 8 The stress result map is calculated for the finite element model of the ship, Figure 9 For Figure 8 The enlarged schematic view of the stress concentration area shows that when there is no transition structure, i.e., when the corner is a right angle, the average stress value in the area within three layers of elements of the stress singular point is about 280 MPa.

[0030] S2, determine the range of the conformal transition structure according to the stress gradient change of the stress concentration area, and delete the grid models of the superstructure side wall, the gunwale strake and the attached structures in the corresponding area from the finite element model; wherein the range of the conformal transition structure includes its lower side length L1, upper side length L2, left side height H1 and right side height H2, Figure 2 Display the geometric parameters of the conformal transition structure.

[0031] In this embodiment, the range of the conformal transition structure submodel is determined by comprehensively considering the stress gradient change of the stress concentration area, the actual plate joint position and the element node position, wherein L1 is 8000 mm, L2 is 4500 mm, H1 is 5300 mm and H2 is 2650 mm. The range of the conformal transition structure completely contains the stress concentration part of the ship, and then the grid models of the superstructure side wall, the ship gunwale strake and the attached structures in the corresponding area are deleted from the multi-cabin section model.

[0032] S3, parameter induction is performed according to the geometric characteristics of the conformal transition structure, and a finite element submodel of the conformal transition structure is automatically established by using a programmatic language; wherein the geometric parameters of the conformal transition structure include the thickness t1 of the gunwale strake, the thickness t2 of the superstructure wall, the length L3 and the height H3 and the thickness t3 of the thickened wall, the height H4 of the thickened wall beyond the main deck, and the radius r of the corner opening; S4, define the connection relationship between the conformal transition structure submodel and the ship finite element model, realize the automatic assembly of the conformal transition structure submodel and the ship finite element model; modify the geometric parameters of the conformal transition structure, update the calculation models of different schemes by using parameterized modeling and automatic connection relationship; Figure 5 The conformal transition structure submodels with different opening radii are automatically updated.

[0033] In this embodiment, the conformal transition structure submodel is assembled with the ship finite element model with reference to the main hull structure, and the connection relationship at the connection between the conformal transition structure and the main hull is defined according to the actual weld type and the weld leg height, wherein the gunwale strake, the superstructure wall and the thickened wall are butt welds between the superstructure side wall and the gunwale strake, and are fillet welds between the main deck. For example, Figure 6As shown, by setting the weld type, weld leg height and other parameters, the automatic connection of the sub-model and the ship finite element model can be realized. By modifying the geometric parameters of the conformal transition structure, using parameterized modeling and automatic connection relationship, updating the calculation model of different schemes can greatly reduce the modeling and model modification workload.

[0034] S5, load calculation on the calculation model of different schemes, extract simulation results, check whether the requirements are met; if yes, output the optimal design scheme; if no, return to step S4, modify the geometric parameters of the conformal transition structure, update the calculation model, recalculate and check; In this embodiment, by automatically loading calculation on different calculation models through the finite element program, extracting simulation results, comprehensive performance evaluation and iterative calculation can be quickly completed, and if the calculation results do not meet the requirements, the scheme can be quickly modified through parameterized modeling and automatic connection relationship, and the optimal scheme meeting the index requirements can be finally selected.

[0035] In this embodiment, a set of design parameters of the conformal transition structure are preferred, and specifically: t1 is 20mm, t2 is 8mm, L3 is 6500mm, H3 is 1800mm, H4 is 550mm, and r is 1000mm. In particular, in order to control the variable and reflect the influence of the semicircular arc transition structure on stress concentration, the thickness of the thickened plate is kept unchanged, that is, the thickness of the upper convex part of the thickened plate is 8mm, and the thickness of the lower part is 20mm. In actual design of ship structure, thickening can be performed according to design requirements to further reduce stress concentration.

[0036] In this embodiment, the boundary conditions and the sagging bending moment load are kept unchanged, Figure 10 is a schematic diagram of the stress results of the finite element calculation after assembling the conformal transition structure, Figure 11 is Figure 10 is an enlarged schematic diagram of the stress concentration area. As can be seen from the figure, the maximum stress value at the edge of the circular arc is about 200MPa, and the average stress value in the three-layer unit area is about 150MPa, which is reduced by 46% compared with the right-angle transition, indicating that the semicircular corner transition structure eliminates stress singularity and significantly reduces stress concentration.

