10. Сивцова Е.П. Расчёт осадки одиночной сваи с учётом работы острия. - Сб. трудов НИИ оснований №53, М., 1963.
11. Цытович H.А. Механика грунтов. - Москва: Госстройиздат, 1963. - 636 с.
Приложение
(основные функции, процедуры и алгоритмы приложения)
функции подсчета коэффициентов b, c, d используемых для формирования матрицы жесткости function det (a11,a12,a13,a21,a22,a23,a31,a32,a33: integer): real;
begin
det: =a11*a22*a33-a11*a23*a32+a12*a23*a31-
a12*a21*a33+a13*a21*a32-a13*a22*a31;
end;
function formb (a,ntetr: integer): real;
begin
if a=cells [ntetr,1] then formb: =-det (1,kordy [ntetr,2],kordz [ntetr,2],1,kordy [ntetr,3],kordz [ntetr,3],1,kordy [ntetr,4],kordz [ntetr,4]);
if a=cells [ntetr,2] then formb: =det (1,kordy [ntetr,3],kordz [ntetr,3],1,kordy [ntetr,4],kordz [ntetr,4],1,kordy [ntetr,1],kordz [ntetr,1]);
if a=cells [ntetr,3] then formb: =-det (1,kordy [ntetr,4],kordz [ntetr,4],1,kordy [ntetr,1],kordz [ntetr,1],1,kordy [ntetr,2],kordz [ntetr,2]);
if a=cells [ntetr,4] then formb: =det (1,kordy [ntetr,1],kordz [ntetr,1],1,kordy [ntetr,2],kordz [ntetr,2],1,kordy [ntetr,3],kordz [ntetr,3]);
end;
function formc (a,ntetr: integer): real;
begin
if a=cells [ntetr,1] then formc: =det (1,kordx [ntetr,2],kordz [ntetr,2],1,kordx [ntetr,3],kordz [ntetr,3],1,kordx [ntetr,4],kordz [ntetr,4]);
if a=cells [ntetr,2] then formc: =-det (1,kordx [ntetr,3],kordz [ntetr,3],1,kordx [ntetr,4],kordz [ntetr,4],1,kordx [ntetr,1],kordz [ntetr,1]);
if a=cells [ntetr,3] then formc: =det (1,kordx [ntetr,4],kordz [ntetr,4],1,kordx [ntetr,1],kordz [ntetr,1],1,kordx [ntetr,2],kordz [ntetr,2]);
if a=cells [ntetr,4] then formc: =-det (1,kordx [ntetr,1],kordz [ntetr,1],1,kordx [ntetr,2],kordz [ntetr,2],1,kordx [ntetr,3],kordz [ntetr,3]);
end;
function formd (a,ntetr: integer): real;
begin
if a=cells [ntetr,1] then formd: =-det (1,kordx [ntetr,2],kordy [ntetr,2],1,kordx [ntetr,3],kordy [ntetr,3],1,kordx [ntetr,4],kordy [ntetr,4]);
if a=cells [ntetr,2] then formd: =det (1,kordx [ntetr,3],kordy [ntetr,3],1,kordx [ntetr,4],kordy [ntetr,4],1,kordx [ntetr,1],kordy [ntetr,1]);
if a=cells [ntetr,3] then formd: =-det (1,kordx [ntetr,4],kordy [ntetr,4],1,kordx [ntetr,1],kordy [ntetr,1],1,kordx [ntetr,2],kordy [ntetr,2]);
if a=cells [ntetr,4] then formd: =det (1,kordx [ntetr,1],kordy [ntetr,1],1,kordx [ntetr,2],kordy [ntetr,2],1,kordx [ntetr,3],kordy [ntetr,3]);
end;
процедура формирования матрицы жесткости
procedure formprmatr (a,b,k: integer);
var ro,G,lya,Mu,E,vv: extended;
begin
Mu: =0.2; E: =360;
G: =E/ (2* (1+Mu));
lya: = (2*Mu*G) / (1-2*Mu);
ro: =2*G+lya;
vv: =1/ (360*V [ (k div 7) +1]);
prmatr [3*a-2,3*b-3*a+1]: =prmatr [3*a-2,3*b-3*a+1] +vv* (formb (a,k) *formb (b,k) *ro+G* (formc (a,k) *formc (b,k) +formd (a,k) *formd (b,k)));
prmatr [3*a-2,3*b-3*a+2]: =prmatr [3*a-2,3*b-3*a+2] +vv* (formb (a,k) *formc (b,k) *lya+formc (a,k) *formb (b,k) *G);
prmatr [3*a-2,3*b-3*a+3]: =prmatr [3*a-2,3*b-3*a+3] +vv* (formb (a,k) *formd (b,k) *lya+formd (a,k) *formb (b,k) *G);
