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1、实用标准文案The fin ite eleme nt an alysisFinite element method, the solving area is regarded as made up of many small in the node conn ected un it (a doma in), the model gives the fun dame ntal equati on of shard ing (sub-doma in) approximati on soluti on, due to the un it (a doma in) can be divided into
2、 various shapes and sizes of differe nt size, so it can well adapt to the complex geometry, complex material properties and complicatedboun darycon diti onsFinite eleme ntmodel: is it real system idealized mathematical abstract ions. Iscomposed of some simple shapes of un it, un it connection throug
3、h the no de, and un der a certa in load.Finite element analysis: is the use of mathematical approximation method for real physical systems (geometry and loadi ng con diti ons were simulated. And by using simple and in teract ingeleme nts,n amelyun it, can use a limitednu mberofunknown variables to a
4、pproach ing infin ite unknown qua ntity of the real system.Lin ear elastic fin ite eleme nt method is a ideal elastic body as the research object,considering the deformationbased on small deformationassumption of. In thiskind of problem, the stress and strain of the material is linear relationship,
5、meet the generalized hooke's law; Stress and strain is linear, linear elastic problem boils down to solvinglinear equations,so only need less computation time. If the efficientmethod of solving algebraic equations can also help reduce the duration of finiteeleme nt an alysis.Lin earelasticfin it
6、e eleme nt gen erallyin eludes lin ear elastic staticsan alysisandlinearelasticdynamics analysis fromtwo aspects. The differeneebetweenthenon li near problem and lin ear elastic problems:1) nonlinear equation is nonlinear, and iteratively solving of general;2) the non li near problem can't use s
7、uperpositi on prin ciple;3) non li near problem is not there is always soluti on, sometimes eve n no soluti on.Finite eleme nt to solve the non li nearproblem can be dividedin to the followi ngthree categories:1) material nonlinear problems of stress and strain is nonlinear, but the stress andstra i
8、n is very small, a lin ear relati on ship betwee n stra in and displaceme nt at thistime, this kind of problem belongs to the material nonlinear problems. Due to theoretically also cannot provide the constitutive relation can be accepted, so, general nonlinear relations between stress and strain of
9、the material based on thetest data, sometimes, to simulate the nonlinear material properties available mathematical model though these models always have their limitations. More importantmaterial nonlinear problems in engineeringpractice are: nonlinearelastic (in cludi ng piecewise lin ear elastic,
10、elastic-plastic and viscoplastic, creep, etc.2) geometricnonlineargeometric nonlinear problems are caused due to thenon li near relati on ship betwee n displaceme nt. When the object the displaceme nt islarger, the strain and displaceme nt relati on ship is non li near relati on ship. Research on th
11、is kind of problemIs assumes that the material of stress and stra in is lin ear relati on ship. It con sists of alarge displaceme nt problem of large strain and large displaceme nt little strai n. Suchas the structure of the elastic buckli ng problem bel ongs to the large displaceme ntlittle stra in
12、, rubber parts forming process for large stra in.3) non li near boun dary problem in the process ing, problems such as seali ng, theimpact of the role of con tact and frictio n can not be igno red, bel ongs to the highlynon li near con tact boun dary. At ordinary times some con tact problems, such a
13、s gear,stamping forming, rolling, rubber shock absorber, interferenee fit assembly, etc., whe n a structure and ano ther structure or exter nal boun dary con tact usually wantto con sider non li near boun dary con diti ons. The actual non li near may appear at thesame time these two or three kinds o
14、f non li near problems.Fin ite eleme nt theoretical basisFinite element method is based on variational principle and the weighted residual method, and the basic solvi ng thought is the computati onal doma in is divided into a fin ite nu mber of non-o verlapp ing un it, with in each cell, select some
15、 appropriate no des as solvi ng the in terpolati on function, the differe ntial equati onof thevariables in the rewritten by the variable or its derivativeselectedinterpolationnode value and the function of linear expression, with the aid of variational principle or weighted residual method, the dis
16、crete solution of differential equation.Using different forms of weight function and interpolationfunction,constitutedifferentfiniteelementmethods.1. Theweighted residual method andtheweighted residual method of weighted residual method of weighted residual method:refersto theweightedfunction is zer