[0037] S6, set the semicircular plate and the reinforcing rib in the calculation model of the optimal design scheme obtained in step S5, perform strength checking on the semicircular plate and the reinforcing rib, and determine whether the requirements are met; if yes, output the design parameters of the entire conformal transition structure and complete the structure design; if no, modify the parameters of the semicircular plate and the reinforcing rib and recheck the strength.

[0038] In this embodiment, setting the semicircular plate and the reinforcing rib in the calculation model of the optimal design scheme obtained in step S5 includes setting the thickness t4 of the semicircular plate, the transition gap width and the span of the reinforcing rib and the size and shape of the stiffeners, the spacing between the stiffeners, and the like. The transition gap is determined by the deformation calculated in step S1, and the transition gap is ensured to not collide with the semicircular wall plate after the conformal transition structure is deformed.

[0039] In this embodiment, the calculation model is simplified, and the semicircular wall plate only bears the wave splash water pressure. The semicircular wall plate is divided into multiple panel grids by multiple stiffeners. The local strength of the multiple panel grids and the stiffeners is checked respectively. The wave splash water pressure P, the long side length a of the panel grid, the short side length b of the panel grid, the thickness t4 of the semicircular wall plate, the stiffener span , the material yield strength , the allowable bending stress , and the allowable shear stress .

[0040] In this embodiment, the panel grid is checked for local strength according to a rectangular absolutely rigid plate with two parallel sides freely supported, the third side rigidly fixed, and the fourth side completely free, and bearing a uniform surface load. The boundary conditions of the panel grid are simplified into completely free boundaries, free support on rigid support boundaries, and rigid fixation on rigid support boundaries.

[0041] In this embodiment, the ratio of the long side to the short side of the panel grid is first calculated, the coefficient k1 of the midpoint of the fixed side of the panel and the coefficient k2 of the midpoint of the completely free side of the panel are obtained from Table 1, and then the bending stress and are calculated. The panel grid strength is checked by comparing the allowable stress to determine whether the requirements are met.

[0042] Table 1

[0043] In this embodiment, the stiffener is checked for local strength according to a single-span beam with both ends rigidly fixed on a rigid support, bearing a uniform load. The effective width of the stiffener , the stiffener plate section modulus , and the shear area are calculated. The bending stress and the shear stress of the stiffener are calculated. The stiffener strength is checked by comparing the allowable stress to determine whether the requirements are met.

[0044] The application provides a conformal transition structure of a superstructure and a side of a ship and a design method. The transition structure can conform to the outer side wall plate of the superstructure and the side top plate of the main hull. The transition structure adopts a transition area mode of forming a semicircular corner opening inward at the root of the lowermost superstructure outer side wall. The stress concentration is reduced, the thickened plate range and the number of welds are reduced, the waste of exposed space outside the superstructure end wall is avoided, the arrangement of the superstructures is realized without changing the minimum gap of the expansion joint, and the utilization rate of the deck space of the ship is improved. The design concept of the conformal structure can maximize the consistency of the appearance of the ship and is beneficial to control the radar reflection area of the whole ship.

[0045] The embodiments described above are part of the embodiments of the application, rather than all the embodiments. The detailed description of the embodiments of the application is not intended to limit the scope of the claimed application, but only represents selected embodiments of the application. All other embodiments obtained by a person of ordinary skill in the art based on the embodiments in the application without creative labor belong to the scope of protection of the application.

Claims

1. A conformal transition structure between a ship's superstructure and its side, characterized by: The conformal transition structure is arranged at the connection between the root of the superstructure end side and the side, including a thickened side wall plate and an upper building wall plate. The side wall plate is conformal with the ship's side top column plate, and the upper end of the side wall plate is basically aligned with the main deck. The upper building wall plate is connected to the side wall plate, and the upper building wall plate is conformal with the superstructure side plate, and the lower end of the upper building wall plate is basically aligned with the main deck; the upper building wall plate is provided with a semicircular corner opening at the root of the superstructure end side, and the lower edge of the corner opening is smoothly connected to the upper end of the side wall plate.