if (3*a-1<=3*b-2) then prmatr [3*a-1,3*b-3*a]: =prmatr [3*a-1,3*b-3*a] +vv* (formc (a,k) *formb (b,k) *lya+formb (a,k) *formc (b,k) *G);
prmatr [3*a-1,3*b-3*a+1]: =prmatr [3*a-1,3*b-3*a+1] +vv* (formc (a,k) *formc (b,k) *ro+G* (formb (a,k) *formb (b,k) +formd (a,k) *formd (b,k)));
prmatr [3*a-1,3*b-3*a+2]: =prmatr [3*a-1,3*b-3*a+2] +vv* (formc (a,k) *formd (b,k) *lya+formd (a,k) *formc (b,k) *G);
if (3*a<=3*b-2) then prmatr [3*a,3*b-3*a-1]: =prmatr [3*a,3*b-3*a-1] +vv* (formd (a,k) *formb (b,k) *lya+formb (a,k) *formd (b,k) *G);
if (3*a<=3*b-1) then prmatr [3*a,3*b-3*a]: =prmatr [3*a,3*b-3*a] +vv* (formd (a,k) *formc (b,k) *lya+formc (a,k) *formd (b,k) *G);
prmatr [3*a,3*b-3*a+1]: =prmatr [3*a,3*b-3*a+1] +vv* (formd (a,k) *formd (b,k) *ro+G* (formc (a,k) *formc (b,k) +formb (a,k) *formb (b,k)));
end;
функция для получения необходимого элемента в прямоугольной матрице
function value (i: integer; j: integer): real;
begin
if (j<=i-m) or (j>=i+m) then value: =0;
if (i>j) then value: =prmatr [j, i-j+1] ;
if (i<=j) then value: =prmatr [i,j-i+1] ;
end;
функция для получения элементов прямоугольной матрицы с учетом ее сжатия
function value2 (i,j: integer): real;
var k,n1: integer;
begin
n1: =kx*ky*kz*3;
for k: =1 to n1 do
begin
if (P [k] =1) and (i>=k) then inc (i);
if (P [k] =1) and (j>=k) then inc (j);
end;
value2: =value (i,j);
end;
процедура сжатия силового вектора
procedure compressf (k: integer);
var i: integer;
begin
for i: =k to 3*kx*ky*kz do F [i]: =F [i+1] ;
inc (Count);
end;
функция, возвращающая значение сигнума от числа
function sign (f: real): shortint;
begin
if f=0 then sign: =0
else sign: =round (abs (f) /f);
end;
алгоритм занесения координат и номеров узлов тетраздров
point: =1;
kp: =ky*kz;
ntetr: =1;
x: =0;
for i: =1 to kx-1 do
begin
y: =0;
for j: =1 to ky-1 do
begin
z: =0;
for k: =1 to kz-1 do
begin
k1: =point+kp;
k2: =point+kz+1;
z: =z+hz [k] ;
cells [ntetr,1]: =k2; kordx [ntetr,1]: =x; kordy [ntetr,1]: =y+hy [j] ; kordz [ntetr,1]: =z;
cells [ntetr,2]: =point; kordx [ntetr,2]: =x; kordy [ntetr,2]: =y; kordz [ntetr,2]: =z-hz [k] ;
cells [ntetr,3]: =point+1; kordx [ntetr,3]: =x; kordy [ntetr,3]: =y; kordz [ntetr,3]: =z;
cells [ntetr,4]: =k1; kordx [ntetr,4]: =x+hx [i] ; kordy [ntetr,4]: =y; kordz [ntetr,4]: =z-hz [k] ;
cells [ntetr+1,1]: =k2; kordx [ntetr+1,1]: =x; kordy [ntetr+1,1]: =y+hy [j] ; kordz [ntetr+1,1]: =z;
cells [ntetr+1,2]: =point+1; kordx [ntetr+1,2]: =x; kordy [ntetr+1,2]: =y; kordz [ntetr+1,2]: =z;
cells [ntetr+1,3]: =k1+1; kordx [ntetr+1,3]: =x+hx [i] ; kordy [ntetr+1,3]: =y; kordz [ntetr+1,3]: =z;
cells [ntetr+1,4]: =k1; kordx [ntetr+1,4]: =x+hx [i] ; kordy [ntetr+1,4]: =y; kordz [ntetr+1,4]: =z-hz [k] ;
cells [ntetr+2,1]: =k2; kordx [ntetr+2,1]: =x; kordy [ntetr+2,1]: =y+hy [j] ; kordz [ntetr+2,1]: =z;
cells [ntetr+2,2]: =k1+1; kordx [ntetr+2,2]: =x+hx [i] ; kordy [ntetr+2,2]: =y; kordz [ntetr+2,2]: =z;
cells [ntetr+2,3]: =k1+kz+1; kordx [ntetr+2,3]: =x+hx [i] ; kordy [ntetr+2,3]: =y+hy [j] ; kordz [ntetr+2,3]: =z;
