1 / 5

What is shape function ? shape function is a function that will give the

What is shape function ? shape function is a function that will give the displacements inside an element if its displacement at all the node locations of the element are known. Shape functions for a beam element : The shape function (N) is given by_

drake-ayers
Download Presentation

What is shape function ? shape function is a function that will give the

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. What is shape function ? shape function is a function that will give the displacements inside an element if its displacement at all the node locations of the element are known. Shape functions for a beam element : The shape function (N) is given by_ N = b1 0 0 b2 0 0 0 b3 b4 0 b5 b6 Here, b1 = (1- x/L) b2= x/L b3 = 1-3x2/L2+2x3/l3 b4 = x-2x2/L+x3/L2 b5 = 3x2/L2-2x2/L3 b6 = -x2/L2+x3/L2 x =length from one end at which shape function is to be found L= length of beam element

  2. Start Float l,x,b1,b2,b4,b5,b6,b[2][7] input l,x Flowchart: TO CALCULATE THE VALUE OF THE SHAPE FUNCTION FOR A GIVEN BEAM ELEMENT. b1=1.0-(x/l); b2=x/l; b3=1.0-(3.0*x*x/(l*l)+(2.0*x*x*x/(l*l*l))); b4=x-(2.0*x*x/l)+(x*x*x/(l*l)); b5=(3.0*x*x/(l*l)-(2.0*x*x*x/(l*l*l))); b6=-(x*x/(l))+(x*x*x/(l*l)); b[1][1]=b1;b[1][2]=0.0;b[1][3]=0.0;b[1][4]=b2;b[1][5]=0.0;b[1][6]=0.0; b[2][1]=0.0;b[2][2]=b3;b[2][3]=b4;b[2][4]=0.0;b[2][5]=b5;b[2][6]=b6; The shape function is as follows i=1 to 2 i++ false true j=1 to 6 j++ false true Output b[ i ][ j ] Stop

  3. Start program Define data type enter the length of beam element l enter length from one end at which shape function is to be found(X) EXPLAINTION: Calculate: bending element b1,b2,b3,b4,b5,b6 Define shape function matrix i is a variable used for rows of matrix, i varies from 1 to 2, in each step i varies by 1 If this condition is false If this condition is true j is a variable used for columns of matrix, j varies from 1 to 6, in each step i varies by 1 If this condition is false If this condition is true Show calculated shape function End of program

  4. Program: /*Compute the value of shape function for a given beam element*/ /*include header files*/ #include<stdio.h> #include<conio.h> #include<math.h> /*define data type of programming variables*/ float l,x,b1,b2,b4,b5,b6,b[2][7]; double b3; int i,j; /*main program starts here*/ void main() { clrscr(); /*input values*/ printf("enter the length of beam element l in cms\n"); scanf("%f",&l); printf("enter length from one end at which shape function is to be found in "); printf("centimeters\n"); scanf("%f",&x); /*calculate beam element*/ b1=1.0-(x/l); b2=x/l; b3=1.0-(3.0*x*x/(l*l)+(2.0*x*x*x/(l*l*l))); b4=x-(2.0*x*x/l)+(x*x*x/(l*l)); b5=(3.0*x*x/(l*l)-(2.0*x*x*x/(l*l*l))); b6=-(x*x/(l))+(x*x*x/(l*l));

  5. /*matrix of beam element*/ b[1][1]=b1;b[1][2]=0.0;b[1][3]=0.0;b[1][4]=b2;b[1][5]=0.0; b[1][6]=0.0; b[2][1]=0.0;b[2][2]=b3;b[2][3]=b4;b[2][4]=0.0;b[2][5]=b5; b[2][6]=b6; printf("the shape function is as follows\n"); /*calculate shape function*/ for(i=1;i<=2;++i) { for(j=1;j<=6;++j) { printf("%10.3f",b[i][j]); } printf("\n"); } getch(); return; }

More Related