2. The conformal transition structure between a ship superstructure and a side according to claim 1, characterized in that: A thickened wall panel is provided between the upper building wall panel and the side wall panel, and the thickened wall panel includes an upper protrusion located above the main deck and connected to the upper building wall panel, and a lower supporting portion located below the main deck and connected to the side wall panel. An arc opening is provided on the upper protrusion, and the arc opening is a component of the corner opening.

3. The conformal transition structure between a ship superstructure and a side according to claim 2, characterized in that: The arc opening height of the convex portion on the thickened wall plate is at least one quarter of the entire corner opening height.

4. The conformal transition structure between a ship superstructure and a side according to claim 2, characterized in that: A semicircular wall panel is provided in the corner opening, and a transition gap is provided between the semicircular wall panel and the corner opening.

5. The conformal transition structure between a ship superstructure and a side according to claim 4, characterized in that: The side wall panels and the upper building wall panels are provided with reinforcing frames, and the semicircular wall panels are fixedly connected to the upper convex parts of the upper building wall panels and the thickened wall panels through a plurality of continuously arranged reinforcing ribs.

6. A method for designing a conformal transition structure between a ship superstructure and a side according to any one of claims 1 to 5, characterized in that: The steps include: S1. Establish a finite element model of the ship, set boundary conditions and loads, and calculate the stress distribution at the connection between the superstructure and the main hull; S2. Determine the extent of the conformal transition structure based on the stress gradient change in the stress concentration area, and delete the mesh models of the superstructure side plates, the sheer strakes, and their attached structures in the corresponding area from the ship finite element model; wherein the extent of the conformal transition structure includes its lower side length L1, upper side length L2, left side height H1, and right side height H2; S3. Parameters are summarized based on the geometric characteristics of the conformal transition structure, and a finite element sub-model of the conformal transition structure is automatically established using a programming language. The geometric parameters of the conformal transition structure include the side panel thickness t1, the upper panel thickness t2, the length L3, height H3, and thickness t3 of the thickened panel, the height H4 of the thickened panel exceeding the main deck, and the radius r of the corner opening. S4. defining the connection relationship between the conformal transition structure sub-model and the ship finite element model to achieve automatic assembly of the conformal transition structure sub-model and the ship finite element model; modifying the geometric parameters of the conformal transition structure, and using parametric modeling and automatic connection relationships to update the calculation models of different schemes; S5. Load the calculation models of different schemes, extract the simulation results, and check whether they meet the requirements; if so, output the optimal design scheme; if not, return to step S4, modify the geometric parameters of the conformal transition structure, update the calculation model, recalculate and check; S6. Set semicircular wall panels and stiffeners in the calculation model of the optimal design solution obtained in step S5, and perform strength check on the semicircular wall panels and stiffeners to determine whether they meet the requirements; if so, output the design parameters of the entire conformal transition structure to complete the structural design; if not, modify the parameters of the semicircular wall panels and stiffeners and recheck the strength.

7. The design method according to claim 6, characterized in that: In step S1, the ship finite element model includes the main hull and the superstructure. The ship finite element model includes at least the entire compartment where the conformal transition structure is located, and half of the front and rear adjacent compartments in the length direction.

8. The design method according to claim 6, characterized in that: In step S4, when the conformal transition structure sub-model and the ship finite element model are assembled, connection parameters are set at the connection according to the actual weld type and weld leg height.

9. The design method according to claim 6, characterized in that: In step S6, the calculation model is simplified. The semicircular wall panel is only subjected to the pressure of wave splash water. The reinforcing ribs divide the semicircular wall panel into multiple panels. The local strength of the multiple panels and the reinforcing ribs are checked separately.

10. The design method according to claim 9, characterized in that: The plate grid is locally strength-checked as a rectangular absolutely rigid plate with two parallel sides freely supported, the third side rigidly fixed, and the fourth side completely free, bearing a uniformly distributed surface load; the reinforcement is locally strength-checked as a single-span beam with both ends rigidly fixed on rigid supports and bearing a uniformly distributed load.

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