cells [ntetr+2,4]: =k1; kordx [ntetr+2,4]: =x+hx [i] ; kordy [ntetr+2,4]: =y; kordz [ntetr+2,4]: =z-hz [k] ;
cells [ntetr+3,1]: =k2; kordx [ntetr+3,1]: =x; kordy [ntetr+3,1]: =y+hy [j] ; kordz [ntetr+3,1]: =z;
cells [ntetr+3,2]: =k1+kz+1; kordx [ntetr+3,2]: =x+hx [i] ; kordy [ntetr+3,2]: =y+hy [j] ; kordz [ntetr+3,2]: =z;
cells [ntetr+3,3]: =k1+kz; kordx [ntetr+3,3]: =x+hx [i] ; kordy [ntetr+3,3]: =y+hy [j] ; kordz [ntetr+3,3]: =z-hz [k] ;
cells [ntetr+3,4]: =k1; kordx [ntetr+3,4]: =x+hx [i] ; kordy [ntetr+3,4]: =y; kordz [ntetr+3,4]: =z-hz [k] ;
cells [ntetr+4,1]: =k2; kordx [ntetr+4,1]: =x; kordy [ntetr+4,1]: =y+hy [j] ; kordz [ntetr+4,1]: =z;
cells [ntetr+4,2]: =k1+kz; kordx [ntetr+4,2]: =x+hx [i] ; kordy [ntetr+4,2]: =y+hy [j] ; kordz [ntetr+4,2]: =z-hz [k] ;
cells [ntetr+4,3]: =point+kz; kordx [ntetr+4,3]: =x; kordy [ntetr+4,3]: =y+hy [j] ; kordz [ntetr+4,3]: =z-hz [k] ;
cells [ntetr+4,4]: =k1; kordx [ntetr+4,4]: =x+hx [i] ; kordy [ntetr+4,4]: =y; kordz [ntetr+4,4]: =z-hz [k] ;
cells [ntetr+5,1]: =k2; kordx [ntetr+5,1]: =x; kordy [ntetr+5,1]: =y+hy [j] ; kordz [ntetr+5,1]: =z;
cells [ntetr+5,2]: =point+kz; kordx [ntetr+5,2]: =x; kordy [ntetr+5,2]: =y+hy [j] ; kordz [ntetr+5,2]: =z-hz [k] ;
cells [ntetr+5,3]: =point; kordx [ntetr+5,3]: =x; kordy [ntetr+5,3]: =y; kordz [ntetr+5,3]: =z-hz [k] ;
cells [ntetr+5,4]: =k1; kordx [ntetr+5,4]: =x+hx [i] ; kordy [ntetr+5,4]: =y; kordz [ntetr+5,4]: =z-hz [k] ;
V [k+ (j-1) * (kz-1) + (i-1) * (kz-1) * (ky-1)]: = (hz [k] *hy [j] *hx [i]) /6;
inc (point);
inc (ntetr,6);
end;
inc (point);
y: =y+hy [j] ;
end;
inc (point,kz);
x: =x+hx [i] ;
end;
алгоритм построения матрицы жесткости и ее компрессии
begin
n: =kx*ky*kz*3;
m: = (ky*kz+1) *3;
for k: =1 to koltetr do
for i: =1 to 4 do
for j: =1 to 4 do
if (cells [k, i] <=cells [k,j]) then formprmatr (cells [k, i],cells [k,j],k);
Count: =0;
for i: =1 to 3*kx*ky*kz do if P [i] =1 then compressf (i-Count);
dec (n,count);
end;
алгоритм решения системы уравнений
begin
s [1,1]: =sqrt (abs (value2 (1,1))); d [1]: =sign (value2 (1,1));
for j: =2 to n do s [1,j]: =value2 (1,j) / (d [1] *s [1,1]);
for i: =2 to n do
begin
for j: =2 to n do
begin
if i>j then s [i,j]: =0;
sum: =0;
for k: =1 to i-1 do sum: =sum+s [k, i] *s [k, i] *d [k] ;
d [i]: =sign (value2 (i, i) - sum);
if i<j then
begin
sum: =0;
for k: =1 to i-1 do sum: =sum+s [k, i] *s [k,j] *d [k] ;
s [i,j]: = (value2 (i,j) - sum) / (s [i, i] *d [i]);
end;
sum: =0;
for k: =1 to j-1 do sum: =sum+d [k] *s [k,j] *s [k,j] ;
s [j,j]: =sqrt (abs (value2 (j,j) - sum));
end;
end;
y [1]: =F [1] / (s [1,1] *d [1]);
for k: =2 to n do
begin
sum: =0;
for i: =1 to k-1 do sum: =sum+s [i,k] *y [i] *d [i] ;
y [k]: = (F [k] -sum) / (s [k,k] *d [k]);
end;
x [n]: =y [n] /s [n,n] ;
for k: =n-1 downto 1 do
begin
sum: =0;
for i: =k+1 to n do sum: =sum+s [k, i] *x [i] ;
x [k]: = (y [k] -sum) /s [k,k] ;
end;
end;
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