CN103761380B - A kind of method simulating large complicated roof water flow form - Google Patents

Abstract

The present invention relates to the analogy method of large complicated roof water flow form, first, newly-built or importing large-span structure Complex Different Shape roofing model；Secondly, current particle is defined gravity laod, wind load, viscosity factor, and and roofing curved surface between friction coefficient；Finally, preset initial time step-length and residual error is allowed in calculating, obtain roofing flowing water form by calculating simulation.The method of the present invention, considers roofing current motive power in motor process, more conforms to practical situation, can simulate roof water flow form rapidly；By Parametric designing, by interactive operation, roof building version can be carried out real-time adjusting and optimizing, simulate roof water flow form；And further the forms such as current displacement can be passed through animated Performance simulation directly perceived result.

Description

A kind of method simulating large complicated roof water flow form

Technical field

The present invention relates to a kind of method simulating large complicated roof water flow form, belong to architectural engineering technology neck Territory.

Background technology

At present, domestic at the design aspect to large stadium building roof, increasingly focus on answering of roofing shape Polygamy and uniqueness, and this to often lead to roof drainage path long, large area rainwater converges at structure effect Sensitizing range, causes structural deterioration even to cause and collapses；Thus in the Architectural Structure Design stage, quickly grasp Roof water flow form, is fully understood by roof drainage function and seems extremely important.

Stage in the early stage, the determination to roofing shape, need to meet as far as possible the requirement of quick draining, this is just Needing drainage path short, current collect at the bearing of structure as far as possible, and water-flow equation is dispersed, room The face curvature is suitable；And for profile it has been determined that, then the approach that needs to flow through from rain water on roof, convergence Rainwater load is angularly made special analysis by the degree of direction and concentration, it is ensured that the safety of structure.

To sum up, it is achieved flow shape can be quickly determined at the large complicated roof building structure design initial stage, will The biggest meaning and value is brought for practical implementation.

Summary of the invention

It is an object of the invention to provide a kind of method for numerical simulation, the simulation reaching quicklook is large complicated The flow shape of roofing, improves drainage path, provides suggestion to Architectural Structure Design.

The technical solution adopted for the present invention to solve the technical problems is: be moved through by calculating each particle The motive powers such as the gravity laod, wind load, viscous drag and the frictional force that are subject in journey, based on newton Two laws, use four step Runge-Kutta explicit solution differential equation of motion, are calculated current particle Displacement point under each time step, and realize rooms such as draining track, water yield build-up areas with animated The performance directly perceived of surface current water form.

A kind of method simulating large complicated roof water flow form, is characterized in that,

First, newly-built or import large-span structure Complex Different Shape roofing model；

Secondly, current particle is defined gravity laod, wind load, viscosity factor, and bent with roofing Friction coefficient between face；

Finally, preset initial time step-length and residual error is allowed in calculating, obtain roofing flowing water shape by calculating simulation State.

By calculating the motive power that each particle is subject in motor process, public based on Newton's second law Formula (1) obtains particle acceleration a, solves the differential equation by numerical integration and obtains the displacement that current particle is new Point, updates each variable the most in time and obtains roof water flow form,

$F=m\·a=m\·\stackrel{\·}{v}---\left(1\right)$

Wherein, F is the bonding force suffered by object, and m is the quality of object,For acceleration.

Active force suffered by current particle includes gravity G, wind load w, viscous drag f_d, frictional force fs, Roofing counter-force N, wherein, current particle contact point tangent line and horizontal direction angle theta,

Viscous drag f_dExpression formula be formula (2), k in formula_dFor viscosity, v is speed, active force Along with Particles Moving is in variable condition,

f_d=k_dV (2)

Contact force between current particle and roofing curved surface, is first according to the minimum distance of current particle and curved surface Judge whether both contact；After contact both judging, calculate contact point in the tangent line of curved surface and normal side To, set up stress equation according to particle at the stress balance of normal direction, in conjunction with friction coefficient, logical Cross formula (3) and formula (4) be calculated the particle frictional force fs size in curved surface tangential direction,

N=mg cos θ+w sin θ (3)

f_s=μ_sN (4)

In formula, m is current mass particle, and g is acceleration of gravity, and wind load w generally protects in motor process Hold constant, directly give constant value, μ_sCoefficient of friction for water droplet Yu roofing.