17、ousing make allowaneeforapproximate solution of the differentialequationmethod is called the weightedresidual method. Is a kind of directly from the soluti on of differe ntial equati on and boun darycon diti ons,to seek the approximate soluti on of boun daryvalueproblems of mathematical methods. Wei
18、ghted residual method is to solve the differe ntial equati on of the approximate soluti on of a ki nd of effective method.Hybrid method for the trial function selected is the most convenient, but under the condition of the same precision, the workload is the largest. For internal method and the boun
19、 dary method basis function must be made in adva nee to meet certa in con diti ons, the an alysis of complex structures tend to have certa in difficulty, but the trial function is established, the workload is small. No matter what method is used, when set up trial function should be paid attention t
20、o are the following:(1) trial function should be composed of a subset of the complete function set. Have been using the trial function has the power series and trigonometric series,spline functions, beisaier, chebyshev, Legendre polynomial, and so on.(2) the trial function should have un til tha n t
21、o elim in ate surplus weighted in tegral expression of the highest derivative low first order derivative continuity.(3) the trial functionshould be special solution with analyticalsolution of theproblem or problemsassociated with it. If computingproblemswith symmetry,should make full use of it. Obvi
22、ously, any in depe ndent complete set of functionscan be used as weight function. Accord ing to the weight function of the differe ntoptio ns for differe ntweightedallowa nee calculati on method, mai nlyin clude:collocation method,subdomainmethod,least squaremethod,momentmethodand galerk in method.
23、The galerk in method has the highest accuracy.Principleof virtual work: balanee equations and geometricequationsof theequivale nt in tegral form of "weak" virtual work prin ciples in clude prin ciple of virtual displacement and virtual stress principle, is the floorboard of the principle o
24、f virtual displaceme nt and virtual stress theory. They can be con sidered with some con trol equati on of equivale nt in tegral "weak" form. Prin ciple of virtual work: get form anybala need force system in any state of deformati oncoord in atecon diti onon thevirtual work is equal to zer
25、o, n amely the system of virtual work force and internalforce of the sum of virtual work is equal to zero. The virtual displacement principle bala need, they on the virtual displaceme nt and virtual stra in by the sum of the work is zero. On the other hand, if the force system in the virtual displac
26、ement (strain)is the equilibriumequati onand force boun darycon diti onsof the equivale ntin tegralform of "weak" Virtualstress prin cipleis geometricequati onanddisplaceme ntboun darycon diti onof the equivale nt in tegral form of "weak".Mecha nicalmea ningof the virtualdisplace
27、me ntprinciple:if the force system isand virtual and is equal to zero for the work, they must bala nee equatio n. Virtual displaceme ntprin cipleformulated the system of forcebala nee,therefore,necessary and sufficient conditions. In general, the virtual displacement principle can not only suitable
28、for lin ear elastic problems, and can be used in the non li near elastic and elastic-plastic non li near problem.Virtual mecha ni cal meaning of stress prin ciple: if the displaceme nt is coord in ated, the virtual stress and virtual boun dary con stra int coun terforce in which they are the sum of
29、the work is zero. On the other hand, if the virtual force system in which they are and is zero for the work, they must be meet the coord in ati on. Virtual stress in principle,therefore, necessary and sufficientconditionfor the expression ofdisplaceme nt coord in ati on. Virtual stress prin ciple ca
30、n be applied to differe nt lin ear elastic and nonlinear elastic mechanics problem. But it must be pointed out thatboth principle of virtualdisplaceme ntand virtual stress principle,rely on theirgeometric equati onandequilibriumequatio nis basedonthe theory of smalldeformati on,theycannotbe directly
31、appliedto mechanicalproblems basedonlarge deformati ontheory.3, theminimumtotalpote ntialen ergy methodofmi nimumtotal pote ntialen ergy method, theminimumstrainen ergy methodofmi nimumtotal pote ntialen ergy method, thepote ntialen ergy function intheobject on the exter nal load will cause deformat
32、i on, the deformati on force duri ng the work done in the form of elastic energy stored in the object, is the strain energy.The con verge neeof the fin ite eleme ntmethod, the con verge neeof the fin iteelement method refers to when the grid gradually encryption, the finite element soluti on seque n
