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ebx,dword ptr [esp+18h] edi,2 ebp edi,1 ecx,dword ptr [edx] ebp,ecx ebp,esi ebp,ebx dword ptr [edx],ebp eax,ecx edx,4 edi,1 esi,ecx 00401022 ebp ebx edi esi

in which p is a vector of the n loads, u is the vector of the corresponding n unknown displacements, and K is the n n stiffness matrix. The parameter n is the sum of the degrees of freedom for all the nodes. The global stiffness matrix K is assembled by placing in appropriate locations the terms from the stiffness matrices of the individual elements. The individual element stiffnesses are ke =

Listing 10.2 A simple data processing function that XORs a data block with a parameter passed to it and writes the result back into the data block.

(19.2)

00401040 00401041 00401045 00401046 00401047 0040104B 0040104C 0040104D 00401051 00401053 00401055 0040105A 00401060 00401063 00401066 00401068 0040106F 00401071 00401074 00401076 push mov push push mov push push mov xor xor mov lea lea cmp ja jmp xor add jmp mov ecx edx,dword ptr [esp+8] ebx ebp ebp,dword ptr [esp+14h] esi edi edi,dword ptr [esp+10h] eax,eax ebx,ebx ecx,1 ebx,[ebx] esi,[ecx-1] esi,8 00401060 dword ptr [esi*4+4010B8h] dword ptr [edx],ebx ecx,1 00401060 edi,dword ptr [edx]

Check your mast rake (shown here by measuring).

Listing 10.3 The data-processing function from Listing 10.2 transformed using a table interpretation transformation. (continued)

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The subscript e indicates that this is the stiffness of a particular element. The matrix C contains the elastic constants. For example, for a linearly elastic body in plane strain and with shear de ned by the engineering shear strain 1 E C= (1 + )(1 2 ) 0 1 0 0 0 1 2 2

10

00401078 0040107B 0040107D 00401080 00401082 00401087 00401089 0040108B 0040108E 00401090 00401093 00401095 00401099 0040109B 0040109E 004010A0 004010A2 004010A5 004010A7 004010AA 004010AD 004010AF 004010B0 004010B1 004010B2 004010B3 004010B4

(19.3)

add jmp cmp ja mov jmp mov add jmp sub jmp mov xor add jmp xor add jmp add add jmp pop pop pop pop pop ret

It is always worth considering how much a piece of technology is likely to help, and whether it is worth it. Would you be better off with some newer sails or a new mast, rather than a fancy compass or a special lightweight gizmo How much time will it employ And could this time be better spent on the water training

E is Young s modulus and is Poisson s ratio. The matrix B relates the strains at any point in the element to the nodal displacements: = Bue (19.4)

ecx,1 00401060 ebp,3 00401071 ecx,9 00401060 ebx,edi ecx,1 00401060 ebp,4 00401055 esi,dword ptr [esp+20h] dword ptr [edx],esi ecx,1 00401060 eax,edi ecx,1 00401060 edx,4 ecx,1 00401060 edi esi ebp ebx ecx

The function s jump table: 0x004010B8 0040107d 00401076 00401095 0040106f 0x004010C8 00401089 004010a0 004010a7 00401090 0x004010D8 004010af

Once again, the subscript e indicates the nodal displacements for this particular element. The integrations prescribed by Equation (19.2), the assembly of the global stiffness matrix, solution of the matrix Equation (19.1), and back substitution to obtain the strains and stresses are all done automatically in contemporary computer codes. Several userfriendly computer codes are available for applications in geotechnical engineering. The meanings of the terms change when the method is applied to a problem other than elastic stress distribution. For example, the most common application to steady-state ow through porous media replaces load with prescribed ow and displacement with pore pressure. Some coupled formulations require that the load and displacement vectors consist of two or more different types of variables. If the problem involves developments

Listing 10.3 (continued)

The function in Listing 10.3 is functionally equivalent to the one in 10.2, but it was obfuscated using a table interpretation transformation. The function was broken down into nine segments that represent the different stages in the original function. The implementation constantly loops through a junction that decides where to go next, depending on the value of ECX. Each code segment sets the value of ECX so that the correct code segment follows. The specific code address that is executed is determined using the jump table, which is included at the end of the listing. Internally, this is implemented using a simple switch statement, but when you think of it logically, this is similar to a little virtual machine that was built just for this particular function. Each instruction advances the instruction pointer , which is stored in ECX. The actual code is the jump table, because that s where the sequence of operations is stored.

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