In motor process, particle rapidity and curvature of curved surface are in variable condition；Calculating relates to ordinary differential Equation solves, and uses explicit four step Runge-Kutta to solve ordinary differential equation, and its local is cut Disconnected error is O (h⁵), between the whole district, global error is O (h⁴), the time step Δ t of corresponding definition, single particle Displacement equation be expressed as shown in formula (5):

$y_{i+1}=y_i+\frac{1}{6}(\mathrm{\Δt}\·K_1+2\mathrm{\Δt}\·K_2+2\mathrm{\Δt}\·K_3+\mathrm{\Δt}\·K_4)---\left(5\right)$

In formula, K₁=f(x_i,y_i)

K₂=f(x_i+Δt,y_i+Δt·K₁)

K₃=f(x_i+Δt,y_i+Δt·K₂)

K₄=f(x_i+2Δt,y_i+2Δt·K₃)

In conjunction with the initial step length Δ t of definition with allow residual epsilon, for estimated value and true value difference between the two, Represent for the difference of Δ t/2 and the value of calculation of Δ t with step-length as formula (6) approximation, when being unsatisfactory for predetermined essence When degree wants the derivation of equation (7), time step Δ t is halved, continues to calculate and compare,

$|y\left(x_{i+1}\right)-y_{i+1,\mathrm{\Δt}/2}|\≈\frac{1}{15}|y_{i+1,\mathrm{\Δt}/2}-y_{i+1,\mathrm{\Δt}}|---\left(6\right)$

|y_i+1,Δt/2-y_i+1,Δt|≤ε (7)

In formula, y (x_i+1) it is true value,_yi+1,Δt/2And y_i+1,ΔtAccording to formula when respectively taking step delta t/2 and Δ t (5) estimated value calculated..

Parametrization plug-in unit Grasshopper based on 3 d modeling software Rhino, newly-built with curved form or Import large-span structure Complex Different Shape roofing model.

The present invention compared with prior art, has the advantage that

The method of the present invention, considers roofing current motive power in motor process, more conforms to Practical situation, by calculating more newly obtained current particle displacement point under each time step, it is achieved to row The performance directly perceived of the roofing flowing water forms such as water track, water yield build-up areas, can simulate roofing current shape rapidly State；By Parametric designing, roof building version can be adjusted excellent in real time by interactive operation Change, simulate roof water flow form；And can be straight by animated by forms such as current displacements further See Performance simulation result.

Accompanying drawing explanation

Fig. 1 is the method calculation flow chart of the present invention；

Fig. 2 is that water droplet is at force diagram suffered by roofing；

Fig. 3 is flow shape result figure sometime.

Detailed description of the invention

The invention will be further described below in conjunction with the accompanying drawings.Following example are only used for clearly illustrating Technical scheme, and can not limit the scope of the invention with this.

This method parametrization based on 3 d modeling software Rhino plug-in unit Grasshopper, first with curved Formula is newly-built or imports large-span structure Complex Different Shape roofing model, and size, global coordinate system are protected with practical situation Hold consistent；Secondly, current particle is defined gravity laod, wind load, viscosity factor, and and room Friction coefficient between the curved surface of face；Finally, preset initial time step-length and residual error is allowed in calculating, by compiling Plug-in unit calculating simulation processed obtains roofing flowing water form.

Concrete calculation process is as it is shown in figure 1, by calculating the various works that each particle is subject in motor process Firmly, obtain particle acceleration a based on Newton's second law formula (1), solve differential by numerical integration Equation obtains the displacement point that current particle is new, updates each variable the most in time and obtains roof water flow form.

$F=m\·a=m\·\stackrel{\·}{v}---\left(1\right)$

Wherein, F is the bonding force suffered by object, and m is the quality of object,For acceleration.

As in figure 2 it is shown, be the particle every force diagram in motor process, the effect of current particle Power mainly includes gravity G, wind load w, viscous drag f_d, frictional force fs, roofing counter-force N, wherein, water Stream particle contact point tangent line and horizontal direction angle theta.

Gravity G and wind load w generally remains constant in motor process, can directly give constant value and determine.

Viscous drag f_dExpression formula be formula (2), k in formula_dFor viscosity, v is speed, active force Along with Particles Moving is in variable condition.

f_d=k_dV (2)

Contact force between current particle and roofing curved surface, is first according to the minimum distance of current particle and curved surface Judge whether both contact；After contact both judging, calculate contact point in the tangent line of curved surface and normal side To, set up stress according to particle at the stress balance of normal direction, in conjunction with friction coefficient, by public affairs Formula (3) and formula (4) are calculated the particle frictional force fs size in curved surface tangential direction.

N=mg cos θ+w sin θ (3)

f_s=μ_sN (4)

In formula, m is current mass particle, and g is acceleration of gravity, μ_sCoefficient of friction for water droplet Yu roofing.

In motor process, particle rapidity and curvature of curved surface are in variable condition；Calculating relates to ordinary differential Equation solves, it is contemplated that the requirement to precision, it is preferred that use explicit quadravalence Runge-Kutta Method solves ordinary differential equation, and its local truncation error is O (h⁵), between the whole district, global error is O (h⁴), right The time step Δ t that should define, the displacement equation of single particle is expressed as shown in formula (5):

$y_{i+1}=y_i+\frac{1}{6}(\mathrm{\Δt}\·K_1+2\mathrm{\Δt}\·K_2+2\mathrm{\Δt}\·K_3+\mathrm{\Δt}\·K_4)---\left(5\right)$

In formula, K₁=f(x_i,y_i)

K₂=f(x_i+Δt,y_i+Δt·K₁)

K₃=f(x_i+Δt,y_i+Δt·K₂)

K₄=f(x_i+2Δt,y_i+2Δt·K₃)。

In formula, y_i+1Particle displacement, y is walked for i+1_iIt is the i-th step particle displacement, x_iIt was the i-th step moment, Δ t is time step, K₁、K₂、K₃、K₄It is respectively in quadravalence Runge-Kutta first, second, third and fourth section Increment coefficient.

Method combines the initial step length Δ t of definition and allows residual epsilon, for estimated value and true value between the two Difference, is represented with step-length for the difference of Δ t/2 and the value of calculation of Δ t, when being unsatisfactory for as formula (6) approximation When predetermined accuracy wants the derivation of equation (7), time step Δ t is halved, continue to calculate and compare, thus when realizing Between the automatically selecting of step-length, effectively meet precision and amount of calculation requirement simultaneously.

$|y\left(x_{i+1}\right)-y_{i+1,\mathrm{\Δt}/2}|\≈\frac{1}{15}|y_{i+1,\mathrm{\Δt}/2}-y_{i+1,\mathrm{\Δt}}|---\left(6\right)$

|y_i+1,Δt/2-y_i+1,Δt|≤ε (7)

In formula, y (x_i+1) it is true value, y_i+1,Δt/2And y_i+1,ΔtAccording to formula when respectively taking step delta t/2 and Δ t (5) estimated value calculated.

Result post processing is showed with reference to following enforcement step:

In result performance, with one or more time step for interval, exist with different frame numbers as shown in Figure 3 Show the particle position of different time sections, on screen between the most each frame between same water droplet particle with line segment even Connect as movement locus；For movement locus, definable different colours distinguishes zones of different or difference is real The current granule of Shi Sudu；Whole result intuitively reflects the roofing such as draining track, water yield build-up areas with animation Flowing water form.

The emulation animation simulation of roof water flow form can be quickly completed by the method for the present invention at short notice, for Architectural Structure Design provides important reference information.

The above is only the preferred embodiment of the present invention, it is noted that common for the art For technical staff, on the premise of without departing from the technology of the present invention principle, it is also possible to make some improvement and change Shape, these improve and deformation also should be regarded as protection scope of the present invention.

Claims (3)

1. the method simulating large complicated roof water flow form, is characterized in that,

First, newly-built or import large-span structure Complex Different Shape roofing model；

Secondly, current particle is defined gravity laod, wind load, viscosity factor, and bent with roofing Friction coefficient between face；

Finally, preset initial time step-length and residual error is allowed in calculating, obtain roofing flowing water shape by calculating simulation State；

Active force suffered by current particle includes gravity G, wind load w, viscous drag f_d, frictional force fs and Roofing counter-force N, wherein, current particle contact point tangent line and horizontal direction angle theta,

Viscous drag f_dExpression formula be formula (2), k in formula_dFor viscosity, v is speed, active force Along with Particles Moving is in variable condition,

f_d=k_d·v (2)

Contact force between current particle and roofing curved surface, is first according to the minimum distance of current particle and curved surface Judge whether both contact；After contact both judging, calculate contact point in the tangent line of curved surface and normal side To, set up stress equation according to particle at the stress balance of normal direction, in conjunction with friction coefficient, logical Cross formula (3) and formula (4) be calculated the particle frictional force fs size in curved surface tangential direction,

N=mg cos θ+w sin θ (3)

f_s=μ_s·N (4)

In formula, m is current mass particle, and g is acceleration of gravity, and wind load w generally protects in motor process Hold constant, directly give constant value, μ_sCoefficient of friction for water droplet Yu roofing.

The method of the large complicated roof water flow form of simulation the most according to claim 1, is characterized in that,

By calculating the motive power that each particle is subject in motor process, public based on Newton's second law Formula (1) obtains particle acceleration a, solves the differential equation by numerical integration and obtains the displacement that current particle is new Point, updates each variable the most in time and obtains roof water flow form,

$F=m\·a=m\·\stackrel{\·}{v}---\left(1\right)$

Wherein, F is the bonding force suffered by object, and m is the quality of object,For acceleration.

The method of the large complicated roof water flow form of simulation the most according to claim 1, is characterized in that, Parametrization plug-in unit Grasshopper based on 3 d modeling software Rhino, or importing newly-built with curved form Large-span structure Complex Different Shape roofing model.