33、ce con verges to the exact soluti on; Or whe n the cell size is fixed, the more freedom degree each unit, the finite element solutions tend to be more precise solutio n. Con verge nce con diti on of the con verge nce con diti on of the fin ite eleme nt fin ite eleme nt con verge nce con diti on of t
34、he con verge nce con diti on of the fin ite eleme nt fin ite eleme nt in eludes the follow ing four aspects: 1) with in the un it,the displacement function must be continuous.Polynomialis single-valuedcontinuousfunction, so choose polynomial as displacement function, to ensurecon ti nu itywith in th
35、e un it. 2) with in the un it, the displaceme nt function mustin clude ofte n stra in. Total can be broke n dow n into each unit of the state of stra in does not depe nd on differe nt locati ons with in the cell stra in and stra in is decided by the poin t locati on of variables. When the size of th
36、e un its is eno ugh hours, un it of each point in the strain tend to be equal, unit deformation is uniform, so often stra in becomes the main part of the stra in. To reflect the state of stra in un it, the unit must in clude the displaceme nt functions ofte n stra in. 3) with in the un it, the displ
37、acement function must include the rigid body displacement. Under normal circumsta nces, the cell for a bit of deformati on displaceme nt and displaceme nt of rigid body displaceme ntin cludi ngtwo parts. Deformatio ndisplaceme ntisassociated with the cha nges in the object shape and volume, thus pro
38、duci ng stra in;The rigid body displaceme nt cha nging the object positi on, don't cha nge the shape and volume of the object, n amely the rigid body displaceme nt is not deformati on displacement. Spatial displacement of an object includes three translational and three rotational displacement,
39、a total of six rigid body displacements. Due to a unit involved in the other unit, other units do rigid body displacement deformation occurs will drive unit, thus, to simulate real displacement of a unit, assume that the eleme nt displaceme nt function must i nclude the rigid body displaceme nt. 4)t
40、hedisplaceme nt fun cti on must be coord in ated in public boun dary of the adjace nt cell.For gen eral unit of coord in ati on is refers to the adjace nt cell in public node havethe same displaceme nt, but also have the same displaceme nt along the edge of the un it, that is to say, to en sure that
41、 the unit does not occur from crack ing and in vade the overlap each other. To do this requires the function on the com mon boun dary can be determinedby the public node function value only. For general unit andcoord in ati onto en sure the con ti nuityof the displaceme nt of adjace nt cellboun dari
42、es. However, betwee n the plate and shell of the adjace nt cell, also requires a displacement of the first derivative continuous, only in this way, to guarantee the strain en ergy of the structure is boun ded. On the whole, coord in ati on refers to the public on the border between neighboring units
43、 satisfy the continuity conditions.The first three, also called completenessconditions,meet the conditionsofcomplete unit is complete unit; Article 4 is coord inationrequirements, meet thecoord in ati onun it coord in ati onun it; Otherwise known as the coord in at ingun its.Complete ness requireme
44、nt is n ecessary for con verge nee, all four meet, con stitutes a n ecessary and sufficie ntcon diti onfor con verge nee.In practicalapplicati on,tomake the selecteddisplaceme ntfun ctio nsall meet the requireme nts ofcomplete ness and harm on y, it is difficult i n some cases can relax the requirem
45、e nt for coord in ati on .It should be poin ted out that, sometimes the coord in ati on un ittha n its corresp ondingcoord in ati onun it, its reas onlies in the n ature of theapproximate soluti on. Assumed displaceme nt function is equivale nt to put the unit un der con stra int con diti ons, the u
46、nit deformati on subject to the con stra in ts, this just some alter native structure compared to the real structure. But the approximatestructure due to allow cell separation, overlap, become soft, the stiffness of the unitor formed (such as round degree betwee n continu ous plate un it in the un i
47、t, andcorner is disc on ti nu ous,just to pin point) for the coord in atio nun it, the error ofthese two effects have the possibility of cancellation,so sometimes use thecoord in ati on un it will get very goodresults. In engin eeri ngpractice, thecoord in ati on of yua n must pass to use "smal
48、l pieces after test". Average un its or no des average process ing method of stress stress average un its or no des average process ing method of stress average un its or no des average process ing method ofstress of the unit average or node average treatment method is the simplest method is to take stress results adjace nt cell or surrounding no des, the average value of stress.1. T ake an average of 2 adjace nt unit stress. Take around no des, the average valueof stressThe basic steps of